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<h2>HL Paper 2</h2><div class="specification">
<p>Two observations about the photoelectric effect are</p>
<p style="text-align: left;">Observation 1: For light below the threshold frequency no electrons are emitted from the metal surface.</p>
<p style="text-align: left;">Observation 2: For light above the threshold frequency, the emission of electrons is almost instantaneous.</p>
</div>

<div class="specification">
<p>The graph shows how the maximum kinetic energy <em>E</em><sub>max</sub> of electrons emitted from a surface of barium metal varies with the frequency <em>f</em> of the incident radiation.</p>
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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain how each observation provides support for the particle theory but not the wave theory of light.</p>
<p><img 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AICRRJ2RQkQIECAAAECBAjkISBQ5DFHXRAgQIAAAQIECBBIIiBQJGFXlAABAgQIECBAgEAeAgJFHnPUBQECBAgQIECAAIEkAgJFEnZFCRAgQIAAAQIECOQhIFDkMUddECBAgAABAgQIEEgiIFAkYVeUAAECBAgQIECAQB4CAkUec9QFAQIECBAgQIAAgSQCAkUSdkUJECBAgAABAgQI5CEgUOQxR10QIECAAAECBAgQSCIgUCRhV5QAAQIECBAgQIBAHgICRR5z1AUBAgQIECBAgACBJAICRRJ2RQkQIECAAAECBAjkISBQ5DFHXRAgQIAAAQIECBBIIiBQJGFXlAABAgQIECBAgEAeAgJFHnPUBQECBAgQIECAAIEkAgJFEnZFCRAgQIAAAQIECOQhIFDkMUddECBAgAABAgQIEEgiIFAkYVeUAAECBAgQIECAQB4CAkUec9QFAQIECBAgQIAAgSQCAkUSdkUJECBAgAABAgQI5CEgUOQxR10QIECAAAECBAgQSCIgUCRhV5QAAQIECBAgQIBAHgICRR5z1AUBAgQIECBAgACBJALZBYrqSDl6iiJKfZUYm4u0OhzlnlIUpf6ojFXnWOpwjJTXRlEsi77KgTmWici9XrCKCPtC/Q8g931df/Uhn4qvjfa98X+ATsnZeG302tg4PLJ/TvyZtuwYtOHaRj+KWq1Wa97eoihixkPNT7tNgAABAgQIECBAgECHCsyWFbJ7h6JDZ6ttAgQIECBAgAABAkkEBIok7IoSIECAAAECBAgQyENAoMhjjrogQIAAAQIECBAgkERAoEjCrigBAgQIECBAgACBPAQEijzmqAsCBAgQIECAAAECSQQEiiTsihIgQIAAAQIECBDIQ0CgyGOOuiBAgAABAgQIECCQRECgSMKuKAECBAgQIECAAIE8BASKPOaoCwIECBAgQIAAAQJJBASKJOyKEiBAgAABAgQIEMhDQKDIY466IECAAAECBAgQIJBEQKBIwq4oAQIECBAgQIAAgTwEBIo85qgLAgQIECBAgAABAkkEBIok7IoSIECAAAECBAgQyENAoMhjjrogQIAAAQIECBAgkERAoEjCrigBAgQIECBAgACBPAQEijzmqAsCBAgQIECAAAECSQQEiiTsihIgQIAAAQIECBDIQ0CgyGOOuiBAgAABAgQIECCQRECgSMKuKAECBAgQIECAAIE8BASKPOaoCwIECBAgQIAAAQJJBASKJOyKEiBAgAABAgQIEMhDQKDIY466IECAAAECBAgQIJBEQKBIwq4oAQIECBAgQIAAgTwEBIo85qgLAgQIECBAgAABAkkEBIok7IoSIECAAAECBAgQyENAoMhjjrogQIAAAQIECBAgkERAoEjCrigBAgQIECBAgACBPAQEijzmqAsCBAgQIECAAAECSQSyCxTVkXL0FEWU+ioxNhdpdTjKPaUoSv1RGavOsdThGCmvjaJYFn2VA3MsE5F7vWAVEfaF+h9A7vu6/upDPhVfG+174/8AnZKz8drotbFxeGT/nPgzbdkxaMO1jX4UtVqt1ry9RVHEjIean3abAAECBAgQIECAAIEOFZgtK2T3DkWHzlbbBAgQIECAAAECBJIICBRJ2BUlQIAAAQIECBAgkIeAQJHHHHVBgAABAgQIECBAIImAQJGEXVECBAgQIECAAAECeQgIFHnMURcECBAgQIAAAQIEkggIFEnYFSVAgAABAgQIECCQh4BAkcccdUGAAAECBAgQIEAgiYBAkYRdUQIECBAgQIAAAQJ5CAgUecxRFwQIECBAgAABAgSSCAgUSdgVJUCAAAECBAgQIJCHgECRxxx1QYAAAQIECBAgQCCJgECRhF1RAgQIECBAgAABAnkICBR5zFEXBAgQIECAAAECBJIICBRJ2BUlQIAAAQIECBAgkIeAQJHHHHVBgAABAgQIECBAIImAQJGEXVECBAgQIECAAAECeQgIFHnMURcECBAgQIAAAQIEkggIFEnYFSVAgAABAgQIECCQh4BAkcccdUGAAAECBAgQIEAgiYBAkYRdUQIECBAgQIAAAQJ5CAgUecxRFwQIECBAgAABAgSSCAgUSdgVJUCAAAECBAgQIJCHgECRxxx1QYAAAQIECBAgQCCJgECRhF1RAgQIECBAgAABAnkICBR5zFEXBAgQIECAAAECBJIICBRJ2BUlQIAAAQIECBAgkIeAQJHHHHVBgAABAgQIECBAIImAQJGEXVECBAgQIECAAAECeQgIFHnMURcECBAgQIAAAQIEkghkFyiqI+XoKYoo9VVibC7S6nCUe0pRlPqjMladY6nDMVJeG0WxLPoqB+ZYJiL3esEqIuwL9T+A3Pd1/dWHfCq+Ntr3xv8BOiVn47XRa2Pj8Mj+OfFn2rJj0IZrG/0oarVarXl7i6KIGQ81P+02AQIECBAgQIAAAQIdKjBbVsjuHYoOna22CRAgQIAAAQIECCQRECiSsCtKgAABAgQIECBAIA8BgSKPOeqCAAECBAgQIECAQBIBgSIJu6IECBAgQIAAAQIE8hAQKPKYoy4IECBAgAABAgQIJBEQKJKwK0qAAAECBAgQIEAgDwGBIo856oIAAQIECBAgQIBAEgGBIgm7ogQIECBAgAABAgTyEBAo8pijLggQIECAAAECBAgkERAokrArSoAAAQIECBAgQCAPAYEijznqggABAgQIECBAgEASAYEiCbuiBAgQIECAAAECBPIQECjymKMuCBAgQIAAAQIECCQRECiSsCtKgAABAgQIECBAIA8BgSKPOeqCAAECBAgQIECAQBIBgSIJu6IECBAgQIAAAQIE8hAQKPKYoy4IECBAgAABAgQIJBEQKJKwK0qAAAECBAgQIEAgD4GMAkU1Do3sjIFyX1xeFFGM/1eKy/u+HU8OjUa1eV7V4Sj3nB895eHpjzcv0za3x2Jkx73R/93JXg7HSHltFKX+qIxN6/rX1NFYjFTK0Xd5qWFeRGn9PbFjZOzXVM9qCRAgQIAAAQIETiWBTALFkRit3B6rF10fT766Ih547WjUarWoHR2KzRf/ZwysXhor+3fE6Mk4vj7Z0x3bHQ+u/2oMHZ0s/PZY2Lstavs2xooFv+7xHolXBvpj+aeejbM3DcXRcfN98cSFL8T65f0x8MqRyY3ykwABAgQIECBAIFOBX/cR50lgq8ahofvjT1f+XZz3+D/Ed27siYXzG211dcfSNTfE/U/dFHHnDXHrEz/P4B2Jk0B6oiWqP4vtDwxErFsfV1/UHePqXd1x0YZb4o4lA3Hdvc+F9ylOFNNyBAgQIECAAIH2FMggULwau7Y9EjtXfT76rvydiYPaabPoivlL18VtN78tytc9EDubTwN69aXYsXl9lMZPj1oS6zdvj5FDTW9jHBqJyrRTqHqir1yZvkwcidGhrU2n/Mxc5kBU+pZFcXlffHuqVv2UrHfPcsrVxLKlvkrjQLy+7oHYvH7J1OlE9fWUKyNxqN7jWCX6Fq+Mu0ZHY/DqC2Le+GlOr89yytPM05Lm2Mae+6Oyq6mX0vrYvKNRa5pp407X4ujdvi/2bVoRC2Z5fvSFl2N/nXP8FLNSFD3lGGnineVXPESAAAECBAgQINBmAu0fKMZ+Etu3DkX3hefG2XN2c2Ys61kV3aODsX33q40RvR6DN305Hp332Rg6Wovaa38bH/2Pu2PR6i0xNB4qDsbQt26ITz373vhm4xSqo/tujHlbPxvXbxtpvNNRP+Xnhli6+uljp/y89tex6NkNsXzDE/FK88Hzzn+M5868KUZqv4x9e34aux+8LAYf+2HsbV5mvJeIdT3vjwXReOdl9ZMx79rBidOJ6r972+mxdeUN8a2hgxELVsSm4Wfi5u7uWPXgT+PorKc5jcVw+fPTTks6uu+LcfazG5p6bZAMfiVuf/wdcfVTv4havdbD58X3VjVq/co79umx6qrfj/PrM2kEj9r23lg454x+5QJ+gQABAgQIECBA4BQQaPvDu+r+l+OF0e5YsqgU898UdF+88PKBqdOeunu/HBs3XBLddYX5i2PNF/ri5j2PxLZdr0ZU98ePdwzHkssunjqFqqv7Q7Hxn/fG9t7FE++EjD0X9143EEvuuCU2TJ7yM/990fv1LbHu+xvj3p0Hjm1R9+pY//H3xvw4LboXLo4PXPrhWDU4EH//rwcby1RjbPfTsTVWRc+yMyNi4p2XPc2nE9V/d/lVsW7VcOz48f6pPo4VmeXW2O74zq274or7/mpqG7u6L4nPf31L3Lzna9E/FY4iovvTcdsXrmz0e1p0L/uDuKj7+ROvNV7+SLzyxH1x64sfjmt6zpvlHaNZttFDBAgQIECAAAECbSvQ9oHircufHksuee9EmJhcyfxSLFqyL7Zu/0mMdZ0dv/uhxTF463fiiV2VGJg8zWhy2WgEgNFSXHjuWdMPnJvXM7X89Btd56+Ma3p/Hndve37i9Kbqv8XTjwzGohuujIvGL6Y+K1Zs2h37Ni2L/ZUnY2BgIAYGvh19K1fE1YOvT1/ZnPcmt/GCuOR9755lGyNe3LNv4vSp2dYx3sebLDPt96pxaPhvov+6/xeffviWuPKc06Y96w4BAgQIECBAgEB+Am0fKLrOPjcu7B49/oHx1NxmOfifem7mjd+MpTc+GnsevjgOPr4pPrZyUZxR1D+GthyVaR+JOhR3rXzXsWsc6tdjzLsgrh4cnbnC6fe73hMf/OTqiK1Px+6xalT3PhMPlM+LdX/0/sY7LfWD8+/G+tI7Y9HKb8SPDtbPjfqt6PnmQDy46kQP8o/E/pf3xvG2ZOo6h+lb9xbu1bd3a1y7YnPEHX8d/SvOmR5g3sIa/QoBAgQIECBAgMCpL9D2gSIWvD961i2N4x8Yvxq7tw/GaPfk6UQnOpgFsXDFmujdtH3imoLd98Uf7r8nVi7/atN3PHwiHtzzXxMfU1v/2NSm/+a6WHmielcsWPbBWBf16zpeib3P/VMMrvpwXHr+2yeero7Etg23xI4rHo9fHN0em3o/HmvWfDRWlF6PPS8eLyI093ZanH3u+dHd/NCM28e/9mTGwnPePRKju77ZCBN/E/f3vu8ETj+bc2WeIECAAAECBAgQaCOB9g8UcWZctPaTsXzwntg068fC1i9u3hq33/XL6L3vmlg+9d0Mr7/xXY1D+2LPi6XGRdEzp3hadC+9Mj67fnV0j+6Nl/f/90Qg6P5p/OClf59+PcOhXbH58hP44rzxMBSx9XuPxMBjzx+7iLleenxb4g2nZVVfOxhNV2bM3MgZ9xuhZdZtrPcaJ3jtyYzVNt+tvhKV/tVRuvjv4+z7/laYaLZxmwABAgQIECDQAQIZBIr6x8JeG48+8/H42cc+Ep9p/ujX6mgMDdwd167+WsQtd8cdMz5WdvSuTfGVgeGJawgOvRTl6zfE1iv643PLz2p81On5cXnfwLGPiT00Ek9vH4ro/ePoqb+TsODS+Nx9l8X3r/tibNnV+DbuQ8MxcPttcVNcGxvXLnyT034mwtCiu2+JWwZ/L6669Nxjy4+HjVIMbn0sdo5OfEFcdfQHsaX/S1FufoNi/DqH0yd21dcPRfOn3o4/uGBZfOaOi2Zs40Svdy266QS28Xh/BQdj6O5rYuWd+6L38f8dd65Z7J2J43F5jgABAgQIECCQoUAGgaI+ldOie8WX4pl9D8WaMytxzRnzJq5pmLc0bvzRO2PNU0PxzMYPTb8AO06PVV/7s1jxsztjYf26hzP+JJ5dsjl2brkyzqmrdC2OTz/0WFz/ridj+eT6zvhEPPmua+KpOz4ysUycFues2Rg7H74s9vctjXnj65lYZvej18bSyS/Ym3PH6Yr5H7gi1q3qju7JkDK17Fmx/M+/EQ9d9MNYWXrbeD+//Zf/Eu9Z/414/OalU0tF13lxRd+6OFL/Hop39Ma2vYePPTd+a0Es7r1nxjb+Rey5bEvseWrDCWzjjNU13a2ODET/Td+LiJei/LFzJ/of/06P+vdsFFGMfy9G9Vf6HqXUJCUAAA0XSURBVIrqSDl6iiKOfRdHU8HJm5PfazG5/snHp/08PPF9HMWy6Ksc5z2dFq7rZG+7ek3fcdKCfYEnz4mXkBN77Wjd/hLRunWd7G1Xr77PmJ/Xjpa/dkw7nmmPO0WtftJ/0//qB4IzHmp61k0CBAgQIECAAAECBDpVYLaskMk7FJ06Un0TIECAAAECBAgQSCsgUKT1V50AAQIECBAgQIBAWwsIFG09PhtPgAABAgQIECBAIK2AQJHWX3UCBAgQIECAAAECbS0gULT1+Gw8AQIECBAgQIAAgbQCAkVaf9UJECBAgAABAgQItLWAQNHW47PxBAgQIECAAAECBNIKCBRp/VUnQIAAAQIECBAg0NYCAkVbj8/GEyBAgAABAgQIEEgrIFCk9VedAAECBAgQIECAQFsLCBRtPT4bT4AAAQIECBAgQCCtgECR1l91AgQIECBAgAABAm0tIFC09fhsPAECBAgQIECAAIG0AgJFWn/VCRAgQIAAAQIECLS1gEDR1uOz8QQIECBAgAABAgTSCggUaf1VJ0CAAAECBAgQINDWAgJFW4/PxhMgQIAAAQIECBBIKyBQpPVXnQABAgQIECBAgEBbCwgUbT0+G0+AAAECBAgQIEAgrYBAkdZfdQIECBAgQIAAAQJtLSBQtPX4bDwBAgQIECBAgACBtAICRVp/1QkQIECAAAECBAi0tYBA0dbjs/EECBAgQIAAAQIE0goIFGn9VSdAgAABAgQIECDQ1gICRVuPz8YTIECAAAECBAgQSCsgUKT1V50AAQIECBAgQIBAWwsIFG09PhtPgAABAgQIECBAIK2AQJHWX3UCBAgQIECAAAECbS0gULT1+Gw8AQIECBAgQIAAgbQC2QWK6kg5eooiSn2VGJvLtjoc5Z5SFKX+qIxV51jqcIyU10ZRLIu+yoE5lonIvV6wigj7Qv0PIPd9XX/1IZ+Kr432vfF/gE7J2Xht9NrYODyyf078mbbsGLTh2kY/ilqtVmve3qIoYsZDzU+7TYAAAQIECBAgQIBAhwrMlhWye4eiQ2erbQIECBAgQIAAAQJJBASKJOyKEiBAgAABAgQIEMhDQKDIY466IECAAAECBAgQIJBEQKBIwq4oAQIECBAgQIAAgTwEBIo85qgLAgQIECBAgAABAkkEBIok7IoSIECAAAECBAgQyENAoMhjjrogQIAAAQIECBAgkERAoEjCrigBAgQIECBAgACBPAQEijzmqAsCBAgQIECAAAECSQQEiiTsihIgQIAAAQIECBDIQ0CgyGOOuiBAgAABAgQIECCQRECgSMKuKAECBAgQIECAAIE8BASKPOaoCwIECBAgQIAAAQJJBASKJOyKEiBAgAABAgQIEMhDQKDIY466IECAAAECBAgQIJBEQKBIwq4oAQIECBAgQIAAgTwEBIo85qgLAgQIECBAgAABAkkEBIok7IoSIECAAAECBAgQyENAoMhjjrogQIAAAQIECBAgkERAoEjCrigBAgQIECBAgACBPAQEijzmqAsCBAgQIECAAAECSQQEiiTsihIgQIAAAQIECBDIQ0CgyGOOuiBAgAABAgQIECCQRECgSMKuKAECBAgQIECAAIE8BASKPOaoCwIECBAgQIAAAQJJBASKJOyKEiBAgAABAgQIEMhDQKDIY466IECAAAECBAgQIJBEQKBIwq4oAQIECBAgQIAAgTwEBIo85qgLAgQIECBAgAABAkkEsgsU1ZFy9BRFlPoqMTYXaXU4yj2lKEr9URmrzrHU4Rgpr42iWBZ9lQNzLBORe71gFRH2hfofQO77uv7qQz4VXxvte+P/AJ2Ss/Ha6LWxcXhk/5z4M23ZMWjDtY1+FLVarda8vUVRxIyHmp92mwABAgQIECBAgACBDhWYLStk9w5Fh85W2wQIECBAgAABAgSSCAgUSdgVJUCAAAECBAgQIJCHgECRxxx1QYAAAQIECBAgQCCJgECRhF1RAgQIECBAgAABAnkICBR5zFEXBAgQIECAAAECBJIICBRJ2BUlQIAAAQIECBAgkIeAQJHHHHVBgAABAgQIECBAIImAQJGEXVECBAgQIECAAAECeQgIFHnMURcECBAgQIAAAQIEkggIFEnYFSVAgAABAgQIECCQh4BAkcccdUGAAAECBAgQIEAgiYBAkYRdUQIECBAgQIAAAQJ5CAgUecxRFwQIECBAgAABAgSSCAgUSdgVJUCAAAECBAgQIJCHgECRxxx1QYAAAQIECBAgQCCJgECRhF1RAgQIECBAgAABAnkICBR5zFEXBAgQIECAAAECBJIICBRJ2BUlQIAAAQIECBAgkIeAQJHHHHVBgAABAgQIECBAIImAQJGEXVECBAgQIECAAAECeQgIFHnMURcECBAgQIAAAQIEkggIFEnYFSVAgAABAgQIECCQh4BAkcccdUGAAAECBAgQIEAgiYBAkYRdUQIECBAgQIAAAQJ5CAgUecxRFwQIECBAgAABAgSSCAgUSdgVJUCAAAECBAgQIJCHgECRxxx1QYAAAQIECBAgQCCJgECRhF1RAgQIECBAgAABAnkICBR5zFEXBAgQIECAAAECBJIIZBcoqiPl6CmKKPVVYmwu0upwlHtKUZT6ozJWnWOpwzFSXhtFsSz6KgfmWCYi93rBKiLsC/U/gNz3df3Vh3wqvjba98b/ATolZ+O10Wtj4/DI/jnxZ9qyY9CGaxv9KGq1Wq15e4uiiBkPNT/tNgECBAgQIECAAAECHSowW1bI7h2KDp2ttgkQIECAAAECBAgkERAokrArSoAAAQIECBAgQCAPAYEijznqggABAgQIECBAgEASAYEiCbuiBAgQIECAAAECBPIQECjymKMuCBAgQIAAAQIECCQRECiSsCtKgAABAgQIECBAIA8BgSKPOeqCAAECBAgQIECAQBIBgSIJu6IECBAgQIAAAQIE8hAQKPKYoy4IECBAgAABAgQIJBEQKJKwK0qAAAECBAgQIEAgDwGBIo856oIAAQIECBAgQIBAEgGBIgm7ogQIECBAgAABAgTyEBAo8pijLggQIECAAAECBAgkERAokrArSoAAAQIECBAgQCAPAYEijznqggABAgQIECBAgEASAYEiCbuiBAgQIECAAAECBPIQECjymKMuCBAgQIAAAQIECCQRECiSsCtKgAABAgQIECBAIA8BgSKPOeqCAAECBAgQIECAQBIBgSIJu6IECBAgQIAAAQIE8hAQKPKYoy4IECBAgAABAgQIJBEQKJKwK0qAAAECBAgQIEAgDwGBIo856oIAAQIECBAgQIBAEgGBIgm7ogQIECBAgAABAgTyEBAo8pijLggQIECAAAECBAgkERAokrArSoAAAQIECBAgQCAPAYEijznqggABAgQIECBAgEASAYEiCbuiBAgQIECAAAECBPIQECjymKMuCBAgQIAAAQIECCQRyC5QVEfK0VMUUeqrxNhcpNXhKPeUoij1R2WsOsdSh2OkvDaKYln0VQ7MsUxE7vWCVUTYF+p/ALnv6/qrD/lUfG20743/A3RKzsZro9fGxuGR/XPiz7Rlx6AN1zb6UdRqtVrz9hZFETMean7abQIECBAgQIAAAQIEOlRgtqyQ3TsUHTpbbRMgQIAAAQIECBBIIiBQJGFXlAABAgQIECBAgEAeAgJFHnPUBQECBAgQIECAAIEkAgJFEnZFCRAgQIAAAQIECOQhIFDkMUddECBAgAABAgQIEEgiIFAkYVeUAAECBAgQIECAQB4CAkUec9QFAQIECBAgQIAAgSQCAkUSdkUJECBAgAABAgQI5CEgUOQxR10QIECAAAECBAgQSCIgUCRhV5QAAQIECBAgQIBAHgICRR5z1AUBAgQIECBAgACBJAICRRJ2RQkQIECAAAECBAjkISBQ5DFHXRAgQIAAAQIECBBIIiBQJGFXlAABAgQIECBAgEAeAgJFHnPUBQECBAgQIECAAIEkAgJFEnZFCRAgQIAAAQIECOQhIFDkMUddECBAgAABAgQIEEgiIFAkYVeUAAECBAgQIECAQB4CAkUec9QFAQIECBAgQIAAgSQCAkUSdkUJECBAgAABAgQI5CEgUOQxR10QIECAAAECBAgQSCIgUCRhV5QAAQIECBAgQIBAHgICRR5z1AUBAgQIECBAgACBJAICRRJ2RQkQIECAAAECBAjkISBQ5DFHXRAgQIAAAQIECBBIIiBQJGFXlAABAgQIECBAgEAeAgJFHnPUBQECBAgQIECAAIEkAgJFEnZFCRAgQIAAAQIECOQhIFDkMUddECBAgAABAgQIEEgiIFAkYVeUAAECBAgQIECAQB4CRa1Wq022UhTF5E0/CRAgQIAAAQIECBAgMKtAU4SI32heovmJ5sfdJkCAAAECBAgQIECAwGwCTnmaTcVjBAgQIECAAAECBAickIBAcUJMFiJAgAABAgQIECBAYDYBgWI2FY8RIECAAAECBAgQIHBCAv8fl1gRc/FtiQoAAAAASUVORK5CYII="></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine a value for Planck’s constant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the work function of a metal.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the work function of barium in eV.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The experiment is repeated with a metal surface of cadmium, which has a greater work function. Draw a second line on the graph to represent the results of this experiment.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>Observation 1:</em><br>particle – photon energy is below the work function<br><em><strong>OR</strong></em><br><em>E = hf</em> and energy is too small «to emit electrons»<br>wave – the energy of an <em>em</em> wave is independent of frequency</p>
<p><br><em>Observation 2:</em><br>particle – a single electron absorbs the energy of a single photon «in an almost instantaneous interaction»<br>wave – it would take time for the energy to build up to eject the electron</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempt to calculate gradient of graph =&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.2 \times {{10}^{ - 19}}}}{{6.2 \times {{10}^{14}}}}">
  <mfrac>
    <mrow>
      <mn>4.2</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>19</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>6.2</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mn>14</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 6.8 - 6.9 \times {10^{ - 34}}">
  <mo>=</mo>
  <mn>6.8</mn>
  <mo>−</mo>
  <mn>6.9</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mrow>
        <mo>−</mo>
        <mn>34</mn>
      </mrow>
    </msup>
  </mrow>
</math></span>&nbsp;«Js»</p>
<p>&nbsp;</p>
<p><em>Do not allow a bald answer of 6.63 x 10<sup>-34</sup> Js or 6.6 x 10<sup>-34</sup> Js.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>minimum energy required to remove an electron «from the metal surface»</p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>energy required to remove the least tightly bound electron «from the metal surface»</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>reading of<em> y</em> intercept from graph in range 3.8 − 4.2 × 10<sup>–19</sup> «J»<br>conversion to <em>eV</em> = 2.4 – 2.6 «eV»</p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>reading of x intercept from graph «5.8 − 6.0 × 10<sup>14 </sup>Hz» and using <em>hf</em><sub>0</sub> to get 3.8 − 4.2 × 10<sup>–19</sup> «J»<br>conversion to <em>eV</em> = 2.4 – 2.6 «eV»</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>line parallel to existing line<br>to the right of the existing line</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The first scientists to identify alpha particles by a direct method were Rutherford and Royds.&nbsp;They knew that radium-226 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{86}^{226}{\text{Ra}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>86</mn>
    </mrow>
    <mrow>
      <mn>226</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>Ra</mtext>
  </mrow>
</math></span>) decays by alpha emission to form a nuclide known as radon (Rn).</p>
</div>

<div class="specification">
<p>At the start of the experiment, Rutherford and Royds put 6.2 x&nbsp;10<sup>–4</sup> mol of&nbsp;pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a&nbsp;larger closed cylinder B.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The experiment lasted for 6 days. The decay constant of radium-226 is 1.4 x&nbsp;10<sup>–11</sup> s<sup>–1</sup>.</p>
</div>

<div class="specification">
<p>At the start of the experiment, all the air was removed from cylinder B. The&nbsp;alpha particles combined with electrons as they moved through the wall of cylinder A to&nbsp;form helium gas in cylinder B.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the nuclear equation for this decay.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that the activity of the radium-226 is almost constant during the&nbsp;experiment.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that about 3 x&nbsp;10<sup>15</sup> alpha particles are emitted by the radium-226 in 6 days.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The experiment was carried out at a temperature of 18 °C. The volume of&nbsp;cylinder B was 1.3 x&nbsp;10<sup>–5</sup> m<sup>3</sup> and the volume of cylinder A was negligible.&nbsp;Calculate the pressure of the helium gas that was collected in cylinder B over the 6 day period. Helium is a monatomic gas.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_2^4\alpha ">
  <msubsup>
    <mi></mi>
    <mn>2</mn>
    <mn>4</mn>
  </msubsup>
  <mi>α</mi>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_2^4{\text{He}}">
  <msubsup>
    <mrow>

    </mrow>
    <mn>2</mn>
    <mn>4</mn>
  </msubsup>
  <mrow>
    <mtext>He</mtext>
  </mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{86}^{222}{\text{Rn}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>86</mn>
    </mrow>
    <mrow>
      <mn>222</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>Rn</mtext>
  </mrow>
</math></span></p>
<p>&nbsp;</p>
<p><em>These <strong>must</strong> be seen on the right-hand&nbsp;side of the equation.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>6 days is 5.18&nbsp;x 10<sup>5</sup> s</p>
<p>activity after 6 days is&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{A_0}{e^{ - 1.4 \times {{10}^{ - 11}} \times 5.8 \times {{10}^5}}} \approx {A_0}">
  <mrow>
    <msub>
      <mi>A</mi>
      <mn>0</mn>
    </msub>
  </mrow>
  <mrow>
    <msup>
      <mi>e</mi>
      <mrow>
        <mo>−</mo>
        <mn>1.4</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mrow>
              <mo>−</mo>
              <mn>11</mn>
            </mrow>
          </msup>
        </mrow>
        <mo>×</mo>
        <mn>5.8</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mn>5</mn>
          </msup>
        </mrow>
      </mrow>
    </msup>
  </mrow>
  <mo>≈</mo>
  <mrow>
    <msub>
      <mi>A</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>A = 0.9999927 <em>A</em><sub>0&nbsp;</sub><em><strong>or</strong> </em>0.9999927&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
  <mi>λ</mi>
</math></span><em>N</em><sub>0</sub></p>
<p><em><strong>OR</strong></em></p>
<p>states that index of e is so small that&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{A}{{{A_0}}}">
  <mfrac>
    <mi>A</mi>
    <mrow>
      <mrow>
        <msub>
          <mi>A</mi>
          <mn>0</mn>
        </msub>
      </mrow>
    </mrow>
  </mfrac>
</math></span> is&nbsp;≈ 1</p>
<p><em><strong>OR</strong></em></p>
<p><em>A – A</em><sub>0</sub>&nbsp;≈ 10<sup>–15</sup>&nbsp;«s<sup>–1</sup>»</p>
<p>&nbsp;</p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>shows half-life of the order of 10<sup>11</sup> s or 5.0&nbsp;x 10<sup>10</sup> s</p>
<p>converts this to year «1600 y» or days and states half-life&nbsp;much longer than experiment compared to experiment</p>
<p>&nbsp;</p>
<p><em>Award <strong>[1 max]</strong> if calculations/substitutions have numerical slips&nbsp;but would lead to correct deduction.</em></p>
<p><em>eg: failure to convert 6 days to seconds but correct substitution&nbsp;into equation will give MP2.</em></p>
<p><em>Allow working in days, but for MP1 must see conversion of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
  <mi>λ</mi>
</math></span> or&nbsp;half-life to day<sup>–1</sup>.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1&nbsp;</strong></em><br><br>use of <em>A</em>&nbsp;= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
  <mi>λ</mi>
</math></span><em>N</em><sub>0</sub></p>
<p>conversion to number of molecules = <em>nN</em><sub>A</sub> =&nbsp;3.7&nbsp;x 10<sup>20</sup></p>
<p><em><strong>OR</strong></em></p>
<p>initial activity =&nbsp;5.2 x 10<sup>9</sup> «s<sup>–1</sup>»</p>
<p>number emitted =&nbsp;(6&nbsp;x 24&nbsp;x 3600)&nbsp;x 1.4&nbsp;x 10<sup>–11</sup>&nbsp;x 3.7&nbsp;x 10<sup>20</sup> <em><strong>or</strong> </em>2.7 x 10<sup>15</sup> alpha particles</p>
<p>&nbsp;</p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>use of <em>N</em> = <em>N</em><sub>0</sub><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{ - \lambda t}}">
  <mrow>
    <msup>
      <mi>e</mi>
      <mrow>
        <mo>−</mo>
        <mi>λ</mi>
        <mi>t</mi>
      </mrow>
    </msup>
  </mrow>
</math></span></p>
<p><em>N</em><sub>0</sub> =&nbsp;<em>n</em> x <em>N</em><sub>A</sub> =&nbsp;3.7 x 10<sup>20</sup></p>
<p>alpha particles emitted «= number of atoms disintegrated = <em>N</em> –&nbsp;<em>N</em><sub>0</sub> =» <em>N</em><sub>0</sub><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {1 - {e^{ - \lambda &nbsp;\times 6 \times 24 \times 3600}}} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>1</mn>
      <mo>−</mo>
      <mrow>
        <msup>
          <mi>e</mi>
          <mrow>
            <mo>−</mo>
            <mi>λ</mi>
            <mo>×</mo>
            <mn>6</mn>
            <mo>×</mo>
            <mn>24</mn>
            <mo>×</mo>
            <mn>3600</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>&nbsp;<em><strong>or</strong> </em>2.7&nbsp;x 10<sup>15</sup> alpha particles&nbsp;</p>
<p>&nbsp;</p>
<p><em>Must see correct substitution or&nbsp;answer to 2+ sf for MP3</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>alpha particles highly ionizing<br><em><strong>OR</strong></em><br>alpha particles have a low penetration power<br><em><strong>OR</strong></em><br>thin glass increases probability of alpha crossing glass<br><em><strong>OR</strong></em><br>decreases probability of alpha striking atom/nucleus/molecule</p>
<p> </p>
<p><em>Do not allow reference to tunnelling.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>conversion of temperature to 291 K</p>
<p><em>p</em> = 4.5 x 10<sup>–9</sup>&nbsp;x 8.31 x «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}">
  <mfrac>
    <mrow>
      <mn>291</mn>
    </mrow>
    <mrow>
      <mn>1.3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>5</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>p</em>&nbsp;= 2.7 x&nbsp;10<sup>15</sup>&nbsp;x 1.3 x&nbsp;10<sup>–23&nbsp;</sup>x «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}">
  <mfrac>
    <mrow>
      <mn>291</mn>
    </mrow>
    <mrow>
      <mn>1.3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>5</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>»<br><br>0.83 <em><strong>or</strong> </em>0.84 «Pa»</p>
<p>&nbsp;</p>
<p><em>Allow ECF for 2.7&nbsp;x&nbsp;10<sup>15</sup> from (b)(ii).</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The de Broglie wavelength <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math> of a particle accelerated close to the speed of light is approximately</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>≈</mo><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mi>E</mi></mfrac></math></p>
<p>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi></math> is the energy of the particle.<br>A beam of electrons of energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo> </mo><mi>eV</mi></math> is produced in an accelerator.</p>
</div>

<div class="specification">
<p>The electron beam is used to study the nuclear radius of carbon-12. The beam is directed from the left at a thin sample of carbon-12. A detector is placed at an angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> relative to the direction of the incident beam.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="378" height="137"></p>
<p>The graph shows the variation of the intensity of electrons with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math>. There is a minimum of intensity for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><msub><mi>θ</mi><mn>0</mn></msub></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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" width="365" height="235"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the wavelength of an electron in the beam is about <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss how the results of the experiment provide evidence for matter waves.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The accepted value of the diameter of the carbon-12 nucleus is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>94</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math>. Estimate the angle <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>θ</mi><mn>0</mn></msub></math> at which the minimum of the intensity is formed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why electrons with energy of approximately <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>10</mn><mn>7</mn></msup><mo> </mo><mi>eV</mi></math> would be unsuitable for the investigation of nuclear radii.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Experiments with many nuclides suggest that the radius of a nucleus is proportional to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mstyle displaystyle="false"><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>60</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>4</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>.</mo><mn>96</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math></strong></em> ✓ </span></p>
<p><em><span class="fontstyle2"><br>Answer to at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">2</mn></math> s.f. (i.e. 3.0)</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«</span><span class="fontstyle1">the shape of the graph suggests that</span><span class="fontstyle0">» </span><span class="fontstyle1">electrons undergo diffraction </span><span class="fontstyle0">«</span><span class="fontstyle1">with carbon nuclei</span><span class="fontstyle0">» </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle1">only waves diffract </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><msub><mi>θ</mi><mn>0</mn></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>96</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>94</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>15</mn></mrow></msup></mrow></mfrac><mo>«</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>599</mn><mo>»</mo></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>37</mn><mo> </mo><mo>«</mo><mpadded lspace="-1px"><mi>degrees</mi></mpadded><mo>»</mo></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>64</mn><mo>/</mo><mn>0</mn><mo>.</mo><mn>65</mn><mo> </mo><mo>«</mo><mi>rad</mi><mo>»</mo></math> </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the de Broglie wavelength of electrons is </span><span class="fontstyle2">«</span><span class="fontstyle0">much</span><span class="fontstyle2">» </span><span class="fontstyle0">longer than the size of a nucleus </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle3"><br></span><span class="fontstyle0">hence electrons would not undergo diffraction<br></span><span class="fontstyle4"><em><strong>OR</strong></em><br></span><span class="fontstyle0">no diffraction pattern would be observed </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">volume of a nucleus proportional to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><msup><mi>A</mi><mstyle displaystyle="false"><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle></msup></mfenced><mn>3</mn></msup><mo>=</mo><mi>A</mi></math> </span><em><strong><span class="fontstyle2">AND </span></strong></em><span class="fontstyle0">mass proportional to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0">the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>mass</mi><mpadded lspace="+1px"><mi>volume</mi></mpadded></mfrac></math> independent of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> </span><span class="fontstyle4">«</span><span class="fontstyle0">hence density the same for all nuclei</span><span class="fontstyle4">» </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><em><span class="fontstyle5">Both needed for MP1</span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>An easy calculation with only one energy conversion to consider and a 'show' answer to help.&nbsp;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was challenging for candidates many of whom seemed to have little idea of the experiment. Many answers discussed deflection, with the idea that forces between the electron and the nucleus causing it to deflect at a particular angle. This was often combined with the word interference to suggest evidence of matter waves. A number of answers described a demonstration the candidates remembered seeing so answers talked about fuzzy green rings.</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered reasonably well with only the odd omission of the sine in the equation.</p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates generally scored poorly on this question. There was confusion between this experiment and another diffraction one, so often the new wavelength was compared to the spacing between atoms. Also, in line with answers to b(i) there were suggestions that the electrons did not have sufficient energy to reach the nucleus or would be deflected by too great an angle to be seen.</p>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question proved challenging and it wasn't common to find answers that scored both marks. Of those that had the right approach some missed out on both marks by describing A as the mass of the nucleus rather than proportional to the mass of the nucleus.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Yellow light of photon energy 3.5&nbsp;x 10<sup>–19</sup> J is incident on the surface of a particular&nbsp;photocell.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The photocell is connected to a cell as shown. The photoelectric current is at its&nbsp;maximum value (the saturation current).</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Radiation with a greater photon energy than that in (b) is now incident on the photocell.&nbsp;The intensity of this radiation is the same as that in (b).</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the light.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Electrons emitted from the surface of the photocell have almost no kinetic energy. Explain why this does not contradict the law of conservation of energy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Radiation of photon energy 5.2 x&nbsp;10<sup>–19</sup> J is now incident on the photocell. Calculate the&nbsp;maximum velocity of the emitted electrons.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the change in the number of photons per second incident on the surface of the photocell.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the effect on the maximum photoelectric current as a result of&nbsp;increasing the photon energy in this way.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>wavelength =&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{E} = \frac{{1.99 \times {{10}^{ - 25}}}}{{{\text{3}}{\text{.5}} \times {\text{1}}{{\text{0}}^{ - 19}}}} = ">
  <mfrac>
    <mrow>
      <mi>h</mi>
      <mi>c</mi>
    </mrow>
    <mi>E</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>1.99</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>25</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <mtext>3</mtext>
      </mrow>
      <mrow>
        <mtext>.5</mtext>
      </mrow>
      <mo>×</mo>
      <mrow>
        <mtext>1</mtext>
      </mrow>
      <mrow>
        <msup>
          <mrow>
            <mtext>0</mtext>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>19</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
</math></span>»&nbsp;5.7 x 10<sup>–7</sup> «m»</p>
<p>&nbsp;</p>
<p><em>If no unit assume m.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«potential» energy is required to leave surface</p>
<p><em>Do not allow reference to “binding energy”.</em><br><em>Ignore statements of conservation of energy.</em></p>
<p><br>all/most energy given to potential «so none left for kinetic energy»</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy surplus =&nbsp;1.7&nbsp;x 10<sup>–19</sup>&nbsp;J</p>
<p>v<sub>max</sub> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{2 \times 1.7 \times {{10}^{ - 19}}}}{{9.1 \times {{10}^{ - 31}}}}} &nbsp;= 6.1 \times {10^5}">
  <msqrt>
    <mfrac>
      <mrow>
        <mn>2</mn>
        <mo>×</mo>
        <mn>1.7</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mrow>
              <mo>−</mo>
              <mn>19</mn>
            </mrow>
          </msup>
        </mrow>
      </mrow>
      <mrow>
        <mn>9.1</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mrow>
              <mo>−</mo>
              <mn>31</mn>
            </mrow>
          </msup>
        </mrow>
      </mrow>
    </mfrac>
  </msqrt>
  <mo>=</mo>
  <mn>6.1</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mn>5</mn>
    </msup>
  </mrow>
</math></span>&nbsp;«m s<sup>–1</sup>»</p>
<p>&nbsp;</p>
<p><em>Award <strong>[1 max]</strong> if surplus of 5.2 x 10<sup>–19</sup>J used&nbsp;(answer: 1.1 x 10<sup>6</sup> m s<sup>–1</sup>)</em></p>
<p>&nbsp;</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«same intensity of radiation so same total energy delivered per square metre per second» </p>
<p>light has higher photon energy so fewer photons incident per second</p>
<p> </p>
<p><em>Reason is required</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1:1 correspondence between photon and electron</p>
<p>so fewer electrons per second</p>
<p>current smaller</p>
<p>&nbsp;</p>
<p><em>Allow ECF from (c)(i)</em><br><em>Allow ECF from MP2 to MP3.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Plutonium-238 (Pu) decays by alpha (&alpha;) decay into uranium (U).</p>
<p>The following data are available for binding energies per nucleon:</p>
<p style="padding-left: 30px;">plutonium&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 7.568&thinsp;MeV</p>
<p style="padding-left: 30px;">uranium&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;7.600&thinsp;MeV</p>
<p style="padding-left: 30px;">alpha particle&nbsp; &nbsp; &nbsp;7.074&thinsp;MeV</p>
</div>

<div class="specification">
<p>The energy in b(i) can be transferred into electrical energy to run the instruments of&nbsp;a spacecraft. A spacecraft carries 33&thinsp;kg of pure plutonium-238 at launch. The decay&nbsp;constant of plutonium is 2.50 &times; 10<sup>&minus;10</sup>&thinsp;s<sup>&minus;1</sup>.</p>
</div>

<div class="specification">
<p>Solar radiation falls onto a metallic surface carried by the spacecraft causing&nbsp;the emission of photoelectrons. The radiation has passed through a filter so it is&nbsp;monochromatic. The spacecraft is moving away from the Sun.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the binding energy of a nucleus.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, a graph to show the variation with nucleon number <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> of the binding energy per nucleon, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>BE</mtext><mi>A</mi></mfrac></math>. Numbers are not required on the vertical axis.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some unstable nuclei have many more neutrons than protons. Suggest the likely decay for these nuclei.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy released in this decay is about 6 MeV.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The plutonium nucleus is at rest when it decays.</p>
<p>Calculate the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>kinetic energy of alpha particle</mtext><mtext>kinetic energy of uranium</mtext></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the power, in kW, that is available from the plutonium at launch.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spacecraft will take 7.2 years (2.3 × 10<sup>8</sup> s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> State and explain what happens to the kinetic energy of an emitted photoelectron.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> State and explain what happens to the rate at which charge leaves the metallic surface.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the energy needed to «completely» separate the nucleons of a nucleus</p>
<p><em><strong>OR</strong></em></p>
<p>the energy released when a nucleus is assembled from its constituent nucleons ✓</p>
<p> </p>
<p><em>Accept reference to protons and </em><em>neutrons.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>curve rising to a maximum between 50 and 100 ✓</p>
<p>curve continued and decreasing ✓</p>
<p> </p>
<p><em>Ignore starting point.<br></em></p>
<p><em>Ignore maximum at alpha particle.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>At a point on the peak of their graph ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>beta minus «decay» ✓</p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct mass numbers for uranium (234) and alpha (4) ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>234</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>600</mn><mo>+</mo><mn>4</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>074</mn><mo>-</mo><mn>238</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>568</mn></math> «MeV» ✓</p>
<p>energy released 5.51 «MeV» ✓</p>
<p> </p>
<p><em>Ignore any negative sign.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>K</mi><msub><mi>E</mi><mi>α</mi></msub></mrow><mrow><mi>K</mi><msub><mi>E</mi><mi>U</mi></msub></mrow></mfrac><mo>=</mo></math>»<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>α</mi></msub></mrow></mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>U</mi></msub></mrow></mfrac></mfrac></mstyle></math>  <em><strong>OR  </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>m</mi><mi>U</mi></msub><msub><mi>m</mi><mi>α</mi></msub></mfrac></math> ✓</p>
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>234</mn><mn>4</mn></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn><mo>.</mo><mn>5</mn></math> ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>117</mn><mn>2</mn></mfrac></math> for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>number of nuclei present <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>33</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mn>238</mn></mfrac><mo>×</mo><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo>«</mo><mo>=</mo><mn>8</mn><mo>.</mo><mn>347</mn><mo>×</mo><msup><mn>10</mn><mn>25</mn></msup><mo>»</mo></math> ✓</p>
<p>initial activity is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>347</mn><mo>×</mo><msup><mn>10</mn><mn>25</mn></msup><mo>«</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>08</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup><mo> </mo><mtext>Bq</mtext><mo>»</mo></math> ✓</p>
<p>power is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>08</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup><mo>×</mo><mn>5</mn><mo>.</mo><mn>51</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>≈</mo><mn>18</mn></math> «kW» ✓</p>
<p> </p>
<p><em>Allow a final answer of 20 </em>kW<em> if 6 </em>MeV<em> used. </em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> and <strong>MP2</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>available power after time <em>t</em> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><msup><mi>e</mi><mrow><mo>−</mo><mn>2</mn><mo>.</mo><mn>50</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></msup><mo>=</mo><mn>17</mn><mo>.</mo><mn>0</mn></math> «kW» ✓</p>
<p> </p>
<p><em><strong>MP1</strong> may be implicit.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(c)(i)</strong>.</em></p>
<p><em>Allow 17.4 </em>kW<em> from unrounded power from <strong>(c)(i)</strong>.</em></p>
<p><em>Allow 18.8 </em>kW<em> from 6 </em>MeV<em>.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>stays the same ✓</p>
<p>as energy depends on the frequency of light ✓</p>
<p> </p>
<p><em>Allow reference to wavelength for <strong>MP2</strong>.</em></p>
<p><em>Award <strong>MP2</strong> only to answers stating that KE decreases due to Doppler effect.</em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreases ✓</p>
<p>as number of photons incident decreases ✓</p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>32</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span> is formed when a nucleus of deuterium (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{1}^{2}{\text{H}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mn>2</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>H</mtext>
  </mrow>
</math></span>) collides with a nucleus of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{31}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>31</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span>. The radius of a deuterium nucleus is 1.5 fm.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State how the density of a nucleus varies with the number of nucleons in the nucleus.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the nuclear radius of phosphorus-31 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{31}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>31</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span>) is about 4 fm.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the maximum distance between the centres of the nuclei for which the production of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>32</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span> is likely to occur.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>32</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span>. Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>32</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span> undergoes beta-minus (β<sup>–</sup>) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by decay constant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a fresh pure sample of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>32</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span> the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s<sup>–1</sup>, the decay constant of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
  <msubsup>
    <mrow>

    </mrow>
    <mrow>
      <mn>15</mn>
    </mrow>
    <mrow>
      <mn>32</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>P</mtext>
  </mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>it is constant ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>R</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{1}}{\text{.20}} \times {10^{ - 15}} \times {31^{\frac{1}{3}}} = 3.8 \times {10^{ - 15}}">
  <mrow>
    <mtext>1</mtext>
  </mrow>
  <mrow>
    <mtext>.20</mtext>
  </mrow>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mrow>
        <mo>−</mo>
        <mn>15</mn>
      </mrow>
    </msup>
  </mrow>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>31</mn>
      <mrow>
        <mfrac>
          <mn>1</mn>
          <mn>3</mn>
        </mfrac>
      </mrow>
    </msup>
  </mrow>
  <mo>=</mo>
  <mn>3.8</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mrow>
        <mo>−</mo>
        <mn>15</mn>
      </mrow>
    </msup>
  </mrow>
</math></span> «m» ✔</p>
<p><em>Must see working and answer to at least 2SF</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>separation for interaction = 5.3 <em><strong>or</strong></em> 5.5 «fm» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy required = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{15{e^2}}}{{4\pi {\varepsilon _0} \times 5.3 \times {{10}^{ - 15}}}}">
  <mfrac>
    <mrow>
      <mn>15</mn>
      <mrow>
        <msup>
          <mi>e</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>4</mn>
      <mi>π</mi>
      <mrow>
        <msub>
          <mi>ε</mi>
          <mn>0</mn>
        </msub>
      </mrow>
      <mo>×</mo>
      <mn>5.3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>15</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span> ✔</p>
<p>= 6.5 / 6.6 ×10<sup>−13</sup> <em><strong>OR</strong></em> 6.3 ×10<sup>−13 </sup>«J» ✔</p>
<p> </p>
<p><em>Allow ecf from (b)(i)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«electron» <span style="text-decoration: underline;">antineutrino</span> also emitted ✔</p>
<p>energy split between electron and «anti»neutrino ✔</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>probability of decay of a nucleus ✔</p>
<p><em><strong>OR</strong></em></p>
<p>the fraction of the number of nuclei that decay</p>
<p>in one/the next second</p>
<p><strong>OR</strong></p>
<p>per unit time ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1 week = 6.05 × 10<sup>5</sup> «s»</p>
<p>17 = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="24{{\text{e}}^{ - \lambda  \times 6.1 \times {{10}^5}}}">
  <mn>24</mn>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mo>−</mo>
        <mi>λ</mi>
        <mo>×</mo>
        <mn>6.1</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mn>5</mn>
          </msup>
        </mrow>
      </mrow>
    </msup>
  </mrow>
</math></span> ✔</p>
<p>5.7 × 10<sup>−7 </sup>«s<sup>–1</sup>» ✔<br><br></p>
<p><em>Award<strong> [2 max]</strong> if answer is not in seconds</em></p>
<p><em>If answer <strong>not</strong> in seconds and <strong>no</strong> unit quoted award<strong> [1 max]</strong> for correct substitution into equation (MP2)</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Particles can be used in scattering experiments to estimate nuclear sizes.</p>
</div>

<div class="specification">
<p>Electron diffraction experiments indicate that the nuclear radius of carbon-12&nbsp;is 2.7&nbsp;x 10<sup>–15</sup> m. The graph shows the variation of nuclear radius with nucleon number. The nuclear radius of the carbon-12 is shown on the graph.</p>
<p><img 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"></p>
</div>

<div class="specification">
<p>The Feynman diagram shows electron capture.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the nature of the particle labelled X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how these experiments are carried out.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the particles must be accelerated to high energies in scattering experiments.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain <strong>one</strong> example of a scientific analogy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot the position of magnesium-24 on the graph.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a line on the graph, to show the variation of nuclear radius with nucleon number.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«electron» neutrino</p>
<p>it has a lepton number of 1 «as lepton number is conserved»</p>
<p>it has a charge of zero/is neutral «as charge is conserved»<br><em><strong>OR</strong></em><br>it has a baryon number of 0 «as baryon number is conserved»</p>
<p><em>Do not allow antineutrino </em></p>
<p><em>Do not credit answers referring to energy</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«high energy particles incident on» thin sample</p>
<p>detect angle/position of deflected particles</p>
<p>reference to interference/diffraction/minimum/maximum/numbers of particles</p>
<p><em>Allow “foil” instead of thin</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>λ </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto \frac{1}{{\sqrt E }}">
  <mo>∝</mo>
  <mfrac>
    <mn>1</mn>
    <mrow>
      <msqrt>
        <mi>E</mi>
      </msqrt>
    </mrow>
  </mfrac>
</math></span> <em><strong>OR</strong></em> <em>λ </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto \frac{1}{E}">
  <mo>∝</mo>
  <mfrac>
    <mn>1</mn>
    <mi>E</mi>
  </mfrac>
</math></span></p>
<p>so high energy gives small <em>λ</em></p>
<p>to match the small nuclear size</p>
<p><strong><em>Alternative 2</em></strong></p>
<p><em>E = hf</em>/energy is proportional to frequency</p>
<p>frequency is inversely proportional to wavelength/<em>c = fλ</em></p>
<p>to match the small nuclear size</p>
<p><em><strong>Alternative 3</strong></em></p>
<p>higher energy means closer approach to nucleus</p>
<p>to overcome the repulsive force from the nucleus</p>
<p>so greater precision in measurement of the size of the nucleus</p>
<p><em>Accept inversely proportional</em></p>
<p><em>Only allow marks awarded from <strong>one</strong> alternative</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>two analogous situations stated</p>
<p>one element of the analogy equated to an element of physics</p>
<p><em>eg: moving away from Earth is like climbing a hill where the contours correspond to the equipotentials</em></p>
<p><em>Atoms in an ideal gas behave like pool balls</em></p>
<p><em>The forces between them only act during collisions</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correctly plotted</p>
<p><em>Allow ECF from (d)(i)</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>single smooth curve passing through both points with decreasing gradient</p>
<p>through origin</p>
<p><img 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"></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>In an electric circuit used to investigate the photoelectric effect, the voltage is varied until the&nbsp;reading in the ammeter is zero. The stopping voltage that produces this reading is 1.40 V.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the photoelectric effect.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the maximum velocity of the photoelectrons is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn><mo> </mo><msup><mtext>km  s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The photoelectrons are emitted from a sodium surface. Sodium has a work function of&nbsp;2.3 eV.</p>
<p>Calculate the wavelength of the radiation incident on the sodium. State an appropriate&nbsp;unit for your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>electrons are ejected from the surface of a metal <strong>✓</strong></p>
<p>after gaining energy from photons/electromagnetic radiation <strong>✓</strong></p>
<p>there is a minimum «threshold» energy/frequency<br><em><strong>OR</strong></em><br>maximum «threshold» wavelength <strong>✓</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mi>V</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>&nbsp;</mo><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></math>» and manipulation to get <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>&nbsp;<strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>4</mn></mrow><mrow><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></mrow></mfrac></msqrt></math>&nbsp; <em><strong>OR&nbsp;&nbsp;</strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>702</mn><mo>«</mo><msup><mtext>km s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><strong>✓</strong></p>
<p><em>Must see either complete substitution or calculation to at least 3 s.f. for <strong>MP2</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>4</mn></math>&nbsp;✓</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow><mrow><mn>3</mn><mo>.</mo><mn>7</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfrac></math>&nbsp;✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup><mo>&nbsp;</mo><mtext>m&nbsp;</mtext><mtext mathvariant="bold-italic">OR</mtext><mtext>&nbsp;340&nbsp;nm</mtext></math>&nbsp;<strong>✓</strong></p>
<p><em><br>Must see an appropriate unit to award<strong> MP3.</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In an experiment to demonstrate the photoelectric effect, monochromatic electromagnetic&nbsp;radiation from source A is incident on the surfaces of metal P and metal Q. Observations&nbsp;of the emission of electrons from P and Q are made.</p>
<p>The experiment is then repeated with two other sources of electromagnetic radiation:&nbsp;B and C. The table gives the results for the experiment and the wavelengths of the&nbsp;radiation sources.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the cause of the electron emission for radiation A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why electrons are never emitted for radiation C.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why radiation B gives different results.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why there is no effect on the table of results when the intensity of source B is doubled.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Photons with energy 1.1 × 10<sup>−18 </sup>J are incident on a third metal surface. The maximum&nbsp;energy of electrons emitted from the surface of the metal is 5.1 × 10<sup>−19 </sup>J.</p>
<p>Calculate, in eV, the work function of the metal.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>photon transfers «all» energy to electron <strong>✓</strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>photon energy is less than both work functions<br><em><strong>OR</strong></em><br>photon energy is insufficient «to remove an electron» <strong>✓</strong></p>
<p><em><br>Answer must be in terms of photon energy.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Identifies P work function lower than Q work function<strong> ✓</strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>changing/doubling intensity «changes/doubles number of photons arriving but» does not change energy of photon<strong> ✓</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>18</mn></mrow></msup><mo>-</mo><mi mathvariant="normal">ϕ</mi></math>&nbsp;✓</strong></p>
<p>work function&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>=&nbsp;«</mtext><mfrac><mrow><mo>(</mo><mn>11</mn><mo>.</mo><mn>0</mn><mo>-</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfrac><mtext>=&nbsp;»&nbsp;3.7&nbsp;«eV»</mtext></math>&nbsp;<strong>&nbsp;✓</strong></p>
<p><em><br>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An apparatus is used to investigate the photoelectric effect. A caesium cathode C is illuminated by a variable light source. A variable power supply is connected between C and the collecting anode A. The photoelectric current <em>I</em> is measured using an ammeter.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A current is observed on the ammeter when violet light illuminates C. With V held constant the current becomes zero when the violet light is replaced by red light of the same intensity. Explain this observation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph shows the variation of photoelectric current <em>I</em> with potential difference <em>V</em> between C and A when violet light of a particular intensity is used.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The intensity of the light source is increased without changing its wavelength.</p>
<p>(i) Draw, on the axes, a graph to show the variation of <em>I</em> with <em>V</em> for the increased intensity.</p>
<p>(ii) The wavelength of the violet light is 400 nm. Determine, in eV, the work function of caesium.</p>
<p>(iii) <em>V</em> is adjusted to +2.50V. Calculate the maximum kinetic energy of the photoelectrons just before they reach A.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>reference to photon<br><em><strong>OR</strong></em><br>energy = <em>hf <strong>or</strong></em> =<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{\lambda }">
  <mfrac>
    <mrow>
      <mi>h</mi>
      <mi>c</mi>
    </mrow>
    <mi>λ</mi>
  </mfrac>
</math></span><br><br>violet photons have greater energy than red photons</p>
<p>when <em>hf </em>&gt; Φ <em><strong>or</strong></em> photon energy&gt; work function then electrons are ejected</p>
<p>frequency of red light &lt; threshold frequency «so no emission»<br><em><strong>OR</strong></em><br>energy of red light/photon &lt; work function «so no emission»</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i<br>line with same negative intercept «–1.15V»<br><br>otherwise above existing line everywhere and of similar shape with clear plateau</p>
<p><em>Award this marking point even if intercept is wrong.</em></p>
<p>&nbsp;</p>
<p>ii<br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{{\lambda e}} = ">
  <mfrac>
    <mrow>
      <mi>h</mi>
      <mi>c</mi>
    </mrow>
    <mrow>
      <mi>λ</mi>
      <mi>e</mi>
    </mrow>
  </mfrac>
  <mo>=</mo>
</math></span>&nbsp;«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{40 \times {{10}^{ - 9}} \times 1.6 \times {{10}^{ - 19}}}} = ">
  <mfrac>
    <mrow>
      <mn>6.63</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>34</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mn>8</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>40</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>9</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>1.6</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>19</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
</math></span>» 3.11&nbsp;«eV»</p>
<p><em>Intermediate answer is 4.97×10<sup>−19</sup>&nbsp;J. </em></p>
<p><em>Accept approach using </em>f<em> rather than c/λ</em><br><br>«3.10 − 1.15 =» 1.96 «eV»<br><em>Award <strong>[2]</strong> for a bald correct answer in eV.<br>Award <strong>[1 max]</strong> if correct answer is given in</em> <em>J</em> (3.12×10<sup>−19&nbsp;</sup>J).</p>
<p>&nbsp;</p>
<p>iii</p>
<p>«KE = <em>qVs =</em>» 1.15 «eV»</p>
<p><em><strong>OR</strong></em></p>
<p>1.84 x 10<sup>−19&nbsp;</sup>«J»</p>
<p><em>Allow ECF from MP1 to MP2.</em></p>
<p>adds 2.50 eV = 3.65 eV</p>
<p><em><strong>OR</strong></em></p>
<p>5.84&nbsp;x 10<sup>−19</sup> J</p>
<p><em>Must see units in this question to identify energy unit used.</em><br><em>Award <strong>[2]</strong> for a bald correct answer that includes units.</em><br><em>Award <strong>[1 max]</strong> for correct answer without units.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>During electron capture, an atomic electron is captured by a proton in the nucleus.&nbsp;The stable nuclide thallium-205 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>) can be formed when an unstable lead (Pb)&nbsp;nuclide captures an electron.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation to represent this decay.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The unstable lead nuclide has a half-life of 15 × 10<sup>6</sup> years. A sample initially&nbsp;contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei&nbsp;being formed each second 30 × 10<sup>6</sup> years later.</p>
<p>&nbsp;</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The neutron number <em>N</em> and the proton number <em>Z</em> are not equal for the nuclide <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>.&nbsp;Explain, with reference to the forces acting within the nucleus, the reason for this.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Thallium-205 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>) can also form from successive alpha (α) and beta-minus (β<sup>−</sup>)&nbsp;decays of an unstable nuclide. The decays follow the sequence α β<sup>−</sup> β<sup>−</sup> α. The diagram&nbsp;shows the position of <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>&nbsp;on a chart of neutron number against proton number.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" 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"></p>
<p>Draw <strong>four</strong> arrows to show the sequence of changes to <em>N</em> and <em>Z</em> that occur as the <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>&nbsp;forms from the unstable nuclide.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Pb</mtext><mprescripts></mprescripts><mn>82</mn><mn>205</mn></mmultiscripts></math>&nbsp;<strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>e&nbsp;&nbsp;</mtext><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mtext mathvariant="bold-italic">AND&nbsp;&nbsp;</mtext><mo>&nbsp;</mo><mmultiscripts><mi>ν</mi><mtext>e</mtext><none></none><mprescripts></mprescripts><mn>0</mn><mn>0</mn></mmultiscripts></math>&nbsp;<strong>✓</strong></p>
<p>&nbsp;</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>calculates&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mrow><mn>15</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo>&nbsp;</mo><mo>«</mo><mo>=</mo><mo>&nbsp;</mo><mn>4</mn><mo>.</mo><mn>62</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>8</mn></mrow></msup><msup><mtext>&nbsp;year</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math>&nbsp;<strong>✓</strong></p>
<p>calculates nuclei remaining&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>=&nbsp;</mtext><mn>0</mn><mo>.</mo><mn>50</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo> </mo><mo>«</mo><mo>=</mo><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>17</mn></msup><mo>»</mo></math>&nbsp;<strong>✓</strong></p>
<p>activity&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>«</mo><mi>λ</mi><mo> </mo><mi>N</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo>&nbsp;</mo><mtext>nuclei&nbsp;per&nbsp;year</mtext><mo>»</mo><mo>=</mo><mn>440</mn><mo> </mo><mo>«</mo><mtext>nuclei&nbsp;per&nbsp;second</mtext><mo>»</mo></math><strong>&nbsp;✓</strong></p>
<p><em><br>Accept conversion to seconds at any stage. </em></p>
<p><em>Award <strong>[3] marks</strong> for a bald correct answer. </em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> and <strong>MP2</strong> </em></p>
<p><em>Allow use of decay equation.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Reference to proton repulsion <em><strong>OR</strong> </em>nucleon attraction <strong>✓</strong></p>
<p>strong force is short range <em><strong>OR</strong> </em>electrostatic/electromagnetic force is long range <strong>✓</strong></p>
<p>more neutrons «than protons» needed «to hold nucleus together»&nbsp;<strong>&nbsp;✓</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"></p>
<p>any α change correct <strong>✓</strong></p>
<p>any β change correct <strong>✓</strong></p>
<p>diagram fully correct<strong>&nbsp;✓</strong></p>
<p><em><br>Award <strong>[2] max</strong> for a correct diagram without arrows drawn. </em></p>
<p><em>For <strong>MP1</strong> accept a (−2, −2 ) line with direction indicated, drawn at any position in the graph. </em></p>
<p><em>For <strong>MP2</strong> accept a (1, −1) line with direction indicated, drawn at any position in the graph. </em></p>
<p><em>Award <strong>[1] max</strong> for a correct diagram&nbsp;with all arrows in the opposite direction.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Radioactive uranium-238 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>U</mtext><mprescripts></mprescripts><mn>92</mn><mn>238</mn></mmultiscripts></mfenced></math>&nbsp;produces a series of decays ending with a stable nuclide of&nbsp;lead. The nuclides in the series decay by either alpha (α) or beta-minus (β<sup>−</sup>) processes.</p>
</div>

<div class="specification">
<p>The graph shows the variation with the nucleon number <em>A</em> of the binding energy per nucleon.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Uranium-238 decays into a nuclide of thorium-234 (Th).</p>
<p><br>Write down the complete equation for this radioactive decay.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Thallium-206&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>206</mn></mmultiscripts></mfenced></math>&nbsp;decays into lead-206&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>Pb</mtext><mprescripts></mprescripts><mn>82</mn><mn>206</mn></mmultiscripts></mfenced></math>.</p>
<p>Identify the quark changes for this decay.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The half-life of uranium-238 is about 4.5 × 10<sup>9</sup> years. The half-life of thallium-206 is about 4.2 minutes.</p>
<p>Compare and contrast the methods to measure these half-lives.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why high temperatures are required for fusion to occur.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to the graph, why energy is released both in fusion and in fission.</p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Uranium-235 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>U</mtext><mprescripts></mprescripts><mn>92</mn><mn>235</mn></mmultiscripts></mfenced></math>&nbsp;is used as a nuclear fuel. The fission of uranium-235 can&nbsp;produce krypton-89 and barium-144.</p>
<p>Determine, in MeV and using the graph, the energy released by this fission.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>U→«</mtext><mprescripts></mprescripts><mn>92</mn><mn>238</mn></mmultiscripts><mmultiscripts><mo>»</mo><mprescripts></mprescripts><mn>90</mn><mn>234</mn></mmultiscripts><mtext>Th+</mtext><mo>«</mo><mmultiscripts><mo>»</mo><mprescripts></mprescripts><mn>2</mn><mn>4</mn></mmultiscripts><mi>α</mi></math><strong>&nbsp;✓</strong><strong>&nbsp;</strong></p>
<p><em>Allow He for alpha.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>udd→uud<strong><br><em>OR</em><br></strong>down quark changes to up quark&nbsp;<strong>✓</strong><strong>&nbsp;</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>measure «radio»activity/«radioactive» decay/A for either<br><em><strong>OR</strong></em><br>take measurements with a Geiger counter. <strong>✓</strong></p>
<p>for Uranium measure number/N of radioactive atoms/<strong><em>OWTTE </em>✓</strong></p>
<p>for Thalium measure «rate of» change in activity over time. <strong>✓</strong></p>
<p>correct connection for either Uranium or Thalium to determine half life<strong> ✓</strong><strong> </strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>links temperature to kinetic energy/speed of particles <strong>✓</strong><strong> </strong></p>
<p>energy required to overcome «Coulomb» electrostatic repulsion <strong>✓</strong><strong> </strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«energy is released when» binding energy per nucleon increases</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>any use of (value from graph) x (number of nucleons) <strong>✓</strong></p>
<p>«235 × 7.6 – (89 × 8.6 + 144 × 8.2) =» 160 «MeV»&nbsp;<strong>✓</strong>&nbsp;</p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Potassium-40&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>K</mtext><mprescripts></mprescripts><mn>19</mn><mn>40</mn></mmultiscripts></mfenced></math>&nbsp;decays by two processes.</p>
<p>The first process is that of beta-minus (&beta;<sup>&minus;</sup>) decay to form a calcium (Ca) nuclide.</p>
</div>

<div class="specification">
<p>Potassium-40 decays by a second process to argon-40. This decay accounts for 11&thinsp;%&nbsp;of the total decay of the potassium-40.</p>
<p>Rocks can be dated by measuring the quantity of argon-40 gas trapped in them. One&nbsp;rock sample contains 340&thinsp;&micro;mol of potassium-40 and 12&thinsp;&micro;mol of argon-40.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation for this decay.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the initial quantity of potassium-40 in the rock sample was about 450 µmol.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The half-life of potassium-40 is 1.3 × 10<sup>9</sup> years. Estimate the age of the rock sample.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Ca</mtext><mprescripts></mprescripts><mn>20</mn><mn>40</mn></mmultiscripts></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mtext>e</mtext><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mo>+</mo></mrow><msub><mover><mi>ν</mi><mo>¯</mo></mover><mtext>e</mtext></msub></math>  <strong><em>OR  <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>β</mi><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mo>+</mo><msub><mover><mi>ν</mi><mo>¯</mo></mover><mtext>e</mtext></msub></math>  ✓</em></strong></p>
<p> </p>
<p><em>Full equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>K</mtext><mprescripts></mprescripts><mn>19</mn><mn>40</mn></mmultiscripts><mo>→</mo><mmultiscripts><mtext>Ca</mtext><mprescripts></mprescripts><mn>20</mn><mn>40</mn></mmultiscripts><mo>+</mo><mrow><mmultiscripts><mtext>e</mtext><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mo>+</mo></mrow><msub><mover><mi>ν</mi><mo>¯</mo></mover><mtext>e</mtext></msub></math></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total K-40 decayed = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>12 μmol</mtext><mrow><mn>0</mn><mo>.</mo><mn>11</mn></mrow></mfrac><mo>=</mo><mn>109</mn></math> «μmol» ✓</p>
<p>so total K-40 originally was 109 + 340 = 449 «μmol»✓ </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mtext>ln</mtext><mfenced><mn>2</mn></mfenced></mrow><msub><mi>t</mi><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></msub></mfrac></math> used to give 𝜆 = 5.3 x 10<sup>-10</sup> per year ✓</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><mo>=</mo><mfenced><mn>449</mn></mfenced><mfenced><msup><mi>e</mi><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>×</mo><mi>t</mi></mrow></msup></mfenced></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mfrac><mn>340</mn><mn>449</mn></mfrac></mfenced><mo>=</mo><mo>-</mo><mn>5</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>×</mo><mi>t</mi></math>  ✓</p>
<p><em><br>t </em>= 5.2 x 10<sup>8</sup> «years» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>340</mn><mn>449</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>76</mn></math> </strong></em>«remaining» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mfenced><mi>p</mi></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>693</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>ln</mi><mfenced><mrow><mn>0</mn><mo>.</mo><mn>76</mn></mrow></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>693</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>40</mn></math> ✓</p>
<p><em>t</em> = 0.40 x 1.3 x 10<sup>9</sup> = 5.2 x 10<sup>8</sup> «years» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 3</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>340</mn><mn>449</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>76</mn></math> «remaining» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>76</mn><mo>=</mo><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mfrac><mi>t</mi><mrow><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></msup></math> ✓</p>
<p><em>t </em>= 0.40 x 1.3 x 10<sup>9 </sup>= 5.2 x 10<sup>8</sup> «years» ✓</p>
<p> </p>
<p><em>Allow 5.3 x 10<sup>8</sup> years for final answer.</em></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong> for an incorrect number of half-lives.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«use the mass of the sample to» determine number of potassium-40 atoms / nuclei in sample ✓</p>
<p>«use a counter to» determine (radio)activity / A of sample ✓</p>
<p>use <em>A = λN</em> «to determine the decay constant / <em>λ</em>» ✓</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was very well done by candidates. The majority were able to identify the correct nuclide of Calcium and many correctly included an electron/beta particle and a properly written antineutrino.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a "show that" question that was generally well done by candidates.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a more challenging question for candidates. Many were able to calculate the decay constant and recognized that the ratio of initial and final quantities of the potassium-40 was important. A very common error was mixing the two common half-life equations up and using the wrong values in the exponent (using half life instead of the decay constant, or using the decay constant instead of the half life). Examiners were generous with ECF for candidates who clearly showed an incorrect number of half-lives multiplied by the time for one half-life.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Describing methods of determining half-life continues to be a struggle for candidates with very few earning all three marks. Many candidates described a method more appropriate to measuring a short half- life, but even those descriptions fell far short of being acceptable.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In an experiment a beam of electrons with energy 440&thinsp;MeV are incident on oxygen-16 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>O</mtext><mprescripts></mprescripts><mn>8</mn><mn>16</mn></mmultiscripts></mfenced></math>&nbsp;nuclei. The variation with scattering angle of the relative intensity of the scattered electrons&nbsp;is shown.<br><br></p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify a property of electrons demonstrated by this experiment.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy <em>E</em> of each electron in the beam is about 7 × 10<sup>−11 </sup>J.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The de Broglie wavelength for an electron is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mi>E</mi></mfrac></math>. Show that the diameter of an oxygen-16 nucleus is about 4 fm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate, using the result in (a)(iii), the volume of a tin-118 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>Sn</mtext><mprescripts></mprescripts><mn>50</mn><mn>118</mn></mmultiscripts></mfenced></math> nucleus. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>wave properties ✓</p>
<p><em><br>Accept reference to diffraction or interference.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>440 x 10<sup>6</sup> x 1.6 x 10<sup>-19</sup>  <em><strong>OR</strong>  </em>7.0 × 10<sup>-11</sup> «J» ✓</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow><mrow><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow></mfrac></math>  <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>440</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math>  <em><strong>OR </strong> </em>2.8 × 10<sup>-15 </sup>«m» seen ✓</p>
<p>read off graph as 46° ✓</p>
<p>«Use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfrac><mi>λ</mi><mrow><mi>sin</mi><mi>θ</mi></mrow></mfrac></math>=» 3.9 × 10<sup>-15</sup> m ✓</p>
<p> </p>
<p><em>Accept an angle between 45 and 47 degrees.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP2</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>∝</mo><msup><mi>A</mi><mfrac><mn>1</mn><mn>3</mn></mfrac></msup></math>   <em><strong>OR  </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>∝</mo><mi>A</mi></math> ✓</p>
<p>volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sn</mtext><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><mfenced><mfrac><msub><mi>A</mi><mrow><mi>S</mi><mi>n</mi></mrow></msub><msub><mi>A</mi><mi>O</mi></msub></mfrac></mfenced><msubsup><mi>r</mi><mi>O</mi><mrow><mo> </mo><mn>3</mn></mrow></msubsup></math> or equivalent working ✓</p>
<p>2.3 to 2.5 × 10<sup>-43 </sup>«m<sup>3</sup>»✓</p>
<p>answer to 1 or 2sf ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><msub><mi>R</mi><mtext>o</mtext></msub><mo>×</mo><msup><mi>A</mi><mfrac><mn>1</mn><mn>3</mn></mfrac></msup></math> ✓</p>
<p>volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sn</mtext><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><msup><mi>R</mi><mn>3</mn></msup></math>  <em><strong>OR</strong>  </em>5.9 x 10<sup>-15</sup> seen ✓</p>
<p>8.5 × 10<sup>-43</sup> «m<sup>3</sup>»✓</p>
<p>answer to 1 or 2sf ✓</p>
<p> </p>
<p><em>Although the question expects candidates to work from the oxygen radius found, allow <strong>ALT 2</strong> working from the Fermi radius.</em></p>
<p><em><strong>MP4</strong> is for any answer stated to 1 or 2 significant figures.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>ai) Well answered.</p>
<p>aii) Well answered.</p>
<p>aiii) This was generally well done but quite a few attempted the small angle approximation. Probably worth a mention in the report.</p>
<p>b) Most gained credit from the first alternative solution, trying to use the data as the question intended. There were the inevitable slips and calculator mistakes. Most got the fourth mark.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Rhodium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,45}^{106}{\text{Rh}}">
  <msubsup>
    <mi></mi>
    <mrow>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mn>45</mn>
    </mrow>
    <mrow>
      <mn>106</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>Rh</mtext>
  </mrow>
</math></span>)&nbsp;decays into palladium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,46}^{106}{\text{Pd}}">
  <msubsup>
    <mi></mi>
    <mrow>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mn>46</mn>
    </mrow>
    <mrow>
      <mn>106</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>Pd</mtext>
  </mrow>
</math></span>)&nbsp;by beta minus (<em>β</em><sup>–</sup>) decay.&nbsp;The diagram shows some of the nuclear energy levels of rhodium-106 and palladium-106.&nbsp;The arrow represents the <em>β</em><sup>–</sup> decay.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.42.36.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/09.d"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Bohr modified the Rutherford model by introducing the condition&nbsp;<em>mvr </em>= <em>n</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
  <mfrac>
    <mi>h</mi>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
    </mrow>
  </mfrac>
</math></span>.&nbsp;Outline the reason for this modification.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed <em>v </em>of an electron in the hydrogen atom is related to the&nbsp;radius <em>r </em>of the orbit by the expression</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v = \sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} ">
  <mi>v</mi>
  <mo>=</mo>
  <msqrt>
    <mfrac>
      <mrow>
        <mi>k</mi>
        <mrow>
          <msup>
            <mi>e</mi>
            <mn>2</mn>
          </msup>
        </mrow>
      </mrow>
      <mrow>
        <mrow>
          <msub>
            <mi>m</mi>
            <mrow>
              <mtext>e</mtext>
            </mrow>
          </msub>
        </mrow>
        <mi>r</mi>
      </mrow>
    </mfrac>
  </msqrt>
</math></span></p>
<p>where <em>k </em>is the Coulomb constant.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the answer in (b) and (c)(i), deduce that the radius <em>r </em>of the electron’s orbit&nbsp;in the ground state of hydrogen is given by the following expression.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="r = \frac{{{h^2}}}{{4{\pi ^2}k{m_{\text{e}}}{e^2}}}">
  <mi>r</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mrow>
        <msup>
          <mi>h</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>4</mn>
      <mrow>
        <msup>
          <mi>π</mi>
          <mn>2</mn>
        </msup>
      </mrow>
      <mi>k</mi>
      <mrow>
        <msub>
          <mi>m</mi>
          <mrow>
            <mtext>e</mtext>
          </mrow>
        </msub>
      </mrow>
      <mrow>
        <msup>
          <mi>e</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electron’s orbital radius in (c)(ii).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what may be deduced about the energy of the electron in the <em>β</em><sup>–</sup> decay.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest why the <em>β</em><sup>–</sup> decay is followed by the emission of a gamma ray photon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the gamma ray photon in (d)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the electrons accelerate and so radiate energy</p>
<p>they would therefore spiral into the nucleus/atoms would be unstable</p>
<p>electrons have discrete/only certain energy levels</p>
<p>the only orbits where electrons do not radiate are those that satisfy the Bohr condition&nbsp;<strong>«</strong><em>mvr</em> =&nbsp;<em>n</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
  <mfrac>
    <mi>h</mi>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
    </mrow>
  </mfrac>
</math></span><strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{m_{\text{e}}}{v^2}}}{r} = \frac{{k{e^2}}}{{{r^2}}}">
  <mfrac>
    <mrow>
      <mrow>
        <msub>
          <mi>m</mi>
          <mrow>
            <mtext>e</mtext>
          </mrow>
        </msub>
      </mrow>
      <mrow>
        <msup>
          <mi>v</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mi>r</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mi>k</mi>
      <mrow>
        <msup>
          <mi>e</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <msup>
          <mi>r</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span></p>
<p><strong><em>OR</em></strong></p>
<p>KE =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
</math></span>PE hence <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
</math></span><em>m</em><sub>e</sub><em>v</em><sup>2</sup> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}\frac{{k{e^2}}}{r}">
  <mfrac>
    <mn>1</mn>
    <mn>2</mn>
  </mfrac>
  <mfrac>
    <mrow>
      <mi>k</mi>
      <mrow>
        <msup>
          <mi>e</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mi>r</mi>
  </mfrac>
</math></span></p>
<p><strong>«</strong>solving for <em>v </em>to get answer<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Answer given – look for correct working</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>combining <em>v</em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} ">
  <msqrt>
    <mfrac>
      <mrow>
        <mi>k</mi>
        <mrow>
          <msup>
            <mi>e</mi>
            <mn>2</mn>
          </msup>
        </mrow>
      </mrow>
      <mrow>
        <mrow>
          <msub>
            <mi>m</mi>
            <mrow>
              <mtext>e</mtext>
            </mrow>
          </msub>
        </mrow>
        <mi>r</mi>
      </mrow>
    </mfrac>
  </msqrt>
</math></span>&nbsp;with <em>m</em><sub>e</sub><em>vr</em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
  <mfrac>
    <mi>h</mi>
    <mrow>
      <mn>2</mn>
      <mi>π</mi>
    </mrow>
  </mfrac>
</math></span>&nbsp;using correct substitution</p>
<p><strong>«</strong><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{m_e}^2\frac{{k{e^2}}}{{{m_{\text{e}}}r}}{r^2} = \frac{{{h^2}}}{{4{\pi ^2}}}">
  <msup>
    <mrow>
      <msub>
        <mi>m</mi>
        <mi>e</mi>
      </msub>
    </mrow>
    <mn>2</mn>
  </msup>
  <mfrac>
    <mrow>
      <mi>k</mi>
      <mrow>
        <msup>
          <mi>e</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <msub>
          <mi>m</mi>
          <mrow>
            <mtext>e</mtext>
          </mrow>
        </msub>
      </mrow>
      <mi>r</mi>
    </mrow>
  </mfrac>
  <mrow>
    <msup>
      <mi>r</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mrow>
        <msup>
          <mi>h</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>4</mn>
      <mrow>
        <msup>
          <mi>π</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span><strong>»</strong></p>
<p>correct algebraic manipulation to gain the answer</p>
<p>&nbsp;</p>
<p><em>Answer given – look for correct working</em></p>
<p><em>Do not allow a bald statement of the answer for MP2. Some further working eg cancellation of m or r must be shown</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>&nbsp;<em>r</em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{(6.63 \times {{10}^{ - 34}})}^2}}}{{4{\pi ^2} \times 8.99 \times {{10}^9} \times 9.11 \times {{10}^{ - 31}} \times {{(1.6 \times {{10}^{ - 19}})}^2}}}">
  <mfrac>
    <mrow>
      <mrow>
        <msup>
          <mrow>
            <mo stretchy="false">(</mo>
            <mn>6.63</mn>
            <mo>×</mo>
            <mrow>
              <msup>
                <mrow>
                  <mn>10</mn>
                </mrow>
                <mrow>
                  <mo>−</mo>
                  <mn>34</mn>
                </mrow>
              </msup>
            </mrow>
            <mo stretchy="false">)</mo>
          </mrow>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>4</mn>
      <mrow>
        <msup>
          <mi>π</mi>
          <mn>2</mn>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>8.99</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mn>9</mn>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>9.11</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>31</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mo stretchy="false">(</mo>
            <mn>1.6</mn>
            <mo>×</mo>
            <mrow>
              <msup>
                <mrow>
                  <mn>10</mn>
                </mrow>
                <mrow>
                  <mo>−</mo>
                  <mn>19</mn>
                </mrow>
              </msup>
            </mrow>
            <mo stretchy="false">)</mo>
          </mrow>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span><strong>»</strong></p>
<p><em>r</em> = 5.3&nbsp;× 10<sup>–11</sup>&nbsp;<strong>«</strong>m<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the energy released is 3.54 – 0.48 = 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p>this is shared by the electron and the antineutrino</p>
<p>so the electron’s energy varies from 0 to 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the palladium nucleus emits the photon when it decays into the ground state <strong>«</strong>from the excited state<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Photon energy</p>
<p><em>E</em> = 0.48&nbsp;×&nbsp;10<sup>6</sup>&nbsp;× 1.6&nbsp;× 10<sup>–19</sup> =&nbsp;<strong>«</strong>7.68 × 10<sup>–14</sup>&nbsp;<em>J</em><strong>»</strong></p>
<p><em>λ</em> =&nbsp;<strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{E} = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{7.68 \times {{10}^{ - 14}}}}">
  <mfrac>
    <mrow>
      <mi>h</mi>
      <mi>c</mi>
    </mrow>
    <mi>E</mi>
  </mfrac>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>6.63</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>34</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mn>8</mn>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>7.68</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>14</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span> =<strong>»</strong> 2.6&nbsp;× 10<sup>–12</sup><strong>&nbsp;«</strong>m<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow ECF from incorrect energy</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (<em>β–</em>) decay to form a stable boron (B) nuclide.</p>
</div>

<div class="specification">
<p>The initial number of nuclei in a pure sample of beryllium-10 is N<sub>0</sub>. The graph shows how the number of remaining <strong>beryllium </strong>nuclei in the sample varies with time.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the missing information for this decay.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the graph, sketch how the number of <strong>boron </strong>nuclei in the sample varies with time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After 4.3 × 10<sup>6</sup> years,</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{{\text{number of produced boron nuclei}}}}{{{\text{number of remaining beryllium nuclei}}}} = 7.">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>number of produced boron nuclei</mtext>
      </mrow>
    </mrow>
    <mrow>
      <mrow>
        <mtext>number of remaining beryllium nuclei</mtext>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mn>7.</mn>
</math></span></p>
<p>Show that the half-life of beryllium-10 is 1.4 × 10<sup>6</sup> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10<sup>11</sup> atoms of beryllium-10. The present activity of the sample is 8.0 × 10<sup>−3</sup> Bq.</p>
<p>Determine, in years, the age of the sample.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by thermal radiation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The temperature in the laboratory is higher than the temperature of the ice sample. Describe <strong>one </strong>other energy transfer that occurs between the ice sample and the laboratory.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}} \to _{{\mkern 1mu} {\mkern 1mu} 5}^{10}{\text{B}} + _{ - 1}^{\,\,\,0}{\text{e}} + {\overline {\text{V}} _{\text{e}}}">
  <msubsup>
    <mi></mi>
    <mrow>
      <mrow>
        <mspace width="0.056em"></mspace>
      </mrow>
      <mrow>
        <mspace width="0.056em"></mspace>
      </mrow>
      <mn>4</mn>
    </mrow>
    <mrow>
      <mn>10</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>Be</mtext>
  </mrow>
  <msubsup>
    <mo stretchy="false">→</mo>
    <mrow>
      <mrow>
        <mspace width="0.056em"></mspace>
      </mrow>
      <mrow>
        <mspace width="0.056em"></mspace>
      </mrow>
      <mn>5</mn>
    </mrow>
    <mrow>
      <mn>10</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>B</mtext>
  </mrow>
  <msubsup>
    <mo>+</mo>
    <mrow>
      <mo>−</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mn>0</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>e</mtext>
  </mrow>
  <mo>+</mo>
  <mrow>
    <msub>
      <mover>
        <mtext>V</mtext>
        <mo accent="false">¯</mo>
      </mover>
      <mrow>
        <mtext>e</mtext>
      </mrow>
    </msub>
  </mrow>
</math></span></p>
<p>antineutrino <em><strong>AND</strong> </em>charge <em><strong>AND</strong> </em>mass number of electron <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{ - 1}^{\,\,\,0}{\text{e}}">
  <msubsup>
    <mi></mi>
    <mrow>
      <mo>−</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mn>0</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>e</mtext>
  </mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overline {\text{V}} ">
  <mover>
    <mtext>V</mtext>
    <mo accent="false">¯</mo>
  </mover>
</math></span></p>
<p>conservation of mass number <strong><em>AND </em></strong>charge&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,5}^{10}{\text{B}}">
  <msubsup>
    <mi></mi>
    <mrow>
      <mspace width="thinmathspace"></mspace>
      <mspace width="thinmathspace"></mspace>
      <mn>5</mn>
    </mrow>
    <mrow>
      <mn>10</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>B</mtext>
  </mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}}">
  <msubsup>
    <mi></mi>
    <mrow>
      <mrow>
        <mspace width="0.056em"></mspace>
      </mrow>
      <mrow>
        <mspace width="0.056em"></mspace>
      </mrow>
      <mn>4</mn>
    </mrow>
    <mrow>
      <mn>10</mn>
    </mrow>
  </msubsup>
  <mrow>
    <mtext>Be</mtext>
  </mrow>
</math></span></p>
<p>&nbsp;</p>
<p><em>Do not accept V.</em></p>
<p><em>Accept </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar V}">
  <mrow>
    <mrow>
      <mover>
        <mi>V</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span><em>&nbsp;without subscript e.</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct shape <em>ie </em>increasing from 0 to about 0.80 N<sub>0</sub></p>
<p>crosses given line at 0.50 N<sub>0</sub></p>
<p><img src="images/Schermafbeelding_2018-08-10_om_19.42.49.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/06.b.i/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>fraction of Be = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{8}">
  <mfrac>
    <mn>1</mn>
    <mn>8</mn>
  </mfrac>
</math></span>, 12.5%, or 0.125</p>
<p>therefore 3 half lives have elapsed</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t_{\frac{1}{2}}} = \frac{{4.3 \times {{10}^6}}}{3} = 1.43 \times {10^6}">
  <mrow>
    <msub>
      <mi>t</mi>
      <mrow>
        <mfrac>
          <mn>1</mn>
          <mn>2</mn>
        </mfrac>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>4.3</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mn>6</mn>
        </msup>
      </mrow>
    </mrow>
    <mn>3</mn>
  </mfrac>
  <mo>=</mo>
  <mn>1.43</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mn>6</mn>
    </msup>
  </mrow>
</math></span>&nbsp;<strong>«</strong>≈ 1.4 × 10<sup>6</sup><strong>»</strong>&nbsp;<strong>«</strong>y<strong>»</strong></p>
<p>&nbsp;</p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>fraction of Be = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{8}">
  <mfrac>
    <mn>1</mn>
    <mn>8</mn>
  </mfrac>
</math></span>, 12.5%, or 0.125</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{8} = {{\text{e}}^{ - \lambda }}(4.3 \times {10^6})">
  <mfrac>
    <mn>1</mn>
    <mn>8</mn>
  </mfrac>
  <mo>=</mo>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mo>−</mo>
        <mi>λ</mi>
      </mrow>
    </msup>
  </mrow>
  <mo stretchy="false">(</mo>
  <mn>4.3</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mn>6</mn>
    </msup>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span> leading to&nbsp;<em>λ</em> = 4.836&nbsp;× 10<sup>–7</sup>&nbsp;<strong>«</strong>y<strong>»</strong><sup>–1</sup></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\ln 2}}{\lambda }">
  <mfrac>
    <mrow>
      <mi>ln</mi>
      <mo>⁡</mo>
      <mn>2</mn>
    </mrow>
    <mi>λ</mi>
  </mfrac>
</math></span> = 1.43&nbsp;× 10<sup>6</sup>&nbsp;<strong>«</strong>y<strong>»</strong></p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p><em>Must see at least one extra sig fig in final answer.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>λ</em>&nbsp;<strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\ln 2}}{{1.4 \times {{10}^6}}}">
  <mfrac>
    <mrow>
      <mi>ln</mi>
      <mo>⁡</mo>
      <mn>2</mn>
    </mrow>
    <mrow>
      <mn>1.4</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mn>6</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span><strong>»</strong> = 4.95&nbsp;× 10<sup>–7</sup>&nbsp;<strong>«</strong>y<sup>–1</sup><strong>»</strong></p>
<p>rearranging of&nbsp;<em>A</em> =&nbsp;<em>λN</em><sub>0</sub>e<sup>–<em>λt</em></sup> to give –<em>λt</em> = ln&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{8.0 \times {{10}^{-3}} \times 365 \times 24 \times 60 \times 60}}{{4.95 \times {{10}^{-7}} \times 7.6 \times {{10}^{11}}}}">
  <mfrac>
    <mrow>
      <mn>8.0</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>365</mn>
      <mo>×</mo>
      <mn>24</mn>
      <mo>×</mo>
      <mn>60</mn>
      <mo>×</mo>
      <mn>60</mn>
    </mrow>
    <mrow>
      <mn>4.95</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>7</mn>
          </mrow>
        </msup>
      </mrow>
      <mo>×</mo>
      <mn>7.6</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mn>11</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>&nbsp;<strong>«</strong>=&nbsp;–0.400<strong>»</strong></p>
<p><em>t</em> =&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 0.400}}{{ - 4.95 \times {{10}^{ - 7}}}} = 8.1 \times {10^5}">
  <mfrac>
    <mrow>
      <mo>−</mo>
      <mn>0.400</mn>
    </mrow>
    <mrow>
      <mo>−</mo>
      <mn>4.95</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>7</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>=</mo>
  <mn>8.1</mn>
  <mo>×</mo>
  <mrow>
    <msup>
      <mn>10</mn>
      <mn>5</mn>
    </msup>
  </mrow>
</math></span>&nbsp;<strong>«</strong>y<strong>»</strong></p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>emission of (infrared) electromagnetic/infrared energy/waves/radiation.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the (peak) wavelength of emitted em waves depends on temperature of emitter/reference to Wein’s Law</p>
<p>so frequency/color depends on temperature</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda &nbsp;= \frac{{2.90 \times {{10}^{ - 3}}}}{{253}}">
  <mi>λ</mi>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>2.90</mn>
      <mo>×</mo>
      <mrow>
        <msup>
          <mrow>
            <mn>10</mn>
          </mrow>
          <mrow>
            <mo>−</mo>
            <mn>3</mn>
          </mrow>
        </msup>
      </mrow>
    </mrow>
    <mrow>
      <mn>253</mn>
    </mrow>
  </mfrac>
</math></span></p>
<p>= 1.1 × 10<sup>–5</sup>&nbsp;<strong>«</strong>m<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Allow ECF from MP1 (incorrect temperature).</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>from the laboratory to the sample</p>
<p>conduction – contact between ice and lab surface.</p>
<p><strong><em>OR</em></strong></p>
<p>convection – movement of air currents</p>
<p>&nbsp;</p>
<p><em>Must clearly see direction of energy transfer for MP1.</em></p>
<p><em>Must see more than just words “conduction” or “convection” for MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iv.</div>
</div>
<br><hr><br><div class="specification">
<p>Hydrogen atoms in an ultraviolet (UV) lamp make transitions from the first excited state to the ground state. Photons are emitted and are incident on a photoelectric surface as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_12.49.40.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08"></p>
</div>

<div class="specification">
<p>The photons cause the emission of electrons from the photoelectric surface. The work function of the photoelectric surface is 5.1 eV.</p>
</div>

<div class="specification">
<p>The electric potential of the photoelectric surface is 0 V. The variable voltage is adjusted so that the collecting plate is at –1.2 V.</p>
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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy of photons from the UV lamp is about 10 eV.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in J, the maximum kinetic energy of the emitted electrons.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>1</sub> = –13.6&nbsp;<strong>«</strong>eV<strong>»</strong>&nbsp;E<sub>2</sub> = –&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{13.6}}{4}">
  <mfrac>
    <mrow>
      <mn>13.6</mn>
    </mrow>
    <mn>4</mn>
  </mfrac>
</math></span> = –3.4&nbsp;<strong>«</strong>eV<strong>»</strong></p>
<p>energy of photon is difference&nbsp;<em>E</em><sub>2</sub> – <em>E</em><sub>1</sub>&nbsp;=&nbsp;10.2&nbsp;<strong>«</strong>≈ 10 eV<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Must see at least 10.2 eV.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>10 – 5.1 = 4.9 <strong>«</strong>eV<strong>»</strong></p>
<p>4.9 × 1.6 × 10<sup>–19</sup> = 7.8 × 10<sup>–19</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Allow </em>5.1 <em>if </em>10.2 <em>is used to give</em> 8.2×10<sup>−19</sup> <strong>«</strong>J<strong>»</strong>.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>EPE produced by battery</p>
<p>exceeds maximum KE of electrons / electrons don’t have enough KE</p>
<p>&nbsp;</p>
<p><em>For first mark, accept explanation in terms of electric potential energy difference of electrons between surface and plate.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4.9&nbsp;<strong>«</strong>V<strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Allow 5.1 if 10.2 is used in (b)(i).</em></p>
<p><em>Ignore sign on answer.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>two equally spaced vertical lines (judge by eye) at approximately 1/3 and 2/3</p>
<p>labelled correctly</p>
<p><img src="images/Schermafbeelding_2018-08-13_om_14.47.13.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08.c.i/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>kinetic energy at collecting plate =&nbsp;0.9&nbsp;<strong>«</strong>eV<strong>»</strong></p>
<p>speed =&nbsp;<strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{2 \times 0.9 \times 1.6 \times {{10}^{ - 19}}}}{{9.11 \times {{10}^{ - 31}}}}} ">
  <msqrt>
    <mfrac>
      <mrow>
        <mn>2</mn>
        <mo>×</mo>
        <mn>0.9</mn>
        <mo>×</mo>
        <mn>1.6</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mrow>
              <mo>−</mo>
              <mn>19</mn>
            </mrow>
          </msup>
        </mrow>
      </mrow>
      <mrow>
        <mn>9.11</mn>
        <mo>×</mo>
        <mrow>
          <msup>
            <mrow>
              <mn>10</mn>
            </mrow>
            <mrow>
              <mo>−</mo>
              <mn>31</mn>
            </mrow>
          </msup>
        </mrow>
      </mrow>
    </mfrac>
  </msqrt>
</math></span><strong>»</strong>&nbsp;= 5.6 × 10<sup>5</sup>&nbsp;<strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p>&nbsp;</p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">Monochromatic light of very low intensity is incident on a metal surface. The light causes the emission of electrons almost instantaneously. Explain how this observation</span></p>
</div>

<div class="specification">
<p><span style="background-color: #ffffff;">In an experiment to demonstrate the photoelectric effect, light of wavelength 480 nm is incident on a metal surface.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img 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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The graph shows the variation of the current<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></em> in the ammeter with the potential <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math></em> of the cathode.</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></span></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">does not support the wave nature of light.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">does support the photon nature of light.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate, in eV, the work function of the metal surface.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></em> with potential <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math></em> after this change.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">«low intensity light would» transfer energy to the electron at a low rate/slowly ✔<br>time would be required for the electron «to absorb the required energy» to escape/be emitted ✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: OWTTE</span></em></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">«in the photon theory of light» the electron interacts with a single photon ✔<br>and absorbs all the energy <em><strong>OR</strong> </em>and can leave the metal immediately ✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Reference to photon-electron collision scores MP1</span></em></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mi>λ</mi></mfrac><mo>-</mo><msub><mi>E</mi><mi mathvariant="normal">K</mi></msub></math> <span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">K</mi></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>«</mo><mi>eV</mi><mo>»</mo></math><span style="background-color: #ffffff;"> ✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>480</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup></mrow></mfrac><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>1</mn><mo> </mo><mo>«</mo><mi>eV</mi><mo>»</mo></math><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></p>
<p><span style="font-size: 14px;"><em><span style="background-color: #ffffff;"><span style="text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;">NOTE: Allow reading from the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>k</mi></msub><mo>=</mo><mn mathvariant="italic">1</mn><mo mathvariant="italic">.4</mo></math>leading to an answer of 1.2 «eV».</span></span></em></span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">similar curve lower than original ✔<br></span></p>
<p><span style="background-color: #ffffff;">with same horizontal intercept ✔</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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" width="401" height="246"></span></p>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A beam of electrons each of de Broglie wavelength 2.4 × 10<sup>–15</sup> m is incident on a thin film of silicon-30&nbsp; <span style="background-color: #ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{}_{14}^{30}{\text{Si}}} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <msubsup>
        <mrow>

        </mrow>
        <mrow>
          <mn>14</mn>
        </mrow>
        <mrow>
          <mn>30</mn>
        </mrow>
      </msubsup>
      <mrow>
        <mtext>Si</mtext>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span></span>. The variation in the electron intensity of the beam with scattering angle is shown.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate, using the result from (a)(i), the nuclear radius of thorium-232&nbsp;<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {{}_{90}^{232}{\text{Th}}} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <msubsup>
        <mrow>

        </mrow>
        <mrow>
          <mn>90</mn>
        </mrow>
        <mrow>
          <mn>232</mn>
        </mrow>
      </msubsup>
      <mrow>
        <mtext>Th</mtext>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest <strong>one</strong> reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why deviations from Rutherford scattering are observed when high-energy alpha particles are incident on nuclei.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>read off between 17 and 19 «deg» ✔</p>
<p>correct use of <em>d</em> =&nbsp;<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{{\sin \theta }}">
  <mfrac>
    <mi>λ</mi>
    <mrow>
      <mi>sin</mi>
      <mo>⁡</mo>
      <mi>θ</mi>
    </mrow>
  </mfrac>
</math></span></span> = 7.8 × 10<sup>−15</sup> «m» ✔</p>
<p>so radius = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{7.8}{2}">
  <mfrac>
    <mn>7.8</mn>
    <mn>2</mn>
  </mfrac>
</math></span> «fm» = 3.9 «fm» ✔</p>
<p><em>Award ecf for wrong angle in MP1.</em></p>
<p><em>Answer for MP3 must show at least 2&nbsp;</em><em>sf.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>R<sub>Th</sub> = R<sub>si&nbsp;</sub> <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {\frac{{{A_{{\text{Th}}}}}}{{{A_{{\text{Si}}}}}}} \right)^{\frac{1}{3}}}">
  <mrow>
    <msup>
      <mrow>
        <mo>(</mo>
        <mrow>
          <mfrac>
            <mrow>
              <mrow>
                <msub>
                  <mi>A</mi>
                  <mrow>
                    <mrow>
                      <mtext>Th</mtext>
                    </mrow>
                  </mrow>
                </msub>
              </mrow>
            </mrow>
            <mrow>
              <mrow>
                <msub>
                  <mi>A</mi>
                  <mrow>
                    <mrow>
                      <mtext>Si</mtext>
                    </mrow>
                  </mrow>
                </msub>
              </mrow>
            </mrow>
          </mfrac>
        </mrow>
        <mo>)</mo>
      </mrow>
      <mrow>
        <mfrac>
          <mn>1</mn>
          <mn>3</mn>
        </mfrac>
      </mrow>
    </msup>
  </mrow>
</math></span></span> or substitution ✔</p>
<p>7.4 «fm» ✔<br><br></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electron wavelength shorter than alpha particles (thus increased resolution)<br><em><strong>OR</strong></em><br>electron is not subject to strong nuclear force ✔</p>
<p>&nbsp;</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>nuclear forces act ✔</p>
<p>nuclear recoil occurs ✔</p>
<p>significant penetration into nucleus / probing internal structure of individual nucleons ✔</p>
<p>incident particles are relativistic ✔</p>
<div class="question_part_label">a.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was left blank by many candidates and many of those who attempted it chose an angle that when used with the correct equation gave an answer close to the given answer of 4 fm. Very few selected the correct angle, calculated the correct diameter, and divided by two to get the correct radius.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was also left blank by many candidates. Many who did answer simply used the ratio of the of the mass numbers of the two elements and failed to take the cube root of the ratio. It should be noted that the question specifically stated that candidates were expected to use the result from 2ai, and not just simply guess at the new radius.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was very poorly answered with the vast majority of candidates simply listing differences between alpha particles and electrons (electrons have less mass, electrons have less charge, etc) rather than considering why high speed electrons would be better for studying the nucleus.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates struggled with this question. The vast majority of responses were descriptions of Rutherford scattering with no connection made to the deviations when high-energy alpha particles are used. Many of the candidates who did appreciate that this was a different situation from the traditional experiment made vague comments about the alpha particles “hitting” the nucleus.</p>
<div class="question_part_label">a.iv.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A particular K meson has a quark structure <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{\bar u}}">
  <mrow>
    <mrow>
      <mrow>
        <mover>
          <mi mathvariant="normal">u</mi>
          <mo stretchy="false">¯</mo>
        </mover>
      </mrow>
    </mrow>
  </mrow>
</math></span>s. State the charge, strangeness and baryon number for this meson.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxQAAACMCAYAAADlXu8iAAAetUlEQVR4Ae3dD3BT55nv8Z/kDMm2xskwZBcJ2jCUsWkGp7R2nWnJLv6TWEt32bAmkDsE16k9wdsJlJQxqPxJ925IYA1eMhDSNMtYCzHJXgjWwLgbigmqyQ3NxLUzSWAaW5PLkF4j0VnKJcbbBnYs3TmSjn1kY5CJYiT56xmPzjl+z/s+7+c94PNY73tkC4fDYfGFAAIIIIAAAggggAACCNyEgP0mzuEUBBBAAAEEEEAAAQQQQCAicJvpYLPZzE1eEUAAAQQQQAABBBBAAIFrCgyd4DSQUBg/MJKKoQWuWQsHEUAAAQQQQAABBBBAYFwJjJQrMOVpXF0GdBYBBBBAAAEEEEAAgeQKkFAk15PaEEAAAQQQQAABBBAYVwIkFONquOksAggggAACCCCAAALJFSChSK4ntSGAAAIIIIAAAgggMK4ESCjG1XDTWQQQQAABBBBAAAEEkitAQpFcT2pDAAEEEEAAAQQQQGBcCZBQjKvhprMIIIAAAggggAACCCRXgIQiuZ7UhgACCCCAAAIIIIDAuBIgoRhXw01nEUAAAQQQQAABBBBIrgAJRXI9qQ0BBBBAAAEEEEAAgXElQEIxroabziKAAAIIIIAAAgggkFwBEorkelIbAggggAACCCCAAALjSoCEYlwNN51FAAEEEEAAAQQQQCC5AiQUyfWkNgQQQAABBBBAAAEExpUACcW4Gm46iwACCCCAAAIIIIBAcgVIKJLrSW0IIIAAAggggAACCIwrARKKcTXcdBYBBBBAAAEEEEAAgeQKkFAk15PaEEAAAQQQQAABBBAYVwIkFONquOksAggggAACCCCAAALJFciQhCKkPn+bDjZUyWmzyRb5zldVw375/L2DYqEueVxOOd0+WY4O/pwtBBBAAAEEEEAAAQQQGJVABiQUvfJ7N2pB3hb95u4n1dkfVjgcVvhys5bpDS3LW6qGzkujQqEwAggggAACCCCAAAIIJCaQ5glFSH2djapd1KIZzf+qLVVFcpg9ys7VQ3U71LJNWrNgq3y9ocREKIUAAggggAACCCCAAAIJC5i33wmfkFoFL6r9wKtqK/+x3Avv0fDO3KVvPvZPOrSrXNOsPzz/no5Ypkc5q57XMevUKEmhYKe8ljI2m0tuj0/+vlhi0uuT2+lUiXunGqryI9OsolOpjOlXRweO2ZxVaji4W+6SIVOtQkF17nWrxJyiVeKWx+dX3wDwZ/J7lshmWyKP/7OBo2wggAACCCCAAAIIIJBKAtbb7FSKK7FYej/U0aZOOeZM15QRemJ3FOjhimLlZg8WCL5yTO/NWCe/MTWqv0f7pv5S5bWN6jSThb52bV9aq8NZywemUPUH6pTVtFy1P++w3PQH1db0gSatO6lw/+/VtrxQ2ecOaVVxnU7N+3ddNur3r9Gklp3a2hYc7FPoE3mfKNcC31dVH7iicLhfl1+6VyeWLdIq7yeKpix3KLf6gMLhA6rOvWPwXLYQQAABBBBAAAEEEEghgcG77BQKKtFQQufP6v2gQ/l5TmUnepIkx1q3NlTMip5jn6rixx9Veds7+iBw1XhvQr3th7S9u1xVNd8ZmEJld/ylHq/8ltqOnVbAMnvKUfmYHpmVI9n/XLlfu6q2nZt1ZP4/afPjs6P1Z89W9Qs7tNZhBhhSb9vLWuH5up7dUKMixwRJdmXPqtQL+xboyIqX1cb0LBOLVwQQQAABBBBAAIEUF0jrhCK5tmfU3WNMOLIrp3SzAoFnVXT+LXm9Xnm9B+VxP6y8mtev32TkHZOA8ufeO5CIRE7Idiov38woLqrjaKuCjpmaPsVIJswvu7KnzVR+sFVHOy6aB3lFAAEEEEAAAQQQQCClBdI6obBPma45jqBOdQcs05CS4N13Wp6qb2hi3lK98O4fIknGXa6t6mhcLJ36WD3m1KjP01Rwi8ruzIo94jb6qNusvBq1fp46ORcBBBBAAAEEEEAAgTEWuG2M20tuczn3yVVZoK3vn9X5kJRzzfToqoKdv9JHE7+j0pmJNP+Z/AeeUc2xeWru2a6Kqea7CBfkc5+RlFAlN26ovFHdR6qVe82Yb3w6JRBAAAEEEEAAAQQQSAWBNL+dnaSiJY+puPV51R8yFzNbWXvV5fmhCha06NKXE13Y3Kee7jNS/rc0O7K+IVZf6L906cIVa+XDtyMJjnP4OyZ9AXWfMhdlT1Khq1yOU+/pdNBYs2F+GY/AfV4lPNXJBOEVAQQQQAABBBBAIA0E0jyhsCu7oEYvNRbpyKLlWre3XUFzwXSfX8caVqq0pkeP71unhQPvNNxoVGI3/K37taftXPSJS6Gg2nf8VCs8p29w8mQV/2i95jfV6zlvV3QaVl+XvM/Va6uZTxhrNIprtWv+Ca1Yv1vtkaTCeNTsIW2qe1HaVqclPNXpBs78GAEEEEAAAQQQQCBVBNI8oTAYczSr+iV1dqxU3m+fljMruh7BNnGR9ul72tf9ujaXTr3GZ1SMNATGDf9KteyZo3fKpinL+JyIaT/RW1+p0qHmtTKXVo949tSF2tG2WncfXqyJxrm5W3Sm9AltK7ecab9HFTuatW/e7+R23i6bLUsTiw/r7pX79drqotgTq/gcipGMb3zctCuU23dhxOIhv0cum03Rzw8ZqVgS6wp1yeNyyuZcf50PWqQ9YyQSGhs8JXG9jIfrRVzrXOuxX1H832j8gsjw36Uj3Y6k+HFbOBwOmzHabDZZds3DvH5eAePin1+jbvdh1ZdO/ry1cT4CCCCAAAIIIIAAAmMuMFKukAHvUIy55XUaNBZuF8pZtVdd5pOgItOltmjj1Ue0pGjSdc7lRwgggAACCCCAAAIIpJ8ACUVSx2yyip96WbvyfSqdGHskbFa5Xux/WC2vPakCy6d1J7VZKkMAAQQQQAABBBBA4BYJMOXpFsHTLAIIIIAAAggggAAC6STAlKd0Gi1iRQABBBBAAAEEEEAgTQSY8pQmA0WYCCCAAAIIIIAAAgikogAJRSqOCjEhgAACCCCAAAIIIJAmAiQUaTJQhIkAAggggAACCCCAQCoKkFCk4qgQEwIIIIAAAggggAACaSJAQpEmA0WYCCCAAAIIIIAAAgikogAJRSqOCjEhgAACCCCAAAIIIJAmAiQUaTJQhIkAAggggAACCCCAQCoKkFCk4qgQEwIIIIAAAggggAACaSJAQpEmA0WYCCCAAAIIIIAAAgikogAJRSqOCjEhgAACCCCAAAIIIJAmAiQUaTJQhIkAAggggAACCCCAQCoKkFCk4qgQEwIIIIAAAggggAACaSJAQpEmA0WYCCCAAAIIIIAAAgikogAJRSqOCjEhgAACCCCAAAIIIJAmAiQUaTJQhIkAAggggAACCCCAQCoKkFCk4qgQEwIIIIAAAggggAACaSJAQpEmA0WYCCCAAAIIIIAAAgikogAJRSqOCjEhgAACCCCAAAIIIJAmAiQUaTJQhIkAAggggAACCCCAQCoKkFCk4qgQEwIIIIAAAggggAACaSJAQpEmA0WYCCCAAAIIIIAAAgikogAJRSqOCjEhgAACCCCAAAIIIJAmAiQUaTJQhIkAAggggAACCCCAQCoKZEBCEVKfv00HG6rktNlki3w7VeLeLa/Prz6rep9fxxqe017/Z9ajbCOAAAIIIIAAAggggMBNCqR9QhE6d0irileqJWu5OvvDCoeN7y69/GCfDi9bpCc9p2NJRUi97XtUteYD9d8kFqchgAACCCCAAAIIIIBAvECaJxQX1LZzszz5P9aGVXPlGOhNjnIf+qE2PPt1vbLxNbX3huJ7zR4CCCCAAAIIIIAAAggkRWDgFjwptY11JaELOvt+YIRW71Bu9QGFA5tVmiP1+jZqVtkWBfW6avL+TE63T729PrmdxvSonWqoyo9Ml4oclxQKdsobN43KJbfHJ39fLDmJnevafUzte90qiU23clY9r2P+XktMxpSsowP125xVaji4W+4SZzQGs2QoqE5LPbYStzzWKVsJt2fE3q69bpdl+pdHvriYeuX3eSIxDE4Rs5YxYvbJM1CHTUPjCfk9ctmccnm6RLpmDiKvCCCAAAIIIIDA+BNI74TCPkOu2go5WmtU/IMGHfS2Dd7wx42lXTmlz6rr+Do5tFiN3X9SoL5UOZEyQbU1faBJ604q3P97tS0vVE5fu7YvrdVhyzSq/kCdspqWq/bnHZZ1GUG1Lm9Q88QfqMWYatXfo31Tf6ny2kZ1xhKP6JSsOp2a9++6bJTxr9Gklp3a2hYcjDD0ibxPlGuB76uqD1xRONyvyy/dqxPLFmmV9xPLDXsi7Xn1REGNfFN+qkBkCliXXso7qWXF6+U9d9VIldTX2ajaZSeV91JXdIpY/2/0dNZ+la08KL+RHfR16Oe1a3Ui71+iMYevKPD0l9RUtlEHYutP7LnVOhoO6Gj1LKX3RTQ4DGwhgAACCCCAAAII3IRA2PIlGfeX6fb1abi7dXv4+w6Fjfij3+XhtY3N4ePdn1o60x/+9Pi6sEOLw43df4oe//R4eK1DYcfa4+HBkrFyjnXh45/2W87/U7i7cXFY5Y3hbuPw9c4daOM/w8fXFoQd1c3hHmtVcedeI65Iq0PiiDvHDGvoudH2BmI0i4VjcUT6OaQfA2UGN/q7G8PlA30YPM4WAggggAACCCCAwPgVGClXyIA/LhvrJX6svYErCnT8h5qbX9W27we0tWaRyvLmqmpgUXai2ZbxbsZmBQLPquj8W/J6vfJ6D8rjflh5Na/foBK7sqfNVL7OqLunT+r9UEebAsqfe69lfYekbKfy8h2xui6q42irgo6Zmj5lgqX+WF3BVh3tuGg5bt28VnudcsyZrilxI5utaXkzFGx6Ux29t8n5je+ouPVnajz0v+W7xrs6dudsPVT8tjY2/kLtvl8MmS5lbZ9tBBBAAAEEEEAAgfEuEHfbmd4YE+Qo+J4qKpaqbu8phS9/pOa1Tr1S88zANJ2E+9d3Wp6qb2hi3lK98O4fJNl1l2urOhoXS6c+Vo+5jiLhChMoGNyisjuzYuseoo+/zcqrUWsCpw4tEtxapjsHHqFr1PVnlmTIruyCVWrpbtD9l36hTYtKlDcxK36NRHaR6lratO/+/6fmTctVlnenbLYha0iGNso+AggggAACCCCAwLgUSOuEIrowuFBu34Xhg5c9SwtrHlW53tb+t89a1iEMLxp/5DP5DzyjmmPz1NxzVr+qf0IVFRWqKJ2qT7vPxBdN5l55o7oHHntrPv7WeO1QfenkUbTkUHnjR+qPPD7XWk84tkDdGHK7snOLVVFdr1+Fw+oPdKj5b85rY9lSbTIts3NVWvGE6n8VULg/oI7mh3R+Y5mKN7XJuuR8FIFRFAEEEEAAAQQQQCADBdI6obDP/K4eLQ+o6eiH17nJfUCPPjB9FAuH+9RjJA7539Jsh2UKUui/dOnCldFdAjn3yVXp1KnugGUht7HoOaDuU+ai7EkqdJXLceo9nQ4ai6bNL2Px9PMqsS2RJ9EP4jPbO/lbBeMevXRJnQ1/K5vLE110bTYRe7U7ClSxvEqVjoDeP3thePJld6ig4nFVVRYo+P5ZnY+re0hl7CKAAAIIIIAAAgiMK4G0Tihkz9WSHVv0UNMqrWzwqnPghvyqgp1NWle7WVe31WlJ7h3Rv8pH1jcY4xvSH/v+OPzGOTL0sRv81v3a03YuWiYUVPuOn2qF5/QoL47JKv7Res1vqtdz3q5oUtHXJe9z9dpq5hOyK6e4Vrvmn9CK9bvVHumD8djWQ9pU96I0EH8iTcfaO/KPWr/jZCyp6JXfu1V1a6RtmyuUa/9Mfs8S2UrWyzvwKNle+d98U+2qUK1rhhR5JKxLbjNm48lQ/rd0tF2qri3TzPS+ahKBpAwCCCCAAAIIIIBAggJpfmtoV/asKv1b5x5VTHpXdc7bY2sQblfBzt/r20+/oZa6ImXHMOwzXXKv+1Q1eV/Wlxf9L318zY/MNm7wV6plzxy9UzZNWcZahGk/0VtfqdKh5rUyl1In6Cv71IXa0bZadx9erIlGXblbdKb0CW0rt9Rkv0cVO5q1b97v5I70IUsTiw/r7pX79drqwfgTaTPa3g7NO/+MnFnG+ok7VXx4klZ27Nbqgrsk3aHcx3eoY+UkHS421kZYyrRs0MKpE2TPXaY9HbWDMdvMeF7Wswvvibzbk9qfQxFLmmwjTIeLQUb7YIv/PJBhyEmsK9Qlj8spm3O9fCN+2CLtGUOQ0NjgKYnrZTxcL+Ja51ofze8trpf0vl6G3YekxwGb8eArM1Tj5tKyax7mNdkCxj/2+TXqdh8e5fqIZAdCfQgggAACCCCAAAIIJCYwUq6Q5u9QJNb5W1fqgnzuQjmr9qrLfDJUZPrUFm28+oiWFE26daHRMgIIIIAAAggggAACSRAgoUgC4shVTFbxUy9rV75PpcajWY3pRVnlerH/YbW89qQKsuEf2Y6fIIAAAggggAACCKSDAFOe0mGUiBEBBBBAAAEEEEAAgVsswJSnWzwANI8AAggggAACCCCAQCYKMOcmE0eVPiGAAAIIIIAAAgggMEYCJBRjBE0zCCCAAAIIIIAAAghkogAJRSaOKn1CAAEEEEAAAQQQQGCMBEgoxgiaZhBAAAEEEEAAAQQQyEQBEopMHFX6hAACCCCAAAIIIIDAGAmQUIwRNM0ggAACCCCAAAIIIJCJAiQUmTiq9AkBBBBAAAEEEEAAgTESIKEYI2iaQQABBBBAAAEEEEAgEwVIKDJxVOkTAggggAACCCCAAAJjJEBCMUbQNIMAAggggAACCCCAQCYKkFBk4qjSJwQQQAABBBBAAAEExkiAhGKMoGkGAQQQQAABBBBAAIFMFCChyMRRpU8IIIAAAggggAACCIyRAAnFGEHTDAIIIIAAAggggAACmShAQpGJo0qfEEAAAQQQQAABBBAYIwESijGCphkEEEAAAQQQQAABBDJRgIQiE0eVPiGAAAIIIIAAAgggMEYCJBRjBE0zCCCAAAIIIIAAAghkogAJRSaOKn1CAAEEEEAAAQQQQGCMBEgoxgiaZhBAAAEEEEAAAQQQyEQBEopMHFX6hAACCCCAAAIIIIDAGAmQUIwRNM0ggAACCCCAAAIIIJCJAiQUmTiq9AkBBBBAAAEEEEAAgTESSO+EItQlj8spm802/LvELY/Pr74xgsz0ZkJ+j1y2JfL4P8v0rtI/BBBAAAEEEEAAgVEIpHdCYXa0vFHd/WGFw+b3FQXqv6oTyxZplfcThcxyvCKAAAIIIIAAAggggEBSBTIjoRhGMkGOokdVVXm7PC8f18dkFMOEOIAAAggggAACCCCAQDIEMjShGKRxzJmuKQO9vKpgp1cNVfmDU6TipkaF1OtbL6fNJffuf1aV05hK9ReaWzJXTud6+XqHZCa9PrmdhXL7LkQb7PPL53GrxJyCFVe3pEh5p1y7j6l972A5Z9XzOubvHQx66FZC512Qz10o29A4I+fa5HT71Cuzf3+vBq/VwSX33nYFe/061lAlZyT+fFU9f1LBuC7/ty6efmPQz1mlhmNDp5UZxk1yl5hT0Vxye3zy95kVxeIscWu32VYk5j/K71kiG9Oqho4++wgggAACCCCAQEoLDNxqp3SUow7uqoLt+/XqhR/o0FMPKCdyfkh9nS9q6YLDynqyVf2R6VFXFHj6S2oqW62fd16ytNKqprcdWufvV3/g13pl3/9UpVr06pv/1zJ9KqTejjfVpHK5CidJfafleXKRlp34quoDVxQOm9OuirWgod2yliOo1uUNap74A7UYMfT3aN/UX6q8tlGdAzfdllAGNm/2vIEKLBuHtOaFDs3YcDIa5/Hvqv3x++Wc9ZxO/9U/qyfcr8sf1Unb/kEbD1mnjB3SmhWmX78utz2s/9z8PUv/ruqcd7UKFrypKfWdUePL/6K8E6tUvOqQzpk5hRFJ2xt6e9Ia+Q2ntloV5XxJudUHFA4fUHXuHZZY2UQAAQQQQAABBBBIZYHMSChaa5SXZV2Yfbuc96+Q58w59Vw2FxFfVPuBV9VdWaWaIoeiHZ8gR/Gjqizv0rEPzluShQJVVv2NZmXbZXd8TV+b+m0tWX3PkOlTF9VxtFWqfFCFOVJv+2vaeGyedm1+QkWOCZKMaVc/1Av7Hlf3mgYdsCxmdqx1a0PFLGUbV4bdocIHC+Roe0cfBK5e91q52fOGV1qgtU+vVkWukWpNkKPwL1XkcKj82XVaFbGxKzv3fs3L/4OOvPt/LMnQbFXvesZSZqE2PL1E3dsPqd1496b3be1c4VX+QD2Ssmer+oUdqjyyWTvbYu/kGAE5FqjqkXuVbbSfe0/UYnigHEEAAQQQQAABBBBIcYHMSCiGLcru1+XuZq3VHi0a+Mv/ZJXWdyhQX6jzvsPyer3yenfLXVaqmtY/3mCY7tI3/65C5a2/1NsfxxKU3g91tEmqdN2nHEWTi2D+tzQ7kkyY1dmVPW2m8nVG3T0jPW8qkTJmfdbXmz3PWsdot7+uubP/IpaMGefGYgi26mjHheg7NkGn5kyfbCljJBVO5eUH1HT0Q11nYtdog6E8AggggAACCCCAQAoIZEZCMQzS+Av791RT+YDU9qoOtF+UFFJf115VOe9UXtnP9O4lY/7Nn8v1kleN5dKp7oDlL/HDKpR9Zplqqz/SxsZfR9ciGNOd8h7TkqJJUuiCzr4fGH7SwJGA3j97wfIOyMAPbtHGDOVNi7w/8gW036mtZXcPrlEx1mNkfV01rcEvoC2qRAABBBBAAAEEELjVArfd6gC+uPYnaMr0mXLoTLSJkF8HVq3TsfnN6tldoalmKmUsWj4VlObcIBL7V/TgYwukZW+qY8Ns6egJ5Vc26pvZRkWTNX2OU3p/pDrMv9pfL+kY6dx0O75Yjd2vXGcdhGXaU7p1jXgRQAABBBBAAAEEhgmYt9XDfpD+B67q/NmPFXSYi6YD6j4l5c+9Vw5Lr0OXLymxW1y7cooWanVeq17d/7r+o2mqHn1gemxqzyQVusrlOPWeTget6yBC6uv5WKf0Rb4jYI5UtqblzTB3vqDXoVO3Yv2LGE9WTuGDqnR8pJOnfx//bkxfuxpKZsrl6Yo//gVFSbUIIIAAAggggAACYydgubUeu0a/+JZC6vO/ocam91S8eqGKcuxSzn1yVTrV2rRfbbGb/lDwpHas/0d5Ep2Nk32f/q5yhjzLV2h7/l/rgZnm04iMZGOpnn3ohFas3632SP3GFKsmrVy2R3nb6rTkC39y0R2a+cBfqzzYor0HfxudvtXXJe9z9dqaaP9uODCd2rppu7yRR9ya/WvR/F21Ko4YP6Af7ZqnIyt+qh3twWjyYMSw6Wmt0ZPavCQ3fm3FDdujAAIIIIAAAggggECqC2RGQjHsKU9Zmlj7rvKe2q/XVhfFniA0WcVP/Ux7in6tMuftkTn+037yjr5S9TM1ry1IcJzu0EzX/1C18USkR7+rmVY942lGLzZr37zfyR2pP0sTf/hbzdvXppY6M4YEm7nJYvbcR/RCa7W0MV8TjbULC/5NlxfV6V/LHTdZ49DTFmrbykKdeW6ubLYsTSz1KX9vs3ZU3BNLFCZoasVmte2bp/PuAmUZMUxcrMN316rjtSdVEJkeNrROc/+zJH4OhVmX5TNCzGYsryG/Ry6b+Rkdlh/EbSaxrlCXPC7n8M8Kob04AWMnobHBUxLX53i4XsS1zrUe+1+S/xuNXxAZ/rt02G/E9DhgC4fDYTNUm80my655mFeLgPGPeX7xe6r9zXZVTDUeD8sXAggggAACCCCAAAKZLzBSrmD9G3vmK3zeHobOqW2PV1dXf1/lJBOfV5PzEUAAAQQQQAABBDJAgIQioUGMTSvI+rY29Vfr5X8o5IPYEnKjEAIIIIAAAggggECmCzDlKdNHmP4hgAACCCCAAAIIIJAEAaY8JQGRKhBAAAEEEEAAAQQQQCBegClP8R7sIYAAAggggAACCCCAwCgESChGgUVRBBBAAAEEEEAAAQQQiBcgoYj3YA8BBBBAAAEEEEAAAQRGIUBCMQosiiKAAAIIIIAAAggggEC8AAlFvAd7CCCAAAIIIIAAAgggMAoBEopRYFEUAQQQQAABBBBAAAEE4gVIKOI92EMAAQQQQAABBBBAAIFRCJBQjAKLoggggAACCCCAAAIIIBAvQEIR78EeAggggAACCCCAAAIIjEKAhGIUWBRFAAEEEEAAAQQQQACBeAESingP9hBAAAEEEEAAAQQQQGAUAiQUo8CiKAIIIIAAAggggAACCMQLkFDEe7CHAAIIIIAAAggggAACoxAgoRgFFkURQAABBBBAAAEEEEAgXoCEIt6DPQQQQAABBBBAAAEEEBiFAAnFKLAoigACCCCAAAIIIIAAAvECtnA4HDYO2Wy2+J+whwACCCCAAAIIIIAAAggMEYilDwNHbzO3hv7APM4rAggggAACCCCAAAIIIDCSAFOeRpLhOAIIIIAAAggggAACCNxQgITihkQUQAABBBBAAAEEEEAAgZEE/j/nVI3N3mLklQAAAABJRU5ErkJggg=="></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Feynman diagram shows the changes that occur during beta minus (β<sup>–</sup>) decay.</p>
<p><img 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"></p>
<p>Label the diagram by inserting the <strong>four</strong> missing particle symbols <strong>and</strong> the direction of the arrows for the decay particles.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>C-14 decay is used to estimate the age of an old dead tree. The activity of C-14 in the dead tree is determined to have <strong>fallen to</strong> 21% of its original value. C-14 has a half-life of 5700 years.</p>
<p>(i) Explain why the activity of C-14 in the dead tree decreases with time.</p>
<p>(ii) Calculate, in years, the age of the dead tree. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>charge:</em> –1«e» <em><strong>or</strong></em> negative <em><strong>or</strong> K</em><sup>−</sup></p>
<p><em>strangeness:</em> –1  </p>
<p><em>baryon number:</em> 0</p>
<p>Negative signs required.<br>Award <strong>[2]</strong> for three correct answers, <strong>[1 max]</strong> for two correct answer and <strong>[0]</strong> for one correct answer.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARYAAACaCAYAAABsSGdYAAAYU0lEQVR4Ae2de2xdRX7Hh9LKVtngbBfVlgixu9rmhRJDK2KvSkigeQDKq8Qk3oKyIYEEmjabaulWQmVREorUdluS7EYLYQks3UfIOiiwoU3ibcmDLrajagkU59Ft6wSnimkrOckftftPqs+Y8Z57fO/1fZw5Z+ac30jX1/c8Zn7znTnf85vfzPx+1127du2akiQICAKCQIQI/FKEeUlWgoAgIAhoBIRYpCMIAoJA5AgIsUQOqWQoCAgCvxwVBH3nz6u9r3eo25pnqdaW2WrixLqospZ8BAFBIGIELl0aUF09PerMmXNqzeqHVUNDfaQlXBeV8fbV176nyWT50iWRCiiZCQKCgD0E9u7r0Jm3r2yLtJDIhkIw4L0LF0QqnGQmCAgCdhFobblDDQ0NRV5IZMQyPDysamtrIxdQMhQEBAH/EIiMWPyrukhcCAE9/u7usfImK1SmHE8XAl4Sy/unPlDYdMKJY4cOd4YPy+8yERgaHlJHj51Q23fu0t82VOUyRUrt5fn6LMTOcfq5rymyWaE4ARgcvKzOn78wpsh8x8ZcJAfGRaCpsVFt3rRRdXWf1J372PETqrl5ppp3110y2zcueuVdkK/PQuwcpx18TV4Si69g+yQ39rJ5c+foD29ONJgdp3YJwfjUiAnKKsSSIPi+FM3aJD4QTFd3j9rxzV2qsXGyngWMev2DL5iInMURyAyxbNn2XHEk5GxZCKCqv/jSy2XdIxcr9czTT2UChswQS1Ya1FavNcOhy5cv6+EQGozPNgBbOFWSb9g4PjQ0XEk2Tt3jNbGwjcB07nDjOIWyp8KA6cjw56QyhCIG3Ggbs66uTg0MfKKn9s06sL6+89EWkkBuXhJLbW2NhgqD4ry5SjFLxP+SokEAQmFGCHsKSfZ/RYNrvlyamiarU6c+VIeOdGqc+/ouqO6ek/ku9eqYl8QybepU3fEZ53/3te9rwGtqahTsL6l6BM6cPadJhc2kLPk2b9Lqc5YcwghA2hCL+XCevsxK9jiSeX6iLstLYmHn9OPr12k1nYeA4RAPAJqLpOoRoLPzkWQfAfrul1c/pHcZXxoYUNOmTtHY8//Euon2BbBUgpfEAha8RUfeqLNHoWlokL1Ko2DIP94gALkYW6EROvzbHPfl28sl/b6AK3IKAllFQIglqy0v9RYELCIgxGIRXMlaEMgqAkIsWW15qbcgYBEBIRaL4ErWgkBWERBiyWrLS70FAYsICLFYBFeyFgSyioAQS1ZbXuotCFhEQIjFIriStSCQVQSEWLLa8lJvQcAiAkIsFsGVrAWBrCIgxJLVlpd6CwIWERBisQiuZC0IZBUBIZastrzUWxCwiIAQi0VwJWtBIKsICLFkteWl3oKARQSEWCyCK1kLAllFQIglqy0v9RYELCIgxGIRXMlaEMgqAqkiFuIMXbo0kNW2lHqnCAH6Mf3Z15QqYiGUAfFZJAkCviNAP7YVmiMObLz10h8HOFKGICAIKPXqa99TDfX1GgqCqRG/izAl8+bOKRhzKodYUL1qa2pVQ0O9HlIMDQ/pzMjU1aBVqIzEGXJVPh87Jv2A0KoSTjXe1jNxsejPLiUCA/IhTZ06RRGJFIKhn6xZ/XDeZy+HWFC9TDRBYvWaVF//6+rx9Y+an2O+KaCxcfKY4zYPHDrcmROKsrl5ps3iMpU3gbII9bnj1C4JAB9Dy0Pib751cLQknre40jNPP6W279ylg/2NR2jLli4eDWRHHzl2/ISOSIrmEk5jbCwQCrF75941R5GRCVpt4viGM+BaHvJ8mYevjeq3IRVkQ8aW2XfoByGq/LOeDx1s86aNatXKNt3heOGgDvMCkRQtAmgp9GfCqvLMLVo4Xw0NDetA8dGWVDi3exctUHv3/Ug/94WuQnEIRsck8iipUJ/I0VhMpu2r2kYjs9HJ6FhUNpgABKbVKvPcOaPXB6+x9T9qGA1BmFU9BGpWatq0KV4bu2xhVU2+jKP50HmOHjuh8TUdLNjJqikj6/cePX5cx2kmzKqJfgi2aBFxxW+mjVEQXtj9sg5VTPnjmRbMee7Ll8ZoLGgBpoL5bjDHBi8PqjNnz2oWM4Ydc87mt5lObmpqzKk8MsepQtqso2t5gy1j6Q2PrdP2LNR2On6ht5Vr8rssz5kz5/SoIPjM8dDyoowzoUA0NU1WxEIPKxH55DCEYggmfM0YjWW8cZbJACCwuyAIavLyZUv0282ct/UdNCiHyyhUyS3bngtfKr+rRIAhs8/ToVVWv+LbsWkEE1oJkyXhFGdAeEYdDMeCI5WwPMawbI7z3JMKKRVjiMXcWOo3ahRjNITjf9sJQmMYdGlg7EI4WDQfuYQb07aMacyf9mU4BKFgKJcZo2hamVkWo4UHc2REEFfCflqMVJCDdt+7r0M/45AM9/AcFhoSV00sFErmMF5cCTXx1KkPtSpuVEgqOjDwSeyzU3HVOalyhFDsIs/L+OzZc5q0MYjyYmSIyRAprgRRmOeoUJmYSAYHB3Nmr7AL5dO2yCMSYiGjuAxNlHXvwgUaeFRx7CoAE2f5hcBP03FjsGX9gmgo9lqWlzIvxZGp2x5tw+IFGVeinQuRQ1AGTCTY2Yx2Nd49OcSCxT88ZmLBHMdLtb0EhbH1P6xOJVn2bBbuMOXM8Cgsvy0Z0pwvWgoGWtT0r/zRRqfaPo24t698UDE7hBZutG40GWPHcKnO4xGKkTWHWHhYw4mM8h0PXxf3byMX2gorAfPZVuKWKS3l8RaFoEvtRGmpd1L14KW9fOkSrYkzI2Ne4q0ts62LZMsAn0Ms1mthoQDTCBayznSWQirxNz8vRxdfkNhSGLmUk7wnlnIqK9cKAoJA+QiMZ9jNl+OYBXL5LpJjgoAgIAiUg4AQSzloybWCgCBQEgJCLCXBJBcJAoJAOQgIsZSDllwrCAgCJSEQu/H2C02/UZJg1Vz0877/qOZ2uVcQiAWBOJ4FKpLE8xA7sdiuaFyNFUvPk0JSj4Dthz6p50GGQqnvulJBQSB+BIRY4sdcShQEUo+AEEvqm1gqKAjEj4AQSwyYs5/JeNyKobhMFgG+4CzJDQQSMd5WUvX+/n71RkeHamlt1Z9K8kjqHhwV0+nZVGZ8biQlS1rLZac7u4PZ5V4s3k1a6+9avbzRWC7296ud23eo7q4u1zAcVx52h0Mq+N3AVyxuCSRFiwC7g4nYgKsBMMbbXRq0RPr76d7eHLCuXLmin4Pw8ZyLEv7hjcaSME5VFc+OVd6iaCtd3Se1tz06PscKufarqsCM3gyWxnES+ELkvmuJD7V/Sc1uaVE/eH3vaKtCKPmOj17gwD9OEwsAws43T5rkAFTVi2AIhs6PYx+cKQnBVI9rOAfIZIRgTmpySQPBhOvo+m8niQV7ypL77ldXr14dxQ/WrjS57KUfJ8UQDB9J9hDA9SOfpFNWHLs7SSxf++qTmlQeWLFCPbJureo8ckTbVyrtFK42ZthRNb58k3L0YwJ/E3EhTSnouxcXq9hixDmY/RZ2jlgwVvV0dytI5S//+hsagekzZuhvjLe+JwyKGBgZArkWSiMpUrPRppA2H3wiQyjBSIM2yrOZ59UrV2xmbyVv54jF1HLSLbl2FaaZlfKXWCAUDLeM90nYALAFyNvTtHg032O1wHVe++69+eab1enTp7Wt8cYbb9QgYXd0PTlLLK4DV458kAkaCsnVWQoILs4gWeXgV8q1DHkOvHnQOS2wFNmLXcML9Y39+7U5YEVbmyaYnc9vL3aLE+ecIxbDyv0f9zsBUBRCsDjOTC27OtwgpCcPZ7FETBlXnWwjG1ognzRpgQsWLdTE8qdP/ona/6MOvaYlOKlRrL2SPOccsWBPmTBhggaz5YutCpbG7vLslq1J4lRV2b4YRAstieehJbwmNiHCat500+dU2wO/59QDjCaYxrRg4UK1Zu0j6tU9r2jbI0MjJjS63utSM24dsT26WG/niAWQWAz0+6vaFSwNofjA0C42bjkyESCL6Vi0lqBXdkiFGaOmpkYdX4rzP/mHd9QLu7+jHl//qFPkUk59fbr2z77+dcWHZRiTPl3TtWmz2zVwckk/WgvkwswQpIIGs2nzV/QKxLQslnOtWzDEYfbk7b87rC5c+FiLh8H5wFs/1uSxfOli/c1Q4w//YIOeFmeRn6T4EDCkEl+JlZfkpMZCdSAXppvNlDPHXGfpypvBjTvbV7apV777t/pDTGyi8kEu7HUK2ob4v6lpsuwmdqPZnJTCWWJxEq2UCwVhPLHhMR3428QNzrcbW6/FOXNOG6RTDolUr0IEhFgqBC7NtzEsKjb7w1oREsMiSYJAPgSEWPKhIseKIoA2M23alJzhkbkB0jl0uFMNDw+rW26ZpJpnzVS//Vu3m9PynREEhFgy0tBRV5N1L+EEqbCZctHC+WrixInq3X/6qTr49t+r66+/XrSbMFgp/50IsSQVkiDlbRlb9ViABokE7S9MS0MqeHAza0qYwmbFMRqMDJvyN0/SzwJ7qMyq8PwSVnY0dmKxHUelMhjkrnIQYBf2rm/vVs/v+Ja6/bZmbY+BPJhJCi8GZPbIBXcF5dQvrmvT/CxESizMFgSnJeNqICknXgRo441PrFf/+M4xvaAOm4vZAxWWpK/vgl6tGz4uv9ONQGTEwuIqOpiovOnuMKZ2kMv99y0yPwt+swFT+kRBeBI/wRDWRoqMWFgGjjrcUF98qtJGJSRPNxHgRcPskLG5hKWkv2CrgaQm3zJJ3XP3PNkiEAbJ4m9IBfvK8mVLIi8lMmIZCblQozerYdwTT12Rt5V3GdJxsbvk223MVoEzZ87pTj04OKhOvPtTdfbcv+oFevmu967yDgvMZlPw5xtSwcgedbru2rVr16LOVPITBEAAjeX1fR1qw2O5zpZ4S2LQDXp1g4RefOll1dw8U7+UBEG/EYhMY/EbhnRIH8fUZTkzGbwJIQoIY8qU39QzSBAIpEIMoOAualb6MlV9acDOmD8dLexPLYRY/GmrkiQt58EvKcPARZUQF0PiCZ/5jBoY+ERrL3V1dZpU8hl0cclQbCtBQJRU/FsJnpVU3GafKCSPEEshZOR4ZAj87j13j5sXmgzkE14HM+6Nnl9g+6GPi7zCzSDEEkZEfieCALNDaDPB4ZERhPVROCJHo/nsZyeqL3z+8+pWh72nGbmz/C3EkuXWd6ju2FbyzU5AKniwYwaDaet/+ahXvf/+B+q//vt/xG2DQ+0XFsVJD3JhIeV3+hFg/ROzSBBJMB1466AmFZxNsaQB73UYfjEAM3yS5CYCQixutkvmpII0IBX2H7FaF9JgrcXZs+dU+6q2HKOuMfwODeeSUOZAc7jCMhRyuHEqFQ1H5PhHDbr1JC+Ok/AnHEzPbt2qej/q1V7gg8eD/9s2MrL6dvOmjXqH9HtdPerwkZ9om8uqlW1j7C4mmkBtTW1QRPnfIQSEWBxqjChFIchVkFhO9/6COAinMhJZcqREQktMnz49yuIrygtygUjGSzjxxtAb5dQ0pHuxv19t+uPNOuTMeDLYPo9H/jc6OnSYD2JtEQrnkbVrdbHFZnpsvwBKrbcMhUpFyqPrWr9IOFql4zEZsbu6usy/OoyE+dF55Ij+l8BYdMpCH3O9C99sBWDoFGWChCFbQs4sue/+HOyiLKeUvGgTZCBWOS8EXgR/vnWbPuZDeFXqKMRSSkt7dg0RDki9vb2jkncePjKqldBZTaLTkgiM5UNiypmNjflmkKqR3wwdj757QhFi5qH2L+mho8GnmrzLvfdrX31Sh735i2/8lfrZhx/oD+FviOH86p49BcnfFW2F+gqxlNvqHlxvhjmnP/oFgfR0d6sHHmzTsZmwp5jU/V6XIrqeISNz3NVv4xKTGSQbCYJ54aXd6vt7f6izh2B40BmaxJEgMmJpzW5pyRmSbdo8EqGMF4QPSWwsPrRSmTIyJsdmYt62ZrjT2joyREKtJvGw8BYkhKcviZ3P7D/CDebP/+3f1fx77s67e7ra+kDOGLnBEGKZd+ccHTTPPODV5l/ofqNlYu8xxvbgtbSXD0mIxYdWqkBGjH0YZRmT83AQTRKtxIzRGQ6ZTmw0nAqKSeQW9h+x7oWZo48C2pcNYf7zYr/63+H/01mf/OefqS3bnquqmGeefqqk+xmOGVuZuSH82xx38VuIxcVWiUAmM7SBVBjuGBuKIRG0mP6P+zXhmHMRFBtbFqzCZT3LoSOd6tSpD/XO6BGfQNFMQe/v6FA7n9+uLl68qEP9MlsUR4jTGZ/ax65euaKC2hEvBOwrviSxsfjSUmXKaQgEYkF9RoMxiWESY3W0FnOdOefTN9PTaC9MUbPXiKX/1a7GhVDm/s6denYIbDDmMmMUB6mAPWWiXdJmZggLqTy7ZaueJeJl4EMSYvGhlSqQkQcBoyzDIVKQQNBm6Lh8mGb2PTFD9Pj6R3U1IBdW7pabeIiTJJSgvGb90RPrN6jbZ87ScrEuCcJBc/IhyVDIh1aqUEbIhA6JhhJ8405nZ/D+/TpXH4dB+eDAqAu54J0O20vf+Qtq+dLFJUeNQHtb8WCbWrN2rcL4nWSiTdCUzAI5ZOEFwPFgOyYp43hlC7GMh5DH5+mMzPyEtRJmh5jOnHHrjMQfoqjhxc5CLKMDbx5U23fu0vuM8rliCJcbtGeEzyXxGwJBpk1+KChjIBKft2Mg8fcAS71tLpKynX+UyLOhkZ3RbGKce9ecyFfqRiFrHHjGUUY+LMTGkg8VOeY9Ahh221e26TjS2Fxe2P0d7X7B+4p5UgEhFk8aSsSsDAGmpfHlQoJcmD2SZB8BIRb7GEsJCSPALmgMu6x7YcUufl7CDqUSFjF1xYvxNmVNyphaUn4EcNTd1NSoDrz5Y0VMaYZKUbpeyF9qNo+K8Tab7Z7pWqOt7N3Xoc6fv6BtMIVCwNoGKa6XgE2DfiGMhFgKISPHU4+Aicg44YYb1Pz596hZs2amvs5xVVCIJS6kpRwnEWALwJ2f7vpGQFYrmw2AfLOehJXKSS+acxK8IkIJsRQBR05lA4Htf/O8+tbOnWrR4qXqps/9mvqV66/TPoBZjYtvFBLL6R9ZtzZnY2A20KmslkIsleEmd6UIATb5sU9o+Yo2VfOrN2j/Lto1Q0O9riUbOVnBjNaSli0QtptPiMU2wpK/Fwi8smeP9iv79uFD6p1jJ/RiOrYHJGXY9QK0IkIKsRQBR05lCwG0FjZusrvYGHanTp1S1mbGbCFWuLZCLIWxkTMZQwDXCbgqwN8tBIPj7r2vd+gd0suXLR4T3yhj8JRVXSGWsuCSi9OOgPEza4K6+bCZ0cU2EWJxsVVEpsQQwFCLZ/5v734xx1DLRkb8vDQ2TtZe6/D/IqkwAkIshbGRMxlFwIT7MFqLgcHEkybE6/JlSyKPbWTKScO3EEsaWlHqEDkCTC/n89bG0AjDbnfPSR2G5N6FC0r2Uhe5kA5nKMTicOOIaO4iQMA0NjMyJAqueXFX4nglE2KJF28pLUUIMCTCBUPSmxldhFSIxcVWEZm8QsCsecGwiysGvNdlPQmxZL0HSP0jQQDDLq4YsMG0r2rL/JoXIZZIupVkIggoTSrGgXfL7DsUjqWymoRYstryUm9rCOBX99DhTm3YbV/5oJWg9daEjyhjIZaIgJRsBIEgAsE1L2gu+NvNUhJiyVJrS11jRwDNhTUvhTYzbtn2XFkyPfP0U2Vdn9TF4qU/KeSl3EwggLby5dUPqb6+86qr+2Qm6kwlRWPJTFNLRQWB+BAQjSU+rKUkQSAzCAixZKappaKuIcDKXXy+sHOa/4OJLQMsvPM1ScAyX1tO5PYegcHLg9qR1PDwsF6te9vEkZkj7QPm031IuMf0MYnG4mOricypQKCpsXHUp25QY7k0MKDrxxoYX5MQi68tJ3KnAoGmpslj6sEQCH8vPjuTEmIZ06xyQBBIDgF2S7OYbtrUKckJEUHJQiwRgChZCAKVItBQPxK7iPshFYZHaVilK8RSaY+Q+wSBCBAwLhaYGUoLqQCLzApF0DkkC0GgWgTQUsbTVNgewDT05cuXtVPvNasfrrZYa/cLsViDVjIWBEpDgCX/aCvFEqTCrmlt1K2rUy++9LJe++KqgVeIpVhryjlBIAYExiMVRGAhHYkhE6mmpkaxDkaIRcMhfwQBQaASBAYGPlGrtNvLGjU0NKxwyxA0/FaSp817xHhrE13JWxCICAHcLrBDmnT02HHtrc4YfiMqItJsZHdzpHBKZoKAHQRY5n/oSKfq67ugjbytLXc47bRbiMVOP5BcBYFMIyBDoUw3v1ReELCDgBCLHVwlV0Eg0wgIsWS6+aXygoAdBP4fwdATOORTdIcAAAAASUVORK5CYII="></p>
<p>correct symbols for both missing quarks</p>
<p>exchange particle and electron labelled W <em><strong>or</strong></em> W<sup>–</sup> and e <em><strong>or</strong></em> e<sup>–</sup></p>
<p><em>Do not allow W<sup>+</sup> <strong>or</strong> e<sup>+</sup> <strong>or</strong> β<sup>+</sup>. Allow β <strong>or</strong> β<sup>–</sup>.</em></p>
<p>arrows for both electron and anti-neutrino correct</p>
<p><em>Allow ECF from previous marking point.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i<br>number of C-14 atoms/nuclei are decreasing<br><em><strong>OR</strong></em><br>decreasing activity proportional to number of C-14 atoms/nuclei<br><em><strong>OR</strong></em><br><em>A </em>= <em>A</em><sub>0</sub>e<sup>–<em>λt</em></sup> so <em>A</em> decreases as <em>t</em> increases<br><em>Do not allow “particles”</em><br><em>Must see reference to atoms or nuclei or an equation, just “C-14 is decreasing” is not enough.</em></p>
<p><br>ii<br>0.21 = (0.5)<em><sup>n</sup></em><br><em><strong>OR</strong></em><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.21 = {e^{ - \left( {\frac{{\ln 2 \times t}}{{5700}}} \right)}}">
  <mn>0.21</mn>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>e</mi>
      <mrow>
        <mo>−</mo>
        <mrow>
          <mo>(</mo>
          <mrow>
            <mfrac>
              <mrow>
                <mi>ln</mi>
                <mo>⁡</mo>
                <mn>2</mn>
                <mo>×</mo>
                <mi>t</mi>
              </mrow>
              <mrow>
                <mn>5700</mn>
              </mrow>
            </mfrac>
          </mrow>
          <mo>)</mo>
        </mrow>
      </mrow>
    </msup>
  </mrow>
</math></span></p>
<p><em>n </em>= 2.252 half-lives or <em>t </em>=1 2834 «y»<br><em>Early rounding to 2.25 gives 12825 y</em></p>
<p>13000 y rounded correctly to two significant figures:<br><em>Both needed; answer must be in year for MP3.</em><br><em>Allow ECF from MP2.</em><br><em>Award <strong>[3]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">In a classical model of the singly-ionized helium atom, a single electron orbits the nucleus in a circular orbit of radius <em>r</em>.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" 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" width="249" height="248"></span></p>
</div>

<div class="specification">
<p><span style="background-color: #ffffff;">The Bohr model for hydrogen can be applied to the singly-ionized helium atom. In this model the radius<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></em>, in m, of the orbit of the electron is given by<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>–</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mi>n</mi><mn>2</mn></msup></math></em>&nbsp;where <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></em> is a positive integer.</span></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the speed <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></em> of the electron with mass <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></em>, is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mrow><mi>m</mi><mi>r</mi></mrow></mfrac></msqrt></math>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Hence, deduce that the total energy of the electron is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>TOT</mi></msub><mo>=</mo><mo>-</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">In this model the electron loses energy by emitting electromagnetic waves. Describe the predicted effect of this emission on the orbital radius of the electron.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the de Broglie wavelength<em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></em> of the electron in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math> state is  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></math> m.<br></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The formula for the de Broglie wavelength of a particle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mi>h</mi><mrow><mi>m</mi><mi>v</mi></mrow></mfrac></math>.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Estimate for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math>, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>circumference</mi><mo> </mo><mi>of</mi><mo> </mo><mi>orbit</mi></mrow><mrow><mi>de</mi><mo> </mo><mi>Broglie</mi><mo> </mo><mi>wavelength</mi><mo> </mo><mi>of</mi><mo> </mo><mi>electron</mi></mrow></mfrac></math>.</span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">State your answer to one significant figure.</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The description of the electron is different in the Schrodinger theory than in the Bohr model. Compare and contrast the description of the electron according to the Bohr model and to the Schrodinger theory.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
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<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">equating centripetal to electrical force <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> to get result ✔</span></p>
<div class="question_part_label">a(i).</div>
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<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">uses (a)(i) to state <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">k</mi></msub><mo>=</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> <em><strong>OR </strong></em>states <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mo>-</mo><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> ✔</span></p>
<p><span style="background-color: #ffffff;">adds « <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>TOT</mi></msub><mo>=</mo><msub><mi>E</mi><mi mathvariant="normal">k</mi></msub><mo>+</mo><msub><mi>E</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math>» to get the result ✔</span></p>
<div class="question_part_label">a(ii).</div>
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<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">the total energy decreases<br><em><strong>OR</strong></em><br>by reference to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>TOT</mi></msub><mo>=</mo><mo>-</mo><mfrac><mrow><mi>k</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mi>r</mi></mfrac></math> ✔</span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">the radius must also decrease ✔</span></span></p>
<p><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">NOTE: <span style="background-color: #ffffff;">Award <strong>[0]</strong> for an answer concluding that radius increases</span></span></span></em></p>
<div class="question_part_label">a(iii).</div>
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<div class="question" style="padding-left: 20px;">
<p>with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn><mo>,</mo><mo> </mo><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mn>9</mn><mo>.</mo><mn>11</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo>×</mo><mn>9</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow></mfrac></msqrt><mo>=</mo><mo>»</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>44</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo> </mo><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo> </mo><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup></mrow><mrow><mn>9</mn><mo>.</mo><mn>11</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>44</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math>  <em><strong>OR  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>05</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math><span style="background-color: #ffffff;">✔</span></strong></em></p>
<div class="question_part_label">b(i).</div>
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<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mi>r</mi></mstyle><mstyle displaystyle="true"><mi>λ</mi></mstyle></mfrac><mo>=</mo><mo>«</mo><mfrac><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mo>×</mo><mn>9</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mstyle><mstyle displaystyle="true"><mn>5</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></mstyle></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>99</mn><mo>»</mo><mo>≅</mo><mn>3</mn></math> <span style="background-color: #ffffff;">✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow ECF from (b)(i)</span></em></p>
<div class="question_part_label">b(ii).</div>
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<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">reference to fixed orbits/specific radii <em><strong>OR</strong> </em>quantized angular momentum in Bohr model ✔<br></span></p>
<p><span style="background-color: #ffffff;">electron described by a wavefunction/as a wave in Schrödinger model <em><strong>OR</strong> </em>as particle in Bohr model ✔<br></span></p>
<p><span style="background-color: #ffffff;">reference to «same» energy levels in both models ✔<br></span></p>
<p><span style="background-color: #ffffff;">reference to «relationship between wavefunction and» probability «of finding an electron in a point» in Schrödinger model ✔</span></p>
<div class="question_part_label">c.</div>
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<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(iii).</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
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