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<h2>HL Paper 2</h2><div class="specification">
<p>The electrical circuit shown is used to investigate the temperature change in a wire that is wrapped around a mercury-in-glass thermometer.</p>
<p style="text-align: center;"><img 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"></p>
<p>A power supply of emf (electromotive force) 24 V and of negligible internal resistance is connected to a capacitor and to a coil of resistance wire using an arrangement of two switches. Switch S<sub>1</sub> is closed and, a few seconds later, opened. Then switch S<sub>2</sub> is closed.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The capacitance of the capacitor is 22 mF. Calculate the energy stored in the capacitor when it is fully charged.</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>The resistance of the wire is 8.0 Ω. Determine the time taken for the capacitor to discharge through the resistance wire. Assume that the capacitor is completely discharged when the potential difference across it has fallen to 0.24 V.</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>The mass of the resistance wire is 0.61 g and its observed temperature rise is 28 K. Estimate the specific heat capacity of the wire. Include an appropriate unit for your answer.</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>Suggest <strong>one</strong> other energy loss in the experiment and the effect it will have on the value for the specific heat capacity of the wire.</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>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}C{V^2} = \frac{1}{2} \times 0.22 \times {24^2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>C</mi>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>0.22</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>24</mn>
<mn>2</mn>
</msup>
</mrow>
</math></span>» = «J»</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{100}} = {e^{ - \frac{t}{{8.0 \times 0.022}}}}">
<mfrac>
<mn>1</mn>
<mrow>
<mn>100</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mfrac>
<mi>t</mi>
<mrow>
<mn>8.0</mn>
<mo>×</mo>
<mn>0.022</mn>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\ln 0.01 = - \frac{t}{{8.0 \times 0.022}}">
<mi>ln</mi>
<mo></mo>
<mn>0.01</mn>
<mo>=</mo>
<mo>−</mo>
<mfrac>
<mi>t</mi>
<mrow>
<mn>8.0</mn>
<mo>×</mo>
<mn>0.022</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.81 «s»</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>c</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{Q}{{m \times \Delta T}}">
<mfrac>
<mi>Q</mi>
<mrow>
<mi>m</mi>
<mo>×</mo>
<mi mathvariant="normal">Δ</mi>
<mi>T</mi>
</mrow>
</mfrac>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6.3}}{{0.00061 \times 28}}">
<mfrac>
<mrow>
<mn>6.3</mn>
</mrow>
<mrow>
<mn>0.00061</mn>
<mo>×</mo>
<mn>28</mn>
</mrow>
</mfrac>
</math></span></p>
<p>370 J kg<sup>–1</sup> K<sup>–1</sup></p>
<p> </p>
<p> </p>
<p><em>Allow ECF from 3(a) for energy transferred.</em></p>
<p><em>Correct answer only to include correct unit that matches answer power of ten.</em></p>
<p><em>Allow use of g and kJ in unit but must match numerical answer, eg: 0.37 J kg<sup>–1</sup> K<sup>–1</sup> receives<strong> [1]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>some thermal energy will be transferred to surroundings/along connecting wires/to<br>thermometer</p>
<p>estimate «of specific heat capacity by student» will be larger «than accepted value»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>not all energy transferred as capacitor did not fully discharge</p>
<p>so estimate «of specific heat capacity by student» will be larger «than accepted value»</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.</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="question">
<p>0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m<sup>3</sup> and a pressure of 1.4 Pa.</p>
<p>(i) State how the internal energy of an ideal gas differs from that of a real gas.</p>
<p>(ii) Determine, in kelvin, the temperature of the gas in the cylinder.</p>
<p>(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify <strong>two</strong> reasons why scientists find such models useful.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>i<br>«intermolecular» potential energy/PE of an ideal gas is zero/negligible<br><br></p>
<p>ii<br><strong>THIS IS FOR USE WITH AN ENGLISH SCRIPT ONLY</strong><br>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{PV}}{{nR}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>P</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>n</mi>
<mi>R</mi>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{1.4 \times 21}}{{0.46 \times 8.31}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.4</mn>
<mo>×</mo>
<mn>21</mn>
</mrow>
<mrow>
<mn>0.46</mn>
<mo>×</mo>
<mn>8.31</mn>
</mrow>
</mfrac>
</math></span><br><em>Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.</em><br><em>Award <strong>[2]</strong> for a bald correct answer in K.</em><br><em>Award <strong>[2 max]</strong> if correct 7.7 K seen followed by –265°C and mark BOD. However, if only –265°C seen, award <strong>[1 max]</strong>.</em><br><br>7.7K<br><em>Do not penalise use of “°K”</em><br><br></p>
<p>ii<br><strong>THIS IS FOR USE WITH A SPANISH SCRIPT ONLY</strong><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{PV}}{{nR}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>P</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>n</mi>
<mi>R</mi>
</mrow>
</mfrac>
</math></span><br><em>Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{1.4 \times 2.1 \times {{10}^{ - 6}}}}{{0.46 \times 8.31}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.4</mn>
<mo>×</mo>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.46</mn>
<mo>×</mo>
<mn>8.31</mn>
</mrow>
</mfrac>
</math></span><br><em>Uses correct unit conversion for volume</em></p>
<p>T = 7.7×10<sup>-6</sup>K<br><em>Award <strong>[2]</strong> for a bald correct answer in K. Finds solution. Allow an ECF from MP2 if unit not converted, ie candidate uses 21m3 and obtains 7.7 K</em><br><em>Do not penalise use of “°K”</em></p>
<p> </p>
<p>iii<br>«models used to»<br>predict/hypothesize / lead to further theories<br><em>Response needs to identify <strong>two</strong> different reasons. (<strong>N.B.</strong> only one in SL).</em></p>
<p>explain / help with understanding / help to visualize<br><em>Do not allow any response that is gas specific. The question is couched in general, nature of science terms and must be answered as such.</em></p>
<p>simulate<br>simplify/approximate</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>The first scientists to identify alpha particles by a direct method were Rutherford and Royds. 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 10<sup>–4</sup> mol of pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANEAAADECAYAAAABIcTHAAAZm0lEQVR4Ae1dC1RV1db+DjR8JHLVfB3EdBiBmpQPxLQaIdVBMzW5pZURhZU1rmZZwvDPHn/Zw0deu9e/USkOy7QsY5hlBiqioqahaVoKmpkP0CQfSJoUnH/MBet4gHMO+7z32sw1Buy912vP9c317bX2XGufabJarVZwYAQYAY8RCPG4JBdkBBgBgQCTiDsCI+AlAkwiLwHk4owAk4j7ACPgJQJMIi8B5OKMAJOI+wAj4CUCTCIvAeTijMAVeoHg4sWLOHr0qBDnwoULOHToEM6fP4+//voLf/zxBwoLC1FZWSnOpcxlZWX48ssv5aXbx+HDhyM8PNxWrkWLFggNDUXfvn1FXPPmzUF/vXr1suXp3LmziLNF8EmjR8AUqMXWoqIiEDmIDCdOnBBHIsGSJUuEErp164YePXrg9OnTaNasGa666iqbcqhz01/d0KZNm7pRbl3//fffIBnqhrNnz6KiosIWffz4cXFO91u1apU4J1mJbERCOlKaJFt0dLStLJ8YHwGfk+jYsWP49ddfcfjwYWzcuBGbNm3Cvn370K9fPzRp0gTt2rUTx/bt2wt0qRNecYVuBkTNGqeRk/5opDxz5owg3alTp8Rxx44duOWWWwSpbrrpJlx33XW4+uqrBdE034AzKoOA1yQi0uzevRvr16/H119/jUuXLqFDhw7o1KkTWrduLaY+9lMmZZDxUlAaUWkaSn+//fYbCKemTZtixIgRSExMRFxcHJPKS4z1UtwjElEH+eyzz/DJJ5/gyJEj6NKli3jStm3bVlfvCzk5ObBYLHrBWkwdS0tLUVJSIh46o0aNwrhx4zBw4EAmlG605L4gbpGIyDNz5kzMmDEDQ4YMAb1k06ij16A3EtXF6eTJkzh48KAg1PTp0/Hkk08ymeqCpMC1ZhLl5eVh8ODBuOeeexAVFaXEe4zeSST7B71b/fjjj4JQ8+fPR0JCgkziowIIaFon2r59O1JTU/HUU0+he/fuShBIAextIpIZnd6R7rzzTjzyyCMgSyYHdRDQNBKZTCY89thjup66qQO5a0n379+P5cuXgz/zco2TnlI1jUQkMM3dOfgXAVq3oqUBDmohoJlEtPhJ6z6OFif12mR6J1IlkNFm7dq14p1TFZlZzmoENE/naHpBuwteeeUVsQZExgU9W+aoeSoYFmir0y+//CJ2ccyZMwfDhg0DTZ95OqcORd0iETWLLElZWVlYsGCBmHqQoYFM3TRS6W3ngR5JRFM2Wici8za9/3Tt2hXPPfecWIAlAwMFJpE6BBL60rJ3zplSaRWe9pLRNIRehmnRkLb10E6Ff/zjH7U2dwYDFj2QSO5cINKcO3cOW7duRVpamlgEpi1BkZGR9aBxhne9jByhCwTcHomcSU0jFG0upb/c3FzbnjnaQ0YjFI1UciOpqvvlXLWd2i+3+fz++++gEYf2DVL7Bw0ahD59+og/LZtTmUTOkNZnvM9I5Kh51LFozk8WJ5rCbNu2TRgm5M5t2pQqPz+Qu7Yl0WR93u7UlvV4cqRRRAb7nd20q/vKK68ExdFmUwq0jtaxY0fExsaKKRqNyFoII+u3PzKJ7NHQ/7lfSdRQ8+WiIu1+pqkhfT9E0x7qpNIKKAkn6yLiUWel8Oeff4rPK2Sau0f7EZE+z5CEoHrkpw50TvliYmIE4YnU9NkGkYj+HE3H3JWjbn4mUV1E9H0dVBJ5Co0kX0PlU1JSsHjx4oayiXRPRw1NlbuZiUnkJmBBzq7ehzyAW9MkPZEjyLrm2/sJAc2LrX66P1fLCCiPAJNIeRVyA4KNgJLvRMEGzd/353cifyPs2/p5JPItnlxbI0TA0CQaMGBAI1QpNznQCBiaRIEGk+/XOBFgEjVOvXOrfYgAk8iHYHJVjRMBts7pUO9sndOhUlyIxCORC3A4iRHQgoChScTWOS1dgPN4i4ChSeQtOFyeEdCCAJNIC0qchxFwgQCTyAU4nMQIaEGArXNaUApwHrbOBRhwL2/HI5GXAHJxRsDQJGLrHHfwQCBgaBIFAkC+ByPAJOI+wAh4iQCTyEsAuTgjwNY5HfYBts7pUCkuROKRyAU4nMQIaEHA0CRi65yWLuBenqqihUgyjcbCoj/p5zNRtHA0TBH/g9yyKvcqqpe7FLkZcTAlLUSRt1XVq9suomo/FiZFwGSKQ0ZuqV2C56eGJpHnsHBJbQg0Q3Tap7AWv47EcDW6UtXBLVi2Jxmz3uiMxdk/oExbQ13mUqPlLpvAiYyAVgRKkZf5DvakJOPR5OGInfkulosRVWt5x/mYRI5xMXBsBUp2LEbGYJrSmGCKSMXsNUUoRwWOZ01AhKOpWVkuMiIcTX/qTOdEvggkzV+D7R9kYDDVbzIhIvXfWFNU+5lfVbIDWbNTESHyxCJ19krsPHGpDu51ZDUlIWNhLorK5XyvZgo4OAPzZV2O5Je1lv2A7MVAStL1aBU1CGMsO7Es/zBkbTKbu0dDk4i8UHCwR4CIMhn94j4CJubivLUS53MTsSf1n5iUVQLz7clIwZdYsvaoXceqQlnBWiyGBUlxbewrc3JegpzHZ+Pzlo/gS6sV1spj+KjTN7CMz8QO2fnLt2POA2Pw31MjkXe+ElbrZjzf7SBWfbjXrs4aWYevRccZO1BJdZ1/CzEbJiFh0goct+/5eV8jv80UFFkvoThvPOIdTi3rtCOkK24e0xc5y7bgoH1ddhJoPiUnXw0FgLwfcggUAn7Du3KfNdNitprT11nP2RpzyrouvZ8VlkxrYeUZa8GsYTXnMkN1uixTWZhpteBea2bhRavVetFamHmvFeap1nXnKq3Wc+us6WbUqb/Sem7dVKvZVqbmWpaRt7Hay2GtqctstWTus1ba8sj4ftb0daesVlmmXl32BWrOHbS9ui2yLgdlNEYZeiRi61ztZ6l4qc4BYmMiEGZLaovEGQWwZqchOqQV+oxIhiXnG+QfJOsbALspULitjDsnIQiLjEIsDqHwWDmA0yjIzkFJbBQiw+y7XxgiY7rVVFwzapREoHfXtrDPhbAIxMQWu20UqG57hJjKyXaEiCmd+3XVbX0t+eomqnhNfo4mTZpk8xxBXiFefvll2DvsUrFdgZI5JOo2jE/bh2mZW1CGms4cMxaj47VM5TRIWVWKw7uKNWSkLDsw87Z21e9uNe9XptAeGJdTorG8zPYnDuZ/g5y69dXUVbJ4LQq8MNEbikRElISEBKxevRotW7YUCNIxMzMT8fHxElFDH4uLi7Fs2TKcOXPGs3aGdMbtY4cDomOVoiB7A2JThqJPrVHDs6pFqZC26No7QmMF9yKz8KLwpE7e1O3/imckQo4oDVZWtgWZ0/JhydxX/W5lX9e5dUjHIsxYXmT3HthgjbUyGIpEe/fuFS4gyemy9GROx/bt2+Pnn38GpRsxSOKQQ+Vp06aJJkpP5PbtrZ6+AHsKi0ETq+pQY2GzLaCGIDz+bkyOycGSZZ9h1eJOGHNz19pTKlnUo2MbxCVZYN5zEMekoUHUU45jhYdqagxBeNztSDHvw+a9J2t37vLtmD04CkkL99eOdyqLNCgkY3xSt/rtCL8eSSkRXhkYlHTy5QwvckNpNptx6NAhMRI1adIEFRUVwiExOR6ma6MEGmnIO3p2djZKS0sxcuRITJ8+HRERLp7yId0wNGM8Ft82A28mxWB6YiegZBMWLd6JhFlLMTq6WTU8YddjREo3TBk3AbBkojCqJt4n4IUgPGE85g29Cw9OjEHu/6Wge1g5irLm4NWZOwBLzU3Cb8ZT825F/wkv4u3INzEp3oyQ8v3IevUFTMG/UDA6GiG47FPXuWjV72BImYnbOznSfxvEjx6LhJn0HvgAoiUGziusl2IoElHroqKi8PTTT+PAgQPCp2urVq3QuXNnrF+/vl7jVYsg4uzatQtfffWVaB8R55lnnhHOlrW1pQnMiVOxtGAZ5j7XH6G30buFBemLlmJpSrydsaEZopLuQ5o5H8fGDEKUr+crIV2Q/PbnaPnua0hs+TBKYEZC+gxMnHU38tbIljRBp+TXkddqOTIz+iE0j2TthYdm/S8Klt6Ffhqnl1VFKzFjZkdMLujrZPoXgrA+Q5FimSXeA+9xZ5pYI6qhdnGTL9eMjAzhyZva98Ybb2Dq1KmiqcuXL8eLL75oMzhIVenxaL+Lm5w7b926VRAnPz8fjz/+uHi/Iy/l/gy0R25owk6M/24Okh0+wf15d7XqNtxIpBb8jqUNCwsDLRQTeT7++GPcf//9GD16NF577TU0a+bLqZXj+6PqOPIWZaFi8ouwMIGcgHQ5mkl0GYugntGIs3v3bkGcnj17iuPAgQPxxBNPBIY4ovVkZHgIMePykZA+D+89EWc3xQsqPLq+OZMoyOrZs2cPtm/fji+++ALXXnst7rrrLrzyyivivS7wotXsyk4L/J1VvqOhSSTfh/SmIEfE+eCDD9C6dWshqsdrPHpraCORx9Ak0pMOaS1n06ZNWLJkCdq2bYukpCS8++67rk3SemoAy+IUAUOTyN465xQBPyZI4tBaDgUmjh/BDmLVhiZRMHClqdjmzZuRlZVlWwR9/vnncc011wRDHL5nABBgEvkAZO8XQX0gBFcRNASYRB5CL03Sn376KWgRlNZyHn74YTd2D3h4Yy6mOwQMTSJfW+ckcYK2CKq77sMCEQKGJpGvVGy/e2DYsGHCQBDYRVBftYTr8QcChiaRN9Y5R2s5qamptrUcfyiD61QTAUOTyF2VOCKO/SKou/Vx/saBQKMnEa/lNI6O7s9WNkoSOSJOgx+0+VMLXLfSCBiaRPbWub///lts9HzzzTdti6DufdCmtJ5ZeD8iYGgSSdw2bNiAI0eOgH4JiIkjUeGjrxBoFCSKi4vDqVOnkJycrMSXrb5SLtcTGAR8/fV8YKTWeBcycVNo0aKFxhKcjRFwHwFDk8h9OLgEI+A+Akwi9zHjEoxALQSYRLXg4AtGwH0EDE0iexO3+9BwCUZAGwKGJpE2CDgXI+AdAoYmkbTOeQcRl2YEXCNgaBK5bjqneoKAmt7D5Y/2V7u/FG42pauWei4s3UeFSeQ+ZlzChoBq3sPru2qpLH4RHR25sLS1seETJlHDGHEOAyMQYh6IcanDgYWfIFt6B3SzvYYmEVvnHPWGOh65G5P3cEdwyDhzFLp2dOR6RWZwfjQ0iZw3u7GmNGbv4Y51XlWyFZlLyjBlxUQkOPQ67ricfayhScTWOXtVA6g6hOz3soD0DDyf3B1hCEFY92FITWmKhe+tw8Gwvhg9uUv1uc0tvXSSdTviNHYys61+ACFmxN3eD+a8rdhdXEFCoGz7CswpHI0Xnr8b0cLPUDiikyfjhfR+lwUuy8d/JmQhdvrUagdflBLWC2n/fRspq1/Hf/JKL+c1D0fqPT0RhiYwR3dx8SP8n2FcTPNaPmBDI27G5IUHcOLYOVy4XKNbZ4YmkVtINILMjdl7eLV66xsWrOf34fN0YOY/n8O7O8561AuYRB7BZtxCxvQe7kJfYd1x97gxsGAV5ny6E2UusjpLYhI5Q0axePoVVnKpOXfuXAwYMAD0CbxHwYjewxsAIqRjV/Q2N5DJRbKhSWR065wkzrPPPoshQ4YIJ2HkGIy+5HXkALlxeg930ftrkqpOHMaukn5ISbreiV9X13UYmkSum65mKo0wy5YtQ1pamvBNS57S6eeLiTjk8JlGIacuKWu8h8fMnIE3c48LF/ZVNu/hz9XzHr7w8QmYEzsEN/vFe/iXeHDiYuwvJwtG2WXv4VItNd7DV5P38O0lQlbYeQ9/XXgPl5m9OJbvx4rMZchJGIvR8W08qsjQJDKKdY5+D08SZ9q0aSgvLxe/FbFy5UqMGzdO/P63U+LU6hbSe/iDqHy1P0JNJoRGzEblw0uxdLIj7+FmWPzoPfyD2FwktgyFydQd47f1EN7DL4tb4z38o1txgryH0zadlvfii3bjUbD0X5q9h1+uj87qW+dMLSdhW8xEL+oE2Ht4bZR1cUV7u3744QebG0rpFOyWW25xOE3zh9DsPVw7qo3ih0q0wxG8nPY/lh8fH49FixYJ/61B+QVW9h7uVkcw9HTOLSSClJmMA+To+NZbbxUew2+44QYcOHAAb731FgYPHhzg3/6u2e0c2h+vVqax93CNfcLQI5EK1rnmzZtj1KhRSE9PtxkEiFjBCew93BPcDU0iTwAJdBkyCMTGxgb6tnw/HyJg6OmcUaxzPtQ3V+UHBAxNIj/gxVUyAvUQYBLVg4QjGAH3EGASuYcX52YE6iFgaBKpYJ2rpxGOUA4BQ5NIOW2wwEoiYGgSsXVOyT6pnNCGJpFy2mCBlUSASaSk2lhoPSHAJNKTNlgWJREwNInYOqdkn1ROaEOTSDltsMBKImBoErF1Tsk+qZzQhiaRctpggZVEgEmkpNpYaD0hwCTSkzZYFiURMDSJ2DqnZJ9UTmhDk0g5bbDASiJgaBKxdU7JPqmc0IYmkXLaYIGVRIBJpKTaWGg9IcAk0pM2WBYlETA0idg6p2SfVE5oQ5NIOW2wwEoiYGgSsXVOyT6pnNCGJpFy2mCBlUSASaSk2lhoPSHAJNKTNlgWJREwNInYOqdkn1ROaEOTSDltsMBKIsAkUlJtLLSeEDA0idjEraeuZlxZDE0i46qNW6YnBAxHotDQUIf4HjlyBFdeeaXDNI5kBLxBwFAkIlf1+/btQ0VFRS1Mzp8/j02bNiEyMrJWPF8wAr5AwGS1Wq0NVWQymaAhW0PVBCSdvG7n5OQIz9vh4eH47bffsGbNGkycOBH33XdfQGTw9iYq4e1tW41Q3nAkIqVs3LhREOfcuXNi9LFYLOjdu7cy+mISKaMqIaghSSRVMGDAAGzbtk1eKnNkEimjKiGood6J1IKepTUKAkwio2iS2xE0BJhEQYOeb2wUBAz9TqSqkvidSC3N8Uiklr5YWh0iYGgSkXWOAyPgbwQMTSJ/g8f1MwKEAJOI+wEj4CUCTCIvAeTijABb53TYB9g6p0OluBCJRyIX4HASI6AFAUOTiK1zWroA5/EWAUOTyFtwuDwjoAUBJpEWlDgPI+ACASaRC3A4iRHQggBb57SgFOA8bJ0LMOBe3o5HIi8B5OKMgKFJxNY57uCBQMDQJAoEgHwPRoBJxH2AEfASASaRlwBycUaArXM67ANsndOhUlyIxCORC3A4iRHQgoChScTWOS1dgPN4i4ChSeQtOFyeEdCCAJNIC0qchxFwgQCTyAU4nMQIaEGArXNaUApwHrbOBRhwL2/HI5GXAHJxRuAKFSC4dOkSSktLhajk8e7aa68FOfSiuAMHDtiaIOOPHz8Oyvf0009j7ty5tvwyXhbo1asXWrZsKeo5evQo2rdvL5I6deoks/CREWgQgaCRyL5Dd+jQAd26dROdef78+bhw4YIQPDk5GX369AHl3bp1q4iLiIgAkcpVaNq0aa1kIgqFuvFNmjQR8WVlZThx4gR++ukncT1ixAhBrtWrV2PLli0ijlxVTpgwQcSTN76zZ8+iWbNmgnhMOgFRo/3n93ei77//XnTQ06dPo02bNhg6dCjI/ePKlStBhKCOePXVV0N2REqTnd5brdA6ka/8ExFxJQkPHTqEkydPCiJdvHgRw4YNE2lZWVmga2pnx44dxQPAkzbwO5EnqAWvjM9IJKdW1MEojB07VowYO3futD2xyf2jrwiiBTJfkkjL/egBQKMaubikQKMohQULFqB58+ZitJVTTpHg5B+TyAkwOo32mETUYY4dOyY6Bj2h6SncunVrdOnSBe3atQsoWXSKrU0siRVNGWnkHThwoHjA0PSxZ8+ethFOFmASSSTUOLpNIhpxsrOzsX//fgwaNEhMz9Roqr6kpOnhqlWrQNNdGrHuuOMO24OHSaQvXTUkjdskopd8mrKQIUC+IzR0k2ClB3o650k7iUw0IpFlUL4XMok8QTJ4ZTStE5Fy169fL6Sk8x49euieQMGD1L0704OIRiJJIJoWc1ALAU0komkbzes5+B+B8vJyDBkyxP834jv4DAFNJKJpEU0xVAu+Mm8Hst0VFRV44IEHAnlLvpeXCGhabB0zZgxo4ZOmHhaLxctbcnFnCOTk5OD999/Hhg0bnGXheB0ioMmwQHKTOZtW7KOjo8WTsnfv3jpsjpoibd68GbNmzRJLAy+99BIiIyPVbEgjlVoziSQ+9LR85513xCWNTomJiax0CY4bx6KiInz77beYN2+e2LkxZcoU3HTTTW7UwFn1goDbJJKC79q1C/n5+fjwww9F1EMPPSSsTLTYyk9SidLlI5Hm8OHDKCgowIoVKwRx+CF0GR+VzzwmkX2jaapHax2yg3z33XegJyvtiaPpX9euXcWua9pTZvRAewRpQXrv3r0oLi4Wu8lpqjZy5EjEx8cjLi5O7FLgB41xeoJPSFQXDmcdifI9+uijYnsQfYYQFhYmFm1phzQFIpzeA40oFE6dOiU2oZJJmghz5swZsUeuf//+SEhIEA8Q2mBL7ezcubPYO6f3trF8niHgFxI5E4V2ONN3O/Spg9yoSu8FFGQnlGVpJJOhVatW6N69u7y0HWnXhCSgLdKNE3s57IvRlib61EEGGklkkA8Be5mIKBRUeAjIdvDRdwgElETuiC2f+LIMPe3rBjkK1I3Xen3jjTc6zCpJIROZHBIJPjpCQLckciQsxzECekRA044FPQrOMjECekGASaQXTbAcyiLAJFJWdSy4XhBgEulFEyyHsggwiZRVHQuuFwSYRHrRBMuhLAL/D5HiZDTfAw6CAAAAAElFTkSuQmCC"></p>
<p>The experiment lasted for 6 days. The decay constant of radium-226 is 1.4 x 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 alpha particles combined with electrons as they moved through the wall of cylinder A to 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 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 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 cylinder B was 1.3 x 10<sup>–5</sup> m<sup>3</sup> and the volume of cylinder A was negligible. 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> </p>
<p><em>These <strong>must</strong> be seen on the right-hand 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 x 10<sup>5</sup> s</p>
<p>activity after 6 days is <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 </sub><em><strong>or</strong> </em>0.9999927 <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 <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 ≈ 1</p>
<p><em><strong>OR</strong></em></p>
<p><em>A – A</em><sub>0</sub> ≈ 10<sup>–15</sup> «s<sup>–1</sup>»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>shows half-life of the order of 10<sup>11</sup> s or 5.0 x 10<sup>10</sup> s</p>
<p>converts this to year «1600 y» or days and states half-life much longer than experiment compared to experiment</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if calculations/substitutions have numerical slips but would lead to correct deduction.</em></p>
<p><em>eg: failure to convert 6 days to seconds but correct substitution 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 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 </strong></em><br><br>use of <em>A</em> = <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> = 3.7 x 10<sup>20</sup></p>
<p><em><strong>OR</strong></em></p>
<p>initial activity = 5.2 x 10<sup>9</sup> «s<sup>–1</sup>»</p>
<p>number emitted = (6 x 24 x 3600) x 1.4 x 10<sup>–11</sup> x 3.7 x 10<sup>20</sup> <em><strong>or</strong> </em>2.7 x 10<sup>15</sup> alpha particles</p>
<p> </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> = <em>n</em> x <em>N</em><sub>A</sub> = 3.7 x 10<sup>20</sup></p>
<p>alpha particles emitted «= number of atoms disintegrated = <em>N</em> – <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 \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> <em><strong>or</strong> </em>2.7 x 10<sup>15</sup> alpha particles </p>
<p> </p>
<p><em>Must see correct substitution or 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> 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> = 2.7 x 10<sup>15</sup> x 1.3 x 10<sup>–23 </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> </p>
<p><em>Allow ECF for 2.7 x 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>A closed box of fixed volume 0.15 m<sup>3</sup> contains 3.0 mol of an ideal monatomic gas. The temperature of the gas is 290 K.</p>
</div>
<div class="specification">
<p>When the gas is supplied with 0.86 kJ of energy, its temperature increases by 23 K. The specific heat capacity of the gas is 3.1 kJ kg<sup>–1</sup> K<sup>–1</sup>.</p>
</div>
<div class="specification">
<p>A closed box of fixed volume 0.15 m<sup>3</sup> contains 3.0 mol of an ideal monatomic gas. The temperature of the gas is 290 K.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, in kJ, the total kinetic energy of the particles of the gas.</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>Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.</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><strong><em>ALTERNATIVE 1</em></strong></p>
<p>average kinetic energy = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span>1.38 × 10<sup>–23</sup> × 313 = 6.5 × 10<sup>–21</sup><strong> «</strong>J<strong>»</strong></p>
<p>number of particles = 3.0 × 6.02 × 10<sup>23</sup> = 1.8 × 10<sup>24</sup></p>
<p>total kinetic energy = 1.8 × 10<sup>24</sup> × 6.5 × 10<sup>–21</sup> = 12 <strong>«</strong>kJ<strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>ideal gas so <em>U</em> =<em> KE</em></p>
<p><em>KE</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span>8.31 × 131 × 3</p>
<p>total kinetic energy = 12 <strong>«</strong>kJ<strong>»</strong></p>
<p> </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>larger temperature implies larger (average) speed/larger (average) KE of molecules/particles/atoms</p>
<p>increased force/momentum transferred to walls (per collision) / more frequent collisions with walls</p>
<p>increased force leads to increased pressure because P = F/A (as area remains constant)</p>
<p> </p>
<p><em>Ignore any mention of PV = nRT.</em></p>
<p><strong><em>[3 marks]</em></strong></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">b.ii.</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>Liquid oxygen at its boiling point is stored in an insulated tank. Gaseous oxygen is produced from the tank when required using an electrical heater placed in the liquid.</p>
<p>The following data are available.</p>
<p style="padding-left: 60px;">Mass of 1.0 mol of oxygen = 32 g</p>
<p style="padding-left: 60px;">Specific latent heat of vaporization of oxygen = 2.1 × 10<sup>5</sup> J kg<sup>–1</sup></p>
</div>
<div class="specification">
<p>An oxygen flow rate of 0.25 mol s<sup>–1</sup> is needed.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Distinguish between the internal energy of the oxygen at the boiling point when it is in its liquid phase and when it is in its gas phase.</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 kW, the heater power required.</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>Calculate the volume of the oxygen produced in one second when it is allowed to expand to a pressure of 0.11 MPa and to reach a temperature of –13 °C.</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>State <strong>one</strong> assumption of the kinetic model of an ideal gas that does not apply to oxygen.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Internal energy is the sum of all the PEs and KEs of the molecules (of the oxygen) ✔</p>
<p>PE of molecules in gaseous state is zero ✔</p>
<p>(At boiling point) average KE of molecules in gas and liquid is the same ✔</p>
<p>gases have a higher internal energy ✔</p>
<p> </p>
<p><em>Molecules/particles/atoms must be included once, if not, award <strong>[1 max]</strong></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>flow rate of oxygen = 8 «g s<sup>−1</sup>» ✔</p>
<p>«2.1 × 10<sup>5</sup> × 8 × 10<sup>−3</sup>» = 1.7 «kW» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><em>Q</em> = «0.25 × 32 × 10<sup>−3</sup> × 2.1 × 10<sup>5</sup> =» 1680 «J» ✔</p>
<p>power = «1680 W =» 1.7 «kW» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>T </em>= 260 «K» ✔</p>
<p><em>V</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{nRT}}{p} = ">
<mfrac>
<mrow>
<mi>n</mi>
<mi>R</mi>
<mi>T</mi>
</mrow>
<mi>p</mi>
</mfrac>
<mo>=</mo>
</math></span>» 4.9 × 10<sup>−3</sup> «m<sup>3</sup>» ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ideal gas has point objects ✔</p>
<p>no intermolecular forces ✔</p>
<p>non liquefaction ✔</p>
<p>ideal gas assumes monatomic particles ✔</p>
<p>the collisions between particles are elastic ✔</p>
<p> </p>
<p><em>Allow the opposite statements if they are clearly made about oxygen eg oxygen/this can be liquified</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.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>
<br><hr><br><div class="specification">
<p>A square loop of side 5.0 cm enters a region of uniform magnetic field at <em>t</em> = 0. The loop exits the region of magnetic field at <em>t</em> = 3.5 s. The magnetic field strength is 0.94 T and is directed into the plane of the paper. The magnetic field extends over a length 65 cm. The speed of the loop is constant.</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>Show that the speed of the loop is 20 cm s<sup>−1</sup>.</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>Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Φ</mi></math> in the loop.</p>
<p><img src="data:image/png;base64,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"></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>Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.</p>
<p><img src="data:image/png;base64,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"></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>There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.</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>The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.</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>Show that the energy dissipated in the loop from <em>t </em>= 0 to <em>t </em>= 3.5 s is 0.13 J.</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>The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg<sup>−1</sup> K<sup>−1</sup>. Estimate the increase in temperature of the wire.</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><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>70</mn><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math> ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>shape as above ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>shape as above ✓</p>
<p> </p>
<p><em>Vertical lines not necessary to score.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(b)(i)</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>maximum flux at «<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo>×</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>94</mn></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>19975</mn><mo>≈</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo> </mo></math>«Wb» ✓</p>
<p>emf = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>20</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo></math>«V» ✓</p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p>emf induced in one turn = <em>BvL</em> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>94</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>0094</mn><mo> </mo></math>«V» ✓</p>
<p>emf <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0094</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo></math>«V» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mo>«</mo><mfrac><mi>V</mi><mi>R</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>4</mn></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>33</mn></math> «A» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mo>«</mo><mi>N</mi><mi>B</mi><mi>I</mi><mi>L</mi><mo>=</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>94</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>33</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>=</mo><mo>»</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>3</mn></math> «N» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>(c)(i)</strong>.</em></p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Energy is being dissipated for 0.50 s ✓</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>F</mi><mi>v</mi><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>50</mn><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>13</mn></math> J»</p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>V</mi><mi>l</mi><mi>t</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>33</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>50</mn><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>13</mn></math> J» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>(b)</strong> and <strong>(c)</strong>. </em></p>
<p><em>Watch for candidates who do not justify somehow the use of 0.5 s and just divide by 2 their answer.</em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>T</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>13</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>018</mn><mo>×</mo><mn>385</mn></mrow></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>T</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> «K» ✓</p>
<p> </p>
<p><em>Allow <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Award <strong>[1]</strong> for a <strong>POT</strong> error in <strong>MP1</strong>.</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.</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 style="background-color: #ffffff;">A container of volume 3.2 × 10<sup>-6</sup> m<sup>3</sup> is filled with helium gas at a pressure of 5.1 × 10<sup>5</sup> Pa and temperature 320 K. Assume that this sample of helium gas behaves as an ideal gas.</span></p>
<p> </p>
<p> </p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">A helium atom has a volume of 4.9 × 10<sup>-31</sup> m<sup>3</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The mass of a helium atom is 6.6 × 10<sup>-27</sup> kg. Estimate the average speed of the helium atoms in the container.</span></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><span style="background-color:#ffffff;">Show that the number of helium atoms in the container is 4 × 10<sup>20</sup>.</span></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><span style="background-color:#ffffff;">Calculate the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{volume of helium atoms}}}}{{{\text{volume of helium gas}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>volume of helium atoms</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>volume of helium gas</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Discuss, by reference to the kinetic model of an ideal gas and the answer to (c)(i), whether the assumption that helium behaves as an ideal gas is justified.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">cii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\text{1}}}{2}m{v^2} = \frac{3}{2}kT/v = \sqrt {\frac{{3kT}}{m}} /\sqrt {\frac{{3 \times 1.38 \times {{10}^{ - 23}} \times 320}}{{6.6 \times {{10}^{ - 27}}}}} ">
<mfrac>
<mrow>
<mtext>1</mtext>
</mrow>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mi>k</mi>
<mi>T</mi>
<mrow>
<mo>/</mo>
</mrow>
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>3</mn>
<mi>k</mi>
<mi>T</mi>
</mrow>
<mi>m</mi>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mn>1.38</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>23</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>320</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span> ✔</span></p>
<p><em><span style="background-color:#ffffff;">v = </span></em><span style="background-color:#ffffff;">1.4 × 10<sup>3</sup></span>«ms<sup>–1</sup>»<span style="background-color:#ffffff;"><sup> <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></sup></span></p>
<p><span style="background-color:#ffffff;"> </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = \frac{{pV}}{{kT}}/\frac{{5.1 \times {{10}^5} \times 3.2 \times {{10}^{ - 6}}}}{{1.38 \times {{10}^{ - 23}} \times 320}}">
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>p</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>k</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>5.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>3.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.38</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>23</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>320</mn>
</mrow>
</mfrac>
</math></span></span></p>
<p><span style="background-color:#ffffff;"><em><strong>OR</strong></em></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = \frac{{pV{N_A}}}{{RT}}/\frac{{5.1 \times {{10}^5} \times 3.2 \times {{10}^{ - 6}} \times 6.02 \times {{10}^{23}}}}{{8.31 \times 320}}">
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>p</mi>
<mi>V</mi>
<mrow>
<msub>
<mi>N</mi>
<mi>A</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mi>R</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>5.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>3.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>6.02</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>8.31</mn>
<mo>×</mo>
<mn>320</mn>
</mrow>
</mfrac>
</math></span> ✔</span></span></p>
<p> </p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = 3.7 \times {10^{20}}">
<mi>N</mi>
<mo>=</mo>
<mn>3.7</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mn>20</mn>
</mrow>
</msup>
</mrow>
</math></span> <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></span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="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 style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times {{10}^{20}} \times 4.9 \times {{10}^{ - 31}}}}{{3.2 \times {{10}^{ - 6}}}} = ">
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>20</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>4.9</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>31</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>3.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>»<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6 \times {10^{ - 5}}">
<mn>6</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</math></span> ✔</span></p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="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 style="background-color:#ffffff;">«For an ideal gas» the size of the particles is small compared to the distance between them/size of the container/gas</span></p>
<p style="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 style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="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 style="background-color:#ffffff;">«For an ideal gas» the volume of the particles is negligible/the volume of the particles is small compared to the volume of the container/gas<br></span></p>
<p style="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 style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="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 style="background-color:#ffffff;">«For an ideal gas» particles are assumed to be point objects ✔</span></p>
<p style="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 style="background-color:#ffffff;">calculation/ratio/result in (c)(i) shows that volume of helium atoms is negligible compared to/much smaller than volume of helium gas/container «hence assumption is justified» ✔</span></p>
<div class="question_part_label">cii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>At HL this was very well answered but at SL many just worked out E=3/2kT and left it as a value for KE.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Again at HL this was very well answered with the most common approach being to calculate the number of moles and then multiply by N<sub>A</sub> to calculate the number of atoms. At SL many candidates calculated n but stopped there. Also at SL there was some evidence of candidates working backwards and magically producing a value for ‘n’ that gave a result very close to that required after multiplying by N<sub>A</sub>.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was well answered with the most common mistake being to use the volume of a single atom rather than the total volume of the atoms.</p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>At HL candidates seemed more able to focus on the key part feature of the question, which was the nature of the volumes involved. Examiners were looking for an assumption of the kinetic theory related to the volume of the atoms/gas and then a link to the ratio calculated in ci). The command terms were slightly different at SL and HL, giving slightly more guidance at SL.</p>
<div class="question_part_label">cii.</div>
</div>
<br><hr><br><div class="specification">
<p>An ideal monatomic gas is kept in a container of volume 2.1 × 10<sup>–4</sup> m<sup>3</sup>, temperature 310 K and pressure 5.3 × 10<sup>5</sup> Pa.</p>
</div>
<div class="specification">
<p>The volume of the gas in (a) is increased to 6.8 × 10<sup>–4</sup> m<sup>3</sup> at constant temperature.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by an ideal gas.</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>Calculate the number of atoms in the gas.</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>Calculate, in J, the internal energy of the gas.</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>Calculate, in Pa, the new pressure of the gas.</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>Explain, in terms of molecular motion, this change in pressure.</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>a gas in which there are no intermolecular forces</p>
<p><strong><em>OR</em></strong></p>
<p>a gas that obeys the ideal gas law/all gas laws at all pressures, volumes and temperatures</p>
<p><strong><em>OR</em></strong></p>
<p>molecules have zero PE/only KE</p>
<p> </p>
<p><em>Accept atoms/particles.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>N</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{pV}}{{kT}} = \frac{{5.3 \times {{10}^5} \times 2.1 \times {{10}^{ - 4}}}}{{1.38 \times {{10}^{ - 23}} \times 310}}">
<mfrac>
<mrow>
<mi>p</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>k</mi>
<mi>T</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>5.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.38</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>23</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>310</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong> 2.6 × 10<sup>22</sup></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>For one atom <em>U</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span><em>kT</em><strong>»</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span> × 1.38 × 10<sup>–23</sup> × 310 / 6.4 × 10<sup>–21</sup> <strong>«</strong>J<strong>»</strong></p>
<p><em>U = </em><strong>«</strong>2.6 × 10<sup>22</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span> × 1.38 × 10<sup>–23</sup> × 310<strong>»</strong> 170 <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p> <em>Allow ECF from (a)(ii)</em></p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow use of U</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span><em>pV</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>p</em><sub>2</sub> = <strong>«</strong>5.3 × 10<sup>5</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.1 \times {{10}^{ - 4}}}}{{6.8 \times {{10}^{ - 4}}}}">
<mfrac>
<mrow>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong> 1.6 × 10<sup>5</sup> <strong>«</strong>Pa<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>volume has increased and<strong>» </strong>average velocity/KE remains unchanged</p>
<p><strong>«</strong>so<strong>» </strong>molecules collide with the walls less frequently/longer time between collisions with the walls</p>
<p><strong>«</strong>hence<strong>» </strong>rate of change of momentum at wall has decreased</p>
<p><strong>«</strong>and so pressure has decreased<strong>»</strong></p>
<p> </p>
<p><em>The idea of average must be included</em></p>
<p><em>Decrease in number of collisions is not sufficient for MP2. Time must be included.</em></p>
<p><em>Accept atoms/particles.</em></p>
<p><strong><em>[2 marks]</em></strong></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">a.iii.</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>Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.</p>
</div>
<div class="specification">
<p>The molar mass of nitrogen is 28 g mol<sup>−1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the intensity of the solar radiation at the location of Titan is 16 W m<sup>−2</sup>.</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>Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the <strong>average </strong>intensity of solar radiation <strong>absorbed</strong> by the whole surface of Titan is 3.1 W m<sup>−2</sup>.</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>Show that the equilibrium surface temperature of Titan is about 90 K.</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>The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km s<sup>−1</sup>. Show that the escape speed from Titan is 2.8 km s<sup>−1</sup>.</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 orbital radius of Titan around Saturn is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and the period of revolution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>T</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mi>R</mi><mrow><mo> </mo><mn>3</mn></mrow></msup></mrow><mrow><mi>G</mi><mi>M</mi></mrow></mfrac></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is the mass of Saturn.</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>The orbital radius of Titan around Saturn is 1.2 × 10<sup>9 </sup>m and the orbital period is 15.9 days. Estimate the mass of Saturn.</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>Show that the mass of a nitrogen molecule is 4.7 × 10<sup>−26</sup> kg.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of 90 K.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>incident intensity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1360</mn><mrow><mn>9</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn><mo>≈</mo><mn>16</mn></math> «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow the use of 1400 for the solar constant.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>exposed surface is ¼ of the total surface ✓</p>
<p>absorbed intensity = (1−0.22) × incident intensity ✓</p>
<p>0.78 × 0.25 × 15.7 <em><strong>OR </strong> </em>3.07 «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow 3.06 from rounding and 3.12 if they use 16</em> W m<sup>−2</sup>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>σT </em><sup>4</sup> = 3.07</p>
<p><em><strong>OR</strong></em></p>
<p><em>T</em> = 86 «K» ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>2</mn><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mo>»</mo><msqrt><mfrac><mrow><mn>0</mn><mo>.</mo><mn>025</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>404</mn></mrow></mfrac></msqrt><mo>×</mo><mn>11</mn><mo>.</mo><mn>2</mn></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>79</mn></math> «km s<sup>−1</sup>» ✓</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equating of gravitational force / acceleration to centripetal force / acceleration ✓</p>
<p>correct rearrangement to reach the expression given ✓</p>
<p> </p>
<p><em>Allow use of <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>T</mi></mfrac></math> for <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></math> «s» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mn>3</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mfenced><mrow><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mo> </mo></math>«kg» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mn>28</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>65</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>26</mn></mrow></msup></math> «kg» ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>k</mi><mi>T</mi><mo>⇒</mo><mo>»</mo><mi>v</mi><mo>=</mo><msqrt><mfrac><mrow><mn>3</mn><mi>k</mi><mi>T</mi></mrow><mi>m</mi></mfrac></msqrt></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>«</mo><msqrt><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>90</mn></mrow><mrow><mn>4</mn><mo>.</mo><mn>651</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>26</mn></mrow></msup></mrow></mfrac></msqrt><mo>=</mo><mo>»</mo><mn>283</mn><mo>≈</mo><mn>300</mn></math> «ms<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow 282 from a rounded mass.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>no, molecular speeds much less than escape speed ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from incorrect <strong>(d)(ii)</strong>.</em></p>
<div class="question_part_label">e.</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.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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).</p>
<p>The following data are available for binding energies per nucleon:</p>
<p style="padding-left: 30px;">plutonium 7.568 MeV</p>
<p style="padding-left: 30px;">uranium 7.600 MeV</p>
<p style="padding-left: 30px;">alpha particle 7.074 MeV</p>
</div>
<div class="specification">
<p>The energy in b(i) can be transferred into electrical energy to run the instruments of a spacecraft. A spacecraft carries 33 kg of pure plutonium-238 at launch. The decay constant of plutonium is 2.50 × 10<sup>−10</sup> s<sup>−1</sup>.</p>
</div>
<div class="specification">
<p>Solar radiation falls onto a metallic surface carried by the spacecraft causing the emission of photoelectrons. The radiation has passed through a filter so it is 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 style="background-color: #ffffff;">Three identical light bulbs, X, Y and Z, each of resistance 4.0 Ω are connected to a cell of emf 12 V. The cell has negligible internal resistance.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">When fully charged the space between the plates of the capacitor is filled with a dielectric with double the permittivity of a vacuum.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch S is initially open. Calculate the total power dissipated in the circuit.</span></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><span style="background-color:#ffffff;">The switch is now closed. State, without calculation, why the current in the cell will increase.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch is now closed. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Deduce the ratio }}\frac{{{\text{power dissipated in Y with S open}}}}{{{\text{power dissipated in Y with S closed}}}}">
<mrow>
<mtext>Deduce the ratio </mtext>
</mrow>
<mfrac>
<mrow>
<mrow>
<mtext>power dissipated in Y with S open</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>power dissipated in Y with S closed</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>.</span></p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.</span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Calculate the energy stored in the capacitor.</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the change in the energy stored in the capacitor.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Suggest, in terms of conservation of energy, the cause for the above change.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">dii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="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 style="background-color:#ffffff;">total resistance of circuit is 8.0 «Ω» ✔</span></p>
<p style="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 style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = \frac{{{{12}^2}}}{{8.0}} = 18">
<mi>P</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>8.0</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>18</mn>
</math></span>«W» <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></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="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 style="background-color:#ffffff;">«a resistor is now connected in parallel» reducing the total resistance<br></span></p>
<p style="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 style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="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 style="background-color:#ffffff;">current through YZ unchanged and additional current flows through X ✔</span></p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="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 style="background-color:#ffffff;">evidence in calculation or statement that pd across Y/current in Y is the same as before ✔<br></span></p>
<p style="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 style="background-color:#ffffff;">so ratio is 1 ✔</span></p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="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 style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = «\frac{1}{2}C{V^2} = \frac{1}{2} \times 6 \times {10^{ - 6}} \times {12^2} =» 4.3 \times {10^{ - 4}}">
<mi>E</mi>
<mo>=</mo>
<mrow>
<mo>«</mo>
</mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>C</mi>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>6</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>12</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<mo>»</mo>
</mrow>
<mn>4.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</math></span>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{J}}">
<mrow>
<mtext>J</mtext>
</mrow>
</math></span>» ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="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;"><em><strong><span style="background-color:#ffffff;">ALTERNATIVE 1</span></strong></em></p>
<p style="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 style="background-color:#ffffff;">capacitance doubles and voltage halves ✔<br></span></p>
<p style="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 style="background-color:#ffffff;">since <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{1}{2}C{V^2}">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>C</mi>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> energy halves <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 style="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;">so change is «–»2.2×10<sup>–4 </sup>«J» <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></p>
<p style="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 style="background-color:#ffffff;"> </span></p>
<p style="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 style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br></span></p>
<p style="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 style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{1}{2}C{V^2}{\text{ and }}Q = CV{\text{ so }}E = \frac{{{Q^2}}}{{2C}}">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>C</mi>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext> and </mtext>
</mrow>
<mi>Q</mi>
<mo>=</mo>
<mi>C</mi>
<mi>V</mi>
<mrow>
<mtext> so </mtext>
</mrow>
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>Q</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>C</mi>
</mrow>
</mfrac>
</math></span> <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><span style="background-color:#ffffff;"><br></span></p>
<p style="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 style="background-color:#ffffff;">capacitance doubles and charge unchanged so energy halves ✔<br></span></p>
<p style="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 style="background-color:#ffffff;">so change is <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 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 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>2.2 <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> 10<sup><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>4 </sup>«<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;">J</span>» ✔</span></p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="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 style="background-color:#ffffff;">it is the work done when inserting the dielectric into the capacitor ✔<br></span></p>
<div class="question_part_label">dii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates scored both marks. ECF was awarded for those who didn’t calculate the new resistance correctly. Candidates showing clearly that they were attempting to calculate the new total resistance helped examiners to award ECF marks.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most recognised that this decreased the total resistance of the circuit. Answers scoring via the second alternative were rare as the statements were often far too vague.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few gained any credit for this at both levels. Most performed complicated calculations involving the total circuit and using 12V – they had not realised that the question refers to Y only.</p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most answered this correctly.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>By far the most common answer involved doubling the capacitance without considering the change in p.d. Almost all candidates who did this calculated a change in energy that scored 1 mark.</p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few scored on this question.</p>
<div class="question_part_label">dii.</div>
</div>
<br><hr><br><div class="specification">
<p>Potassium-40 <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> decays by two processes.</p>
<p>The first process is that of beta-minus (β<sup>−</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 % 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 rock sample contains 340 µmol of potassium-40 and 12 µmol 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>The diagram shows the gravitational field lines of planet X.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how this diagram shows that the gravitational field strength of planet X decreases with distance from the surface.</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>The diagram shows part of the surface of planet X. The gravitational potential at the surface of planet X is –3<em>V</em> and the gravitational potential at point Y is –<em>V</em>.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxQAAAGcCAYAAABA/+YNAAAgAElEQVR4Ae3dDXRV1Z338d8NjBaHIgvlGRNhVV08Ce3CGgQc+4BLRAvjjC6YWNtnHCEWfJvhpcWHgFXBxhcqL0tHwdaWlxJ0bNUhCx6flgI2xSk4lkLB6pqSLMuSIRLWEimlEayjuc/alwRPTk6Sm5tz9r37nO9dS3PPvfvs/d+fvXNz/5yzz0ml0+m0eCCAAAIIIIAAAggggAACOQgU5bAPuyCAAAIIIIAAAggggAACGYG+XodUKuXd5DkCCCCAAAIIIIAAAggg0EHAe5JTu4TCvGGSCm+BDnvzAgIIIIAAAggggAACCCRSIChX4JSnRE4FOo0AAggggAACCCCAQDgCJBThOFILAggggAACCCCAAAKJFCChSOSw02kEEEAAAQQQQAABBMIRIKEIx5FaEEAAAQQQQAABBBBIpAAJRSKHnU4jgAACCCCAAAIIIBCOAAlFOI7UggACCCCAAAIIIIBAIgVIKBI57HQaAQQQQAABBBBAAIFwBEgownGkFgQQQAABBBBAAAEEEilAQpHIYafTCCCAAAIIIIAAAgiEI0BCEY4jtSCAAAIIIIAAAgggkEgBEopEDjudRgABBBBAAAEEEEAgHAESinAcqQUBBBBAAAEEEEAAgUQKkFAkctjpNAIIIIAAAggggAAC4QiQUITjSC0IIIAAAggggAACCCRSgIQikcNOpxFAAAEEEEAAAQQQCEeAhCIcR2pBAAEEEEAAAQQQQCCRAiQUiRx2Oo0AAggggAACCCCAQDgCJBThOFILAggggAACCCCAAAKJFCChSOSw02kEEEAAAQQQQAABBMIRIKEIx5FaEEAAAQQQQAABBBBIpAAJRSKHnU4jgAACCCCAAAIIIBCOAAlFOI7UggACCCCAAAIIIIBAIgVIKBI57HQaAQQQQAABBBBAAIFwBEgownGkFgQQQAABBBBAAAEEEilAQpHIYafTCCCAAAIIIIAAAgiEI9A3nGqopTuBBx98MFOkurpabc/NC/7toHr8Zfzb7BMk0NEWt44mQXJ+J/82+wQJdLTFraNJkJzfyb/NPkECHW1xy87E79TdttHvroz//ULfxz+j/PH7t/3ls+mfzX388QZtB8XDayELpH0PSb5X2AxDYNGiRWFUY6UOYo2OGdtobF1yNQIuxUus0cxZ5gGurs0B1+J16bMrut+GaGoOyhU45SnkBI3qEEAAAQQQQAABBBBIkkDK5C7eDqdSKXOIwvsSz0MQMKc5mcNwPBBAAAEEEEAAAQQQcFUgKFfgCIWroxlh3N41HhE2E0rVLsVqOuxSvMQayhQNrATbQJZev+iSq+msS/ESa6+nZ2AFLrkyZwOHkBdbBUgomAoIIIAAAggggAACCCCQswAJRc507IgAAggggAACCCCAAAKsoWAOIIAAAggggAACCCCAQFYCrKHIiimaQi6dJ0ms0cwBUyu20di65Mo8iGYOuObqWrwu/Y4RK79jrv1+RTdi9mrmlCd71rSEAAIIIIAAAggggEDsBEgoYjekdAgBBBBAAAEEEEAAAXsCJBSWrLkHhSVomkEAAQQQQACBxAvwvcvuFCChsOTt0jmdlkhoBgEEEEAAAQQQiESA712RsHZaKQlFpzS8gQACCCCAAAIIIIAAAt0JkFB0J8T7CCCAAAIIIIAAAggg0KkACUWnNLyBAAIIIIAAAggggAAC3QmQUHQnxPsIIIAAAggggAACCCDQqQAJRac0vIEAAggggAACCCCAAALdCZBQdCfE+wgggAACCCCAAAIIINCpAAlFpzS8gQACCCCAAAIIIIAAAt0JpNLpdNpbKJVKyfeS922eI4AAAggggAACCCCAQEIFgnIFjlBYmgwu3WCFWKObFNhGY+uSqxFwKV5ijWbOMg9wdW0OuBavS59d0f022KuZhMKeNS0hgAACCCCAAAIIIBA7ARKK2A0pHUIAAQQQQAABBBBAwJ4AayjsWdMSAggggAACCCCAAAJOC7CGIo/D59K5fMQa3UTBNhpbl1yNgEvxEms0c5Z5gKtrc8C1eF367Irut8FezZzyZM+alhBAAAEEEEAAAQQQiJ0ACUXshpQOIYAAAggggAACCCBgT4CEwp41LSGAAAIIIIAAAgggEDsBFmVbGlJzLl91dbWl1mgGAQQQQAABBBBIrgDfu6IbexZlR2cbq5pdWsjkUqxmkrgUL7FG92uNbTS2LrnyeRDNHMA1OlfXbKOVoHa/AKc8+UXYRgABBBBAAAEEEEAAgawFSCiypqIgAggggAACCCCAAAII+AVYQ+EXYRsBBBBAAAEEEEAAAQQCBVhDEchi50WXzu0l1ujmBLbR2LrkagRcipdYo5mzzANcXZsDrsXr0mdXdL8N9mrmlCd71rSEAAIIIIAAAggggEDsBEgoYjekdAgBBBBAAAEEEEAAAXsCJBSWrLkHhSVomkEAAQQQQACBxAvwvcvuFCChsOTNuXyWoGkGAQQQQAABBBIvwPcuu1OAhMKuN60hgAACCCCAAAIIIBArARKKWA0nnUEAAQQQQAABBBBAwK4ACYVdb1pDAAEEEEAAAQQQQCBWAiQUsRpOOoMAAggggAACCCCAgF0BEgq73rSGAAIIIIAAAggggECsBFLpdDrt7VHQ7bS97/M8N4HeXG3AXPrMu79/Oygifxn/NvsECUh+J/920F7+Mv5t9gkSwNqo+OeKfztIzl/Gv80+QQJYJ3G+Bf1u+F/rbjsbN38dhb6P/zfEH79/218+m/7lcx9v26YvPMIXCMwVTELhfUjybvI8JIFFixaFVFP01RBrdMbYRmPrkqsRcCleYo1mzjIPcHVtDrgWr0ufXdH9NkRTc1CuwBGK8BM3akQAAQQQQAABBBBAIJYCQUcoWENhaai9pyxZajLnZog1Z7pud8S2W6KcCrjkajroUrzEmtOUzGonbLNi6nEhXHtMlvUO2GZNlbiCJBSJG3I6jAACCCCAAAIIIIBAeAIkFOFZUhMCCCCAAAIIIIAAAokTYA1F4oacDiOAAAIIIIAAAgggkJsAayhycwtlL847DIWxQyUuuZrgXYqXWDtMt9BewDY0ynYVueRqAncpXmJtN9VC23DJlTkb2rDHsiJOeYrlsNIpBBBAAAEEEEAAAQTsCJBQ2HGmFQQQQAABBBBAAAEEYilAQhHLYaVTCCCAAAIIIIAAAgjYEWBRth3nzLmy3ALeEjbNIIAAAggggECiBcz6FL53RTMFWJQdjWvsanVpkZhLsZqJ4lK8xBrdrza20di65MrnQTRzANfoXF2zjVaC2v0CnPLkF2EbAQQQQAABBBBAAAEEshYgociaioIIIIAAAggggAACCCDgFyCh8ItEtM15fBHBUi0CCCCAAAIIIOAT4HuXDyTiTRKKiIHbqnft3N62uPmJAAIIIIAAAgi4JsD3LrsjRkJh15vWEEAAAQQQQAABBBCIlQAJRayGk84ggAACCCCAAAIIIGBXgITCkjfn8lmCphkEEEAAAQQQSLwA37vsTgESCkvenMtnCZpmEEAAAQQQQCDxAnzvsjsFSCjsetMaAggggAACCCCAAAKxEiChiNVw0hkEEEAAAQQQQAABBOwKkFDY9aY1BBBAoLAFmhu0bXmlSlIppVIpPbHxdW1rOOGL+ajqFoxWatJaNbT43mrbPFGnBSUlmrR2vzor0laUnwgggAACbguQULg9fkSPAAIIhCfQclC137hFi9+brO1/+kTp9B81bfhJLS67Rcv3HPe0019Dyi6R3nxbjc1B6cJx7fnB41paVqXFXy0Vf2g8dDxFAAEEYijA53wMB5UuIYAAAj0XaNGJ7d/XrM0TtfD+KSrtb/48DNB5ZV/U1Im/0eMv/kafHqc4SxdcNEzFTW/rnSMfdWiq5d06fffxg5o+u0IjM/V0KMILCCCAAAIxEugbo77QFQQQQACBnAWKNGDCYh0+nE0FReo/ZJgu1VbVNzZLpZ/x7HRU259arLWXzlX9lM9xdMIjw1MEEEAgrgIkFHEdWfqFAAII9FagpUnv/mqHVr1ZoZVrx2mAp76iCy5SefFh7XvnqFp0fmvi0KLmPc/q4aUXaNnuCpVyDNwjxlMEEEAgvgKpdDqd9nbPLMLzveR9m+cIIIAAArEX+FANa6epbMZLkkZo2uPP6LFvjFWxN0Fo2a+110/QA+XPaf+SCaeTDbMG444bNEvV+vWqCl3oLR97MzqIAAIIJEMgKFfg497S2Lt0gxVijW5SYBuNrUuuRqDw4/2MSqe/mPnHpYX3lOvC/3uzRt1Rq3e966+LLtK4r41T0753dCTzeusajLWf1yML/jYvyUThu7af/y7FS6ztxy6sLZdc3fjs+nRkXLP9NHI3n5FQuDluRI0AAghkIfCxmmrvzlz+1fyLUqf/DVuuPR8HV5fqf7HuXXibtPbH2vL2h55CrQuzt/5MO8zrzbv1g4dfVNmyefpquzUVnl14igACCCAQSwHWUMRyWOkUAgggYAT6qrjiGaXTz4TAccC3ANu7MPt9vfvWej1e/zda+Vy5+ofQGlUggAACCLgjwBoKd8aKSBFAAIEIBVrXTTwwTD/f/4gmDGg7gN2iE3UPaPit0nPtXpdkbl43fL60cqEGr3hYv5u9QasquLJThINE1QgggEDeBVhDkcchcOlcPmKNbqJgG42tS65GoDDj/YxKvzpPy8q2qubf/lPNrUO16P9U6rGHt+rLj9yiK84kGa1v9i9R2aXHtWPFUj2uf9Q/Txya18vEFqZr53PepXiJtfNx7M07LrmafroUr0ux9mYOFcq+bf8EVSjxEAcCCCCAQL4E+l+he57/viYfW6bS1jUXD284oGELn9fT00d0PJWp6HxdVD5Qr23/s6YunKpR3MQuXyNHuwgggEBeBUgo8spP4wgggEBhCRQVj1LFvBodTqczV3laVHmdpk8o7ZhMZMI+XxOW7FY6vVtLJpxfWB0hGgQQQAABawIkFNaoaQgBBBBAAAEEEEAAgfgJkFDEb0zpEQIIIIAAAggggAAC1gRIKKxR0xACCCCAAAIIIIAAAvETIKGI35jSIwQQQAABBBBAAAEErAmQUFijpiEEEEAAAQQQQAABBOInQEJhaUyrq6sttUQzCCCAAAIIIIBAsgX43mV3/PvabS65rZkbrDC5kzv+9BwBVwUOHTqk2traDuGPGDHizGtDhw5Vv379zmzzBAEEEMi3AN+77I5AKp1Op71NBt1O2/s+z3MT6M0dG00i4t3fvx0Ukb+Mf5t9ggSUSfqwZr75f1/820Gzx1/Gv+3qPm+88Ybee+89jR07Vjt37sx049SpU9q7d2+HLk2ePDlTdvDgwTr77LP18MMPq6amRn37dv5vV34n/3aHRsTvqTHxO/m3cetolI1bkKP/te62C70d/9zIpj8u7eON1fSNR/gCgbmCSSi8D8ncy4hH2AKLFi0Ku8rI6iPWyGjT2EZj65KrEXAp3u5iPXnyZLq+vj7z34YNG9Lmv6qqqvTkyZPNP1Zl/hszZkz60Ucfzbxnykb16C7WqNrNtV6X4iXWXEe56/1ccjU9cSlel2LtepYU3rtBuULn/2wUfkKT6BrJkhM9/HQegdgKmFOdSktLM/1r+1lRUXGmvw0NDXrnnXdkfm7evFk33XRT5r2qqipdeeWVMqdOte13ZieeIIAAAr0U4HtXLwF7uDuLsnsIlmtx72k0udbBfggggIBrAiZZmDhxombNmqVVq1bp5MmTmdOlTCKxfv16lZWV6YorrtDKlSu1b98+17pHvAggUKACfO+yOzAcobDrTWsIIIBAogXMEY3y8vLMf9OmTdOxY8e0e/fuzH8jR47UmDFjZF4fN25cpkyiseg8Aggg4IgARygcGSjCRAABBOIoMGjQoMwRjPvuuy9z9OKJJ57Qf/3Xf8kkF+bIhTmKYZIOHggggAAChStAQlG4Y0NkCCCAQKIEzNELczWppUuX6v3339e9996buWTteeedp/nz53NKVKJmA51FAAGXBEgoXBotYkUAAQQSImCOXJjF3Rs3bjxziVpz1GLKlClnLl+bEAq6iQACCBS8AAlFwQ8RASKAAALJFjBrLtqOWlx33XWZ9RUkFsmeE/QeAQQKS4CEorDGg2gQQAABBDoRMEctzNWizOlQZuH23LlzOWLRiRUvI4AAAjYFSChsatMWAggggECvBdpOh3r11VflPWJx5MiRXtdNBQgggAACPRdImfvveXcLvJ22twDPEUAAAQQQKCABcxWo559/XrNnz5a5Yd6cOXM0ZMiQAoqQUBBAAIH4CATlChyhsDS+Lt1ghVijmxTYRmPrkqsRcCleF2JtOxVq5syZ+sMf/qChQ4dmLjd76tSpaCZcSLW6YNvWVWJtkwj3p0uupucuxetSrOHOqvzURkKRH3daRQABBBAIWcBcXtbcjXvLli2ZO2//wz/8gxoaGkJuheoQQAABBPwCJBR+EbYRQAABBJwWmDhxosz6CnNjvLKyMieOVjgNTvAIIJB4AdZQJH4KAIAAAgjEV2Dfvn268847VVJSkrn0bGlpaXw7S88QQAABCwKsobCA3FkTLp3LR6ydjWLvX8e294ZBNbjkauJ3KV7XYzX3sDBHK0wiYY5W1NbWBk2hvLzmum1e0LJoFNcskHIsgm2OcAnYjVOeEjDIdBEBBBBIskC/fv0yRyfM2oqbbrpJ8+fPV6Ev2E7yeNF3BBBwT4CEwr0xI2IEEEAAgRwEzNqKQ4cOZRZqX3311WpsbMyhFnZBAAEEEPALkFD4RdhGAAEEEIitgLk/xY9+9CONHz8+c3nZnTt3xravdAwBBBCwJcCibEvS5rzD6upqS63RDAIIIIBAdwIrV67M3AyvpqZG06ZN66447yOAgEMCfO+KbrBYlB2dbaxqZtFVdMOJbTS2LrkaAZfijXOss2bN0o4dO1RZWZm5b0U0s7PzWuNs23mvo38H1+iMXbKNToGagwQ45SlIhdcQQAABBBIhMHbsWO3duzdzrwoWaydiyOkkAghEIEBCEQEqVSKAAAIIuCNgLi1rLie7fft2zZkzhytAuTN0RIoAAgUiQEJhaSBYP2EJmmYQQACBHATMYm2TVLzxxhskFTn4sQsChSbA9y67I0JCYcmb8w4tQdMMAgggkKMASUWOcOyGQAEK8L3L7qCQUNj1pjUEEEAAgQIWIKko4MEhNAQQKFgBEoqCHRoCQwABBBDIhwBJRT7UaRMBBFwWIKGwNHqcy2cJmmYQQACBEAS8ScUTTzwRQo1UgQACNgX43mVTWyKhsOTNuXyWoGkGAQQQCEmgLanYuHFjXu5TEVI3qAaBRArwvcvusPe12xytIYAAAggg4I6ASSrMEYpx48aptLRUEydOdCd4IkUAAQQsCXCEwhI0zSCAAAIIuClgbn63ZcsWTZo0Sfv27XOzE0SNAAIIRChAQhEhLlUjgAACCMRDwByZWLFihe688041NjbGo1P0AgEEEAhJgIQiJEiqQQABBBCIt8CsWbN02WWXySz2PHXqVLw7S+8QQACBHgiQUPQAi6IIIIAAAskWWLJkSeZu2mvWrEk2BL1HAAEEPAIsyvZg8BQBBBBAAIGuBAYNGqQf/OAHGjlyZOY/s76CBwIIIJB0AY5QJH0G0H8EEEAAgR4JlJeXq6amRnPnzmU9RY/kKIwAAnEVSKXT6bS3c6lUSr6XvG/zHAEEEEAAAQQk3XHHHRmHVatW4YEAAggkRiAoV+AIhaXhd+kGK8Qa3aTANhpbl1yNgEvxEmvnc9bYrF69WrW1tZ0X6uIdbLvA6cVbuPYCr5tdse0GKMFvk1AkePDpOgIIIIBA7gLmpncbNmzQTTfdxKlPuTOyJwIIxECAhCIGg0gXEEAAAQTyI1BRUaHbb79dTz31VH4CoFUEEECgAARYQ1EAg0AICCCAAALuCpgb3Q0dOjRzN21zAzweCCCAQJwFWEORx9HlvMNo8F1yNQIuxUus0cxZ5kH8XM2pT+aqTw888ECPbnjH71g0cwHXaFz57IrONQ41c4TC0ij25gPO3JXVu79/O6gL/jL+bfYJElDmDrhYM9/8vy/+7aDZ4y/j32afIIH4/M59/PHHWrdunb7zne/o97///ZnOMg86jvEZHM8Tv5N/21P0zFN/me62zY7dlfG/H8d9zgC2PvH32b/tL5+NST738bZt+sIjfIGgIxTmErHtHlKHl9q9z0ZuAosWLcptxzzsRazRoWMbja1LrkbApXiJNfs5u2PHDnMZ9vT777+f1U7YZsXU40K49pgs6x2wzZoq1gWDcgUWZYefuFEjAggggEACBcxds80C7cceeyyBvafLCCCQZAFOebI0+uY0Gg69WcKmGQQQQCBPAg0NDSorK1N9fb1KS0vzFAXNIoAA37uimwNBpzxxhCI6b2dr9q4hKPROuBSrsXQpXmKNbvZjG41tIbiaJKKqqipzw7vuelkI8XYXY9v7xNomEe5Pl1xNz12LN9zRorauBEgoutLhPQQQQAABBHooYE57WrZsmczRCh4IIIBAEgRIKJIwyvQRAQQQQMCaQE+OUlgLioYQQACBCAVIKCLE9VbN+gmvBs8RQACBeAu0HaUwN73jgQAC9gX43mXXnITCkjfnHVqCphkEEECgAATMUQqTVGzcuLEAoiEEBJInwPcuu2NOQmHXm9YQQAABBBIicNttt2n27Nk6duxYQnpMNxFAIKkCJBRJHXn6jQACCCAQqYC5L8WYMWO0ffv2SNuhcgQQQCDfAiQUlkaAc/ksQdMMAgggUEAC9957r9avX19AEREKAskQ4HuX3XEmobDkzbl8lqBpBgEEECgggfHjx2vTpk3at29fAUVFKAjEX4DvXXbHmITCrjetIYAAAggkSGDQoEF69NFH9dOf/jRBvaarCCCQNAESiqSNOP1FAAEEELAqcPXVV+v+++/XqVOnrLZLYwgggIAtARIKW9K0gwACCCCQSIHLL788szj7N7/5TSL7T6cRQCD+AiQU8R9jeogAAgggkEeBfv36adq0aXr11VfzGAVNI4AAAtEJkFBEZ0vNCCCAAAIIZATGjRvHaU/MBQQQiK0ACUVsh5aOIYAAAggUikB5eXkmFE57KpQRIQ4EEAhTgIQiTE3qQgABBBBAoBMBc7UnTnvqBIeXEUDAaYFUOp1Oe3uQSqXke8n7Ns8RQAABBBBAIAeBnTt3au7cudq1a1cOe7MLAgggUBgCQbkCRygsjY1LN1gh1ugmBbbR2LrkagRcipdYw5uzn//85/XrX/9aDQ0NmUqxDc/WWxOuXo1wn2MbrmecaiOhiNNo0hcEEEAAgYIVMDe5mzx5st56662CjZHAEEAAgVwESChyUWMfBBBAAAEEchC47rrr9Prrr+ewJ7sggAAChSvAGorCHRsiQwABBBCImYBZR2EuIctaxZgNLN1BIEECrKHI42Bz3mE0+C65GgGX4iXWaOYs8yDZrmYdhXk0NjbyeRDRVOCzKyJY/oZFBxuDmjnlKQaDSBcQQAABBNwQMOsoxowZo4MHD7oRMFEigAACWQiQUGSBRBEEEEAAAQTCEhg/frx+//vfh1Ud9SCAAAJ5FyChyPsQEAACCCCAQJIErrzySq70lKQBp68IJECAhCIBg0wXEUAAAQQKR+Cv/uqvtGzZssIJiEgQQACBXgqQUPQSkN0RQAABBBDoicDgwYMzxU+dOtWT3SiLAAIIFKwACUXBDg2BIYAAAgjEUaC0tDTTrZMnT8axe/QJAQQSKEBCkcBBp8sIIIAAAvkVMFd6On78eH6DoHUEEEAgJAESipAgu6umurq6uyK8jwACCCCQEAFzpaf//u//Tkhv6SYC9gX43mXXnITCkrdLN9qxREIzCCCAQGIFBg4cqKNHjya2/3QcgagF+N4VtXD7+kko2nuwhQACCCCAQOQCw4cP14cffhh5OzSAAAII2BAgobChTBsIIIAAAggggAACCMRUoG9M+1Vw3eJcvoIbEgJCAAEE8iZwySWX6LXXXstb+zSMQLYCDQ0NevHFF/Xb3/5Wb775pg4ePKgbb7xR11xzjQYNGpRtNdbL8b3LLjlHKCx5cy6fJWiaQQABBBwQOOeccxyIkhCTLGDuk3LbbbfJXEBg4cKFeumll7R//37V1NToK1/5is477zz9+Mc/LlgivnfZHRqOUNj1pjUEEEAAAQQQQKCgBUwyMWnSJP3yl7/sMs7bb79dR44c0Te/+c0uy/Fm/AU4QhH/MaaHCCCAAAIIIIBA1gJz5szpNpkwlX3wwQdavHixzGlRPJItQEKR7PGn9wgggAACeRQw/xLMA4FCEmhsbNSmTZuyDum9997TvHnzsi5PwXgKkFDEc1zpFQIIIIBAAQuUlpZmojt06FABR0loSRSoq6uTSRJ68nj55Zd17NixnuxC2ZgJkFDEbEDpDgIIIIAAAgggkKtAd+smguodNmwYN2oMgknQa6l0Op329jeVSsn3kvdtnuco0JurDZhLn3n3928HheQv499mnyABye/k3w7ay1/Gv80+QQJYGxX/XPFvB8n5y/i32SdIoDCtH3roIc2cOVMrV67kMz6Cv3NBvxv+17rbzub31F9Hoe/j/w3xx3/48GGtXr3aX6zbbTOXzZWfOnv42/FvB+3nL+PfDtrH+5opzyN8gcBcwSQU3odk8gkeYQssWrQo7Cojq49YI6NNYxuNrUuuRsCleIk1mjlrajV/b+vr66NrIMSamQchYnqqKkTXhQsXZuammZ/Z/jds2LD0oUOHPD3L/9NCtM2/SjgRBOUKHKEIP3GjRgQQQAABBLoUMAtfhw4dqvfff7+gbw7WZSd4M5YCO3fu1N///d/3aB3FxRdfrAMHDsTSg051FAg6QsEaio5OkbziPWUpkgZCrJRYQ8T0VYWtDySkTZdcTZddipdYQ5qkvmpOnjyZeaWQ7zTsDZl54NUI73khuo4dO1YmQcj2ccEFF9evgj0AACAASURBVOjb3/52tsWtlStEW2udz0NDJBR5QKdJBBBAAAEEEECgUAW+//3va/DgwVmFN2bMGN18881ZlaVQfAVIKOI7tvQMAQQQQAABBBDosUB5ebl+/OMfa8iQIZ3uaxKOG2+8US+88IL69evXaTneSIYAayiSMc70EgEEEECggATMnYXLysq4qmIBjQmhdBQw95b4l3/5Fz333HPq06dPZr3Prl279KUvfUnf+ta3MglFx714Je4CrKHI4wi7dC4fsUY3UbCNxtYlVyPgUrzEGs2cfeuttzRy5MhoKo+gVuZBBKgOfBaYNT7m8sZmwfUvfvELmdObzPqf1157reCTCZfmbDSzy26tnPJk15vWEEAAAQQQyAhwmggTwSUBc/qTuc8E89alUbMXKwmFPWtaQgABBBBAICPQ3NyMBAIIIBAbARKK2AwlHUEAAQQQcEXAnPLU1YJXV/pBnAgggIARIKFgHiCAAAIIIGBZ4A9/+IPlFmkOAQQQiE6AhCI6W2pGAAEEEEAgUGD16tVZX+c/sAJeRAABBApIgISigAaDUBBAAAEE4i9gLsVpHn/xF38R/87SQwQQSIQACUUihplOIoAAAggUisDRo0czoQwYMKBQQiIOBBBAoFcCJBS94st+5+rq6uwLUxIBBBBAILYCZkH27bffHtv+0bGYCDTv0vJrSpS65gntaW4J6FSLTtTdp5LUpZpRe1BBJQJ2svYS37usUWcaIqGw5M0NVixB0wwCCCBQ4AL79+/XxRdfXOBREl7iBfqP1t3LqzR++zLNe2a3OlzouHm3fvDwOml6tR6a8rmCu8oP37vszmASCrvetIYAAgggkHCBXbt2afjw4QlXoPuFL1Ck/qO+ruXLLtf2qof0zJ7jnpCPa88zD6mqvkIrH7pBF/Jt0mOTzKdMgWSOO71GAAEEEMiDwKlTp7Rp0yaNGDEiD63TJAI9FRioUXcv0rLxv1HVvB+q6aO0pBY17/mh5lVJy15+RBUXntXTSikfQ4G+MexTQXaJc/kKclgICgEEELAqUF9fn2mvtLTUars0hkDOAq2nPv1k9DJt7fu3am7erWfmPS0te153jxqYc7VR78j3rqiF29fPEYr2HpFtcS5fZLRUjAACCDgjcODAARZkOzNaBHpawJz6NFPPbajQsVde0cyZC1SlmVp+92j1L2AivnfZHRwSCrvetIYAAgggkGCBzZs366qrrkqwAF13U+AsXTilStePPKX16/9Sy5Z/XaP68xXSzbGMJmpmQzSu1IoAAggggEA7AbN+wtwh+4tf/GK719lAwAmBor/U2f36SMVf1OX/k3uoODFmFoMkobCITVMIIIAAAskVaFs/UVZWllwEeo4AArEUIKGI5bDSKQQQQACBQhPYsWOHqqqq1K9fv0ILjXgQQACBXgmQUPSKj50RQAABBBDITuCVV17Rddddl11hSiGAAAIOCZBQODRYhIoAAggg4KZAY2Nj5v4To0ePdrMDRI0AAgh0IUBC0QUObyGAAAIIIBCGQF1dnSZPnqxBgwaFUR11IJAHgfN18XV3KH14sSYM4OtjHgagoJtMpdNpc9vDM49UKiXfS2fe4wkCCCCAAAII9FxgypQpqqio0LRp03q+M3sggAACBSQQlCuQYloaIJdusEKs0U0KbKOxdcnVCLgUL7H2fs42NDRkTne64YYb2lWGbTuO0DZwDY2yQ0XYdiDhhVYBEgqmAgIIIIAAAhEKbN26NXN3bE53ihCZqhFAIK8CJBR55adxBBBAAIE4C5ib2a1fv14333xznLtJ3xBAIOECrKFI+ASg+wgggAAC0Qns3LlT48aN08mTJ7n/RHTM1IwAAhYFWENhEdvfFOcd+kXC2XbJ1fTYpXiJNZw5GlQLtkEqvX+tEF3XrVunFStWBCYThRhvZ6NArJ3J9O51l1xNT12K16VYezeLCmPvvoURBlEggAACCCAQLwGzGHv16tU6dOhQvDpGbxBAAAGfAGsofCBsIoAAAgggEIaAWYxdVVWlIUOGhFEddSCAAAIFK8ARioIdGgJDAAEEEHBV4NixY5o9e7Z27NjhaheIGwEEEMhagCMUWVNREAEEEEAAgewEnn/++cydsceOHZvdDpRCAAEEHBbgCIXDg0foCCCAAAKFJ8DRicIbEyJCAIFoBThCEa0vtSOAAAIIJEyAoxMJG3C6iwAC4ggFkwABBBBAAIGQBDg6ERIk1SCAgFMCHKGwNFzV1dWWWqIZBBBAAIF8CXB0Il/ytItAewG+d7X3iHqLhCJq4db6ucGKJWiaQQABBPIkYO47Ya7s9O1vfztPEdAsAgi0CfC9q03Czs9UOp1Oe5sKup22932e5ybQm4ltsmzv/v7toIj8Zfzb7BMkIPmd/NtBe/nL+LfZJ0gAa6Pinyv+7SA5fxn/NvsECdixfuWVV2Su6tSvX78zQTA+He3P4Hie+J38256iZ576y3S3bXbsroz//Tjucwaw9Ym/z/5tf/lsTPK5j7dt0xce4QsE5gomofA+JHk3eR6SwKJFi0KqKfpqiDU6Y2yjsXXJ1Qi4FC+xZjdnd+zYYf5xLn3o0KHsdmAeZO3U04LM2Z6KZV8e2+yt4lwyKFfglKfwE7fAGsmSA1l4EQEEEHBe4NSpU5o7d65qamq4K7bzo0kH4iLA9y67I0lCYcnbe8qSpSZpBgEEEEDAgsBLL72UaeXmm2+20BpNIIBANgJ878pGKbwyXDY2PEtqQgABBBBImIBZiF1ZWam9e/e2WzuRMAa6iwACCRfgCEXCJwDdRwABBBDITcCc6jR//nw9+uijKi8vz60S9kIAAQRiIEBCEYNBpAsIIIAAAvYF1qxZo8OHD2fWT9hvnRYRQACBwhHglKfCGQsiQQABBBBwRGDfvn2Ze05wqpMjA0aYCCAQqQBHKCLlpXIEEEAAgbgJHDt2THfeeadWrFjBqU5xG1z6gwACOQmQUOTExk4IIIAAAkkVWLBggS677DLNmDEjqQT0GwEEEGgnwClP7TjYQAABBBBAoHOB9evX64033lBtbS1XdeqciXcQQCBhAilzJz9vnwNvp+0twHMEEEAAAQQSKLBz506NGzdOO3bs0NixYxMoQJcRQAABKShX4JQnSzPDpRusEGt0kwLbaGxdcjUCLsVLrKfnbGNjYyaZMHfDDiuZwJbPA5fmAJ9d0czXuNRKQhGXkaQfCCCAAAKRCJhF2BUVFZn7TUybNi2SNqgUAQQQcFmAhMLl0SN2BBBAAIFIBczN69oWYc+dOzfStqgcAQQQcFWANRSujhxxI4AAAghEKmCSiTlz5mQWYb/66qsswo5Um8oRQMAVAdZQ5HGkXDpPklijmyjYRmPrkqsRcCneJMdq+h7lFZ2SbBvNJ8HpWnGNThfb6Gxdr5lTnlwfQeJHAAEEEAhdYOXKldq+fXvm8rBDhgwJvX4qRAABBOIkQEIRp9GkLwgggAACvRYwyYS534S51wTJRK85qQABBBIgQEKRgEGmiwgggAAC2QmQTGTnRCkEEEDAK8Cdsr0aPEcAAQQQSKSAdwE2RyYSOQXoNAII9EKAIxS9wGNXBBBAAAH3BUgm3B9DeoAAAvkV4AhFfv1pHQEEEEAgjwLmDtizZs3KRMCRiTwOBE0jgIDTAhyhcHr4CB4BBBBAIFeBhoaGzB2wBw8erB/96EcswM4Vkv0QQCDxAiQUlqZAdXW1pZZoBgEEEECgO4GtW7eqrKxM06ZN01NPPcVN67oD430EHBPge5fdASOhsOTt0s1gLJHQDAIIIGBdwKyXMFdymjRpkjZs2JA53alfv37W46BBBBCIVoDvXdH6+mtnDYVfhG0EEEAAgVgKmPUS5l8tzd2v9+7dq/Ly8lj2k04hgAACtgU4QmFbnPYQQAABBKwLmFOcKioqMu3+7Gc/I5mwPgI0iAACcRYgobA0upzLZwmaZhBAAAGPgDnFafHixZlTnMzVnFatWqVBgwZ5SvAUAQTiKMD3LrujSkJhyZtz+SxB0wwCCCDQKrBv3z5dffXV2rVrl+rr6zMLsMFBAIFkCPC9y+44k1DY9aY1BBBAAIGIBY4dO6b58+dr5MiRmUXX5pKwpaWlEbdK9QgggEByBViUndyxp+cIIIBArAQ+/vhjmZvTPfbYYyopKckclSCRiNUQ0xkEEChQARKKAh0YwkIAAQQQyF5g586dmcvAbtu2Tffee++ZBdjZ10BJBBBAAIFcBTjlKVc59kMAAQQQyLuAudu1Ob1p3LhxuuSSS2Su4NR2Nae8B0cACCCAQEIESCgSMtB0EwEEEIiTQFsiYe52bR6HDh3SmDFjuIJTnAaZviCAgDMCJBTODBWBIoAAAgj4Ewlz9aalS5dqyJAh4CCAAAII5EmAhCJP8DSLAAIIIJCdgLmXhFkjMWXKFLUdkWhLJFh0nZ0hpRBAAIEoBVLpdDrtbSCVSsn3kvdtniOAAAIIIGBFoLGxUXV1dVq5cqV+/etfa8WKFbrllls4rcmKPo0ggAACwQJBuQJHKIKtQn/VpRusEGvow3+mQmzPUIT6xCVX03GX4rUdqzkasXXrVt1xxx0aOnRo5jKwjzzyiE6ePJm5p0RXd7m2HWtvJ7FL8RJrb0c7eH+XXPnsCh5DXj0twGVjmQkIIIAAAnkVMDei2717d+a/+++/P7O4etq0adxHIq+jQuMIIIBA9gIkFNlbURIBBBBAICQBs7j69ddf1y9/+UutXr36TBKxd+9elZeXh9QK1SCAAAII2BBgDYUNZdpAAAEEEixgTmMyi6gPHDiQSSKWLVuW0bj99tt11VVX6corrxSLqxM8Qeg6Agg4JcAaijwOl0vnSRJrdBMF22hsXXI1Ai7F25NYzalL5siDuSJTbW1t5oZzV1xxhc455xyNHDlSmzdv1ogRI2SOQpg1EatWrZI5tSmsZKInsUYzE3tWq0vxEmvPxjbb0i65mj65FK9LsWY7Xwq5HEcoLI1ObyZ2dXV1u19i/3ZQF/xl/NvsEyQg+Z3820F7+cv4t9knSABro+KfK/7tIDl/Gf922PuYG8Z98MEH+trXvqYXXnjhTPV//vOf9d5772W233///cwRiLY3S0pKdNFFF+muu+7KLLAeOHCgzjvvvLa32/30x+/fble4dcNfxr/NPkECbsy3tsjDGNOgOvyvdbdt4umujP/9Qt+nzbjtpz9+/3ZbOe9Pfxn/trds23N/Gf92WznvT38Z/7a3bNBzU55H+AJBRyhIKMJ3DqzRJBSuTGxiDRzCUF7ENhTGDpW45GqCdylec++Hzo4gmFOVzKN///6ZBMI876xspmDE/3PJ1VC4FC+xRjN5XXJlzkYzB1ysNSihYFG2iyNJzAgggIAlgcsuu8yZfwyxREIzCCCAAAI+Ae5D4QNhEwEEEEAAAQQQQAABBLIXIKHI3oqSCCCAAAIIIIAAAggg4BMgofCBsIkAAggggAACCCCAAALZC5BQZG9FSQQQQAABBBBAAAEEEPAJkFD4QKLadOUKT1H1n3oRQAABBBBAAAFbAnzvsiV9uh0SCkve5tJwPBBAAAHbAi0NazUp9VWtbfjQdtOt7Z1Qw7andF/NfrV0FkHzLi2/pkQllTXa3+wv1aLm/TWqLLlUM2oPdl5HZ3XzOgIIJFKA7112h52Ewq43rSGAAALJEjixW2sqH9OeT7rodv/Runt5lcrWf0v/9MxuNXuLNu/WM//0LW27vloPTfmc+KPlxeE5AgggUBgCfDYXxjgQBQIIIJBggSL1H/V1LV92ubZXPaRn9hw/bdFyULXfmKEqVenlJ6foQv5iJXiO0HUEEChkAT6eLY0O5/JZgqYZBBIjcFR1C0YrNelp1b3+tCpLUjJ3L01ds0A1e5q6PDWopWmPapdXqsSUz/w3SQvW1qmh7XSjE3VaUFKiSau26d03XtE1reVKKp/QtoYT7YRbmnapZsGk1npKdM2CtaprK2PqGX6tljY1aeuMz6tPyX2qO+E/pamtuoEadc/T2jD9oKrm/VB7mj/UuxuXadbaz2nZ8q9rVH/+XLVJ8RMBBLoX4HtX90ZhluATOkzNLuriXL4ucHgLAQRyF9g6S7d+T5q5589Kp/+o+tl9tG70HXq87V/5/TU379Ljt9ylTX3u1J5P0kqn0/rk8Dz1efZO3dXudKMmbb1zuX53drleTqeV/qRRz134M028a432tCYeLe/W6o5RM1R3wSIdztS1X98r26lbx9+n2nc/kgZM0JL9P9f84mJNXPM7fXJ4sSYM6OLPTtHnNOWhak2vX6Z5M2fo1pte1fUbntY9owb6e8E2Aggg0KUA37u65An9zS4+2UNviwoRQAABBMIWKJ6plYvv0BXFZ0kaoNKKe7Rw/hE9/uJv1P5Ygmm4RSd2bdTj9RNVOeNLKm79C1BUfJVum3q5tm97S4c9BxCK5y/QVcPPV3+za1GxRl83SsXb/0NvHP5I0lFtf2qx1l46V/d/Y2xrXQM0fPoSPTf1dc16akdA+913vujCG/TQygrVr39e9dNZN9G9GCUQQACB/AuQUOR/DIgAAQQQyF3g0ss1IpNMtFXRX0PKLlHTs69od4fTi4o0YMJiHT78iK448u+qra1Vbe2/ae2CySqb8VJbBZ38LFL/IcN0qQ6ovrFZOvFbbXl2j4rLL9IF7f6SdNV+J1V7X25p0q9+8qqaJDVtrtOvmkzywgMBBBBAoJAF2v0ZKORAiQ0BBBBAoAcCTW/rnSMBX8ab39Laysv02bJbtOJX75tDDxo4aal2r7lZevNtNbato8iyqaal1+rcM2sxzJqMflkkJ51VfkL71z10et3Ez3+iZWW1uunWp8+cYtXZXryOAAIIIJBfgb75bZ7WEUAAAQQiESgeposuOEs64q39QzW8+JBmbLtaGxofV8WF5jQp8zALvA9IGta6ne0PszaiTpunD+/8cq4dz7vqpPIWNe9Zo3+asUtfXvMj3T3hC9K5VfrJ6GWa98xYvTzvitOnXnWyNy8jgAACCORPgCMU+bOnZQQQQKD3Ah2OKjSrsf6Aiqdep9EdFkCffk/+06RaPtDxo3/uWSwDvqhJU0v05s7/VJNn3YV0XHuW36DUpLVqaPd619W3NP1ci+cty6ybWHzbCPVXJ5eS7boa3kUAAQQQyIMACUUe0GkSAQQQCE2gaZ0efnRj6yVfT2j/2gW69dkrtXLOOA3o0MggjZ40UcVbX9C67e+evrRsS5N2PblIs9a+1aF01y+cr/Fz7tP1mx/UfU/ubE0qTqihdqnmVUnLFleo1PyF6V+iskvPOV3VyWYFnlHVclAbH7hH39Fdeu6RGzz3mxioUXc/pjXTzKVkn1Qd6ym6HhLeRQABBPIkQEKRJ3iaRQABBEIRGD9VU8cc0KOlfZRKnasJr45QzfbFntOZvK0UacD42Xp5Xbn+49oh6mPWPgy5V/8+tFIbN8xXsbdoFs+LLpyiJ7c/qauPPKSSPmb9xLkav2mQZu9e9emlXosu0fULpuojcx+Kv5yuF9/+0Ffzce15fKZuytxv4hua0G6BuUlIRui2xeZSst/WrQ/8P73bg6MevobYRAABBBCISCCVNhch9zzMTY58L3ne5SkCCCCAQGEImHUPf6Nr9/2z6jdPP300oDACIwoEEEAAgRgLBOUKHKGwNOAu3WCFWKObFNhGY+uSqxFwKV5ijWbOMg9wdW0OuBavS59d0f022KuZhMKeNS0hgAACCCCAAAIIIBA7AS4bG7shpUMIIJAMgfM1YclutTtnNRkdp5cIIIAAAgUmwBqKAhsQwkEAAQQQQAABBBBAoFAFWEORx5Fx6Vw+Yo1uomAbja1LrkbApXiJNZo5yzzA1bU54Fq8Ln12RffbYK9m1lDYs6YlBBBAAAEEEEAAAQRiJ0BCEbshpUMIIIAAAggggAACCNgTIKGwZ01LCCCAgEMCLWpuqNUrNU/InC+bmrRWDdxUzqHxI1QEEEDAngBXebJnTUsIIICAOwItDXpx9iy9Oeh6NR54QRfyz0/ujB2RIoAAApYF+BNhGZzmEEAAAacE+p2tz/KXwqkhI1gEEEDAtgB/JmyL0x4CCCAQlkBzg+rWLtA15pSkzH+TtGBtnRqaW89NOlGnBSUplSyo04kzbbboRN19KkmN1oK6o5KOqm7BaKWuWaBVyytV0lZXn89rxtYm/em1Z3XumbIfqWlPrZZXXtraXiqz39q6BjWfqV9SS5P21HwaV0nlE9rW8GkEpmhL0y7VLJjUWk+JrlmwVnW+Mt4qeY4AAgggULgCJBSFOzZEhgACCHQhcFx7nrlHt776BX3vT58onU7rk8Pz1OfZOzX7xQb1eLnD9p9qx6AqNaT/rMP17+hPn/xOayYW67P/a6r+mN6tJRMGqXnP07rlxk3qM3OrPkmnlTZlF56jZ6+9R8/sOX461paDqr1jokav66PZ9X9UOv1H1V39lirH36fadz/KlGl5t1Z3jJqhugsW6fAnpp79+l7ZTt3qKdNFx3kLAQQQQKDABEgoLA1IdXW1pZZoBgEEEiHQckRvbNuvS6/+a5X2P/1RXlT8ZS3+xdvaMn24evzhXnyjKr/yBfXXWSou/Zz6d0A8pl0v/qvqp1ZqxhXFrfWfpeLxX9PUifu17Y0jmSSm5e2f6/trz9b8hfeoonSApAEa/pV/1FTV6vtbDqhFR7X9qcVae+lc3f+NsSrOBDpAw6cv0XNTX9esp3Z4jqZ0CIIXEEAAgawE+N6VFVNohXr8Nye0lhNWETdYSdiA010EohYoukCXfXm4tj7wQ23cVada/2lHobd/viYs2a3DS0brSN0m1dbWqrZ2lRZcO0Eztp5sbe1Dvb3jZ9qqS1Q2xJOSDJigJYcPn050TvxWW57do+Lyi3RBu79A/TWk7BI1PfuKdp/o8fGV0HtLhQgg4LYA37vsjl+7j3O7TdMaAggggEDuAgM1at7zqn/ur3V8wxLddG2ZPpuKci1Ci5r316iy5FyVXftd/eq4+dL/PzTpe7VaM1F6s/5w+3UU3XSsaem1OrdtvUbmZz+VzXipm714GwEEEECgEAVIKApxVIgJAQQQyEpggEonVGj6ki2n1zPsXqm/O/KErh3/mOrC/ld+cxnZb3xL267foMZPtmjJ9K+oomKyJpScVP2bTVlF+2mhYk1c87vWdRhmDYXnv8OLNWEAf5o+teIZAgggUPgCfGpbGiPO5bMETTMIJFbgLBWPmqI7K29UcdPbeufIR1L/EpVdWhyOSPNh1b8pXTr2C63rHk5X2/Kn4zLXijr9+IyGjfsbTdQB1Td6rvvUsl9rJ5Wcvjle/y9q0tQSvbnzP9XU7sym49qz/AZuoNdGyU8EEOiVAN+7esXX451JKHpMltsOnMuXmxt7IYBAJwKZL+nDdM2C2k8vE9vcoFe27JGm/29NGvYZqegijfvaODU9+6/6t/3msq3m7tcb9ejD69TTYwoacDoR2PrsC9re1Hq1pqadevK+B7XWU1nRsEla8K3ztPThp1WXKfeRmra/oGe3Xq5liytUWnS+xs+5T9dvflD3PbmzNak4oYbapZpXpdYynfSZlxFAAIEsBfjelSVUSMVIKEKCpBoEEEDAqkDRcN227gXNHrxJ4z/b5/T9HD57szYNvksvP3JD652tP6PSrz6irfd8rAc+f65SqSG6cc0Humnh/ZrY42DP1/hvflfrrnhN15acnWlvyL3/oaGV39WG+aM+ra3oQk14ZJ1233ZSD2fKna2Sh0/qtt2rdM+ogZlyRRdO0ZPbn9TVRx5SSR9zD41zNX7TIM32lPm0Qp4hgAACCBS6QN9CD5D4EEAAAQSCBYqKR6liXk3mv+ASkvqX6svzanR4Xk27IlvSM89sm6s3pZec2Tz9pGi4pm85rIMPPihz8VfzKCq+QpVLtqjSX3bCblW0lmktqFGVS/SLDgXbChWpf+kETV9i/mt7jZ8IIIAAAq4KpNJmNZznYe626nvJ8y5PcxUwh944ny9XPfZDAAEEEEAAAQSyF+B7V/ZWPS0ZlCtwylNPFRNQ3qXzDl2K1Uwdl+Il1uh+2bGNxtYlVz4PopkDuEbn6ppttBLU7hcgofCLsI0AAggggAACCCCAAAJZC3DKU9ZUvSvYm385M6dKeff3bwdF5i/j32afIAFlTkvDmvnm/33xbwfNHn8Z/zb7BAnwO2dU/HPFvx0k5y/j32afjq7ZWAc5+l/rbrvQ2/HPjWz649I+3lhN33iELxB0ypNZL9HuIXV4qd37bOQmsGjRotx2zMNexBodOrbR2LrkagRcipdYo5mzzANcXZsDrsXr0mdXdL8N0dQclCtwhCL8xI0aEUAAAQQQQAABBBCIpUDQEQrWUFgaau9pNJaazLkZYs2Zrtsdse2WKKcCLrmaDroUL7HmNCWz2gnbrJh6XAjXHpNlvQO2WVMlriAJReKGnA4jgAACCCCAAAIIIBCeAAlFeJbUhAACCCCAAAIIIIBA4gRYQ5G4IafDCCCAAAIIIIAAAgjkJsAaitzcQtmL8w5DYexQiUuuJniX4iXWDtMttBewDY2yXUUuuZrAXYqXWNtNtdA2XHJlzoY27LGsiFOeYjmsdAoBBBBAAAEEEEAAATsCJBR2nGkFAQQQQAABBBBAAIFYCpBQxHJY6RQCCCCAAAIIIIAAAnYESCjsONMKAggggAACCCCAAAKxFCChiOWw0ikEEEAAAQQQQAABBOwIkFDYcaYVBBBAAAEEEEAAAQRiKUBCEcthpVMIIIAAAggggAACCNgRIKGw46zq6mpLLdEMAggggAACCCCQbAG+d9kdfxIKS96u3bzGEgvNIIAAAggggAACoQvwvSt00i4rJKHokoc3EUAAAQQQQAABBBBAoCsBEoqudHgPAQQQQAABBBBAAAEEuhQgoeiSJ7w3OZcvPEtqQgABBBBAAAEEuhLge1dXOuG/R0IRvmlgjZzLF8jCxfZAsQAABXBJREFUiwgggAACCCCAQOgCfO8KnbTLCkkouuThTQQQQAABBBBAAAEEEOhKgISiKx3eQwABBBBAAAEEEEAAgS4FUul0Ou0tkUql5HvJ+zbPcxQwh944ny9HPHZDAAEEEEAAAQR6IMD3rh5g9bBoUK7AEYoeIiahuEvnHboUq5k7LsVLrNH9tmMbja1LrnweRDMHcI3O1TXbaCWo3S9AQuEXYRsBBBBAAAEEEEAAAQSyFiChyJqKgggggAACCCCAAAIIIOAXIKHwi7CNAAIIIIAAAggggAACWQuwKDtrKgoigAACCCCAAAIIIJBsARZl53H8XVosSKzRTRRso7F1ydUIuBQvsUYzZ5kHuLo2B1yL16XPruh+G+zVzClP9qxpCQEEEEAAAQQQQACB2AmQUMRuSOkQAggggAACCCCAAAL2BFhDYc+alhBAAAEEEEAAAQQQcFqANRR5HD6XzuUj1ugmCrbR2LrkagRcipdYo5mzzANcXZsDrsXr0mdXdL8N9mrmlCd71rSEAAIIIIAAAggggEDsBEgoYjekdAgBBBBAAAEEEEAAAXsCJBT2rGkJAQQQQAABBBBAAIHYCZBQxG5I6RACCCCAAAIIIIAAAvYESCjsWdMSAggggAACCCCAAAKxEyChiN2Q0iEEEEAAAQQQQAABBOwJkFDYs6YlBBBAAAEEEEAAAQRiJ0BCYWlIq6urLbVEMwgggAACCCCAQLIF+N5ld/xJKCx5c4MVS9A0gwACCCCAAAKJF+B7l90pkEqn02lvk0G30/a+z/PcBHozsU2W7d3fvx0Ukb+Mf5t9ggQkv5N/O2gvfxn/NvsECWBtVPxzxb8dJOcv499mnyABrJM434J+N/yvdbedjZu/jkLfx/8b4o/fv+0vn03/8rmPt23TFx7hCwTlCiQU4TtTIwIIIIAAAggggAACsRQISig45SmWQ02nEEAAAQQQQAABBBCwI0BCYceZVhBAAAEEEEAAAQQQiKUACUUsh5VOIYAAAggggAACCCBgR4CEwo4zrSCAAAIIIIAAAgggEEsBEopYDiudQgABBBBAAAEEEEDAjgAJhR1nWkEAAQQQQAABBBBAIJYCJBSxHFY6hQACCCCAAAIIIICAHQESCjvOtIIAAggggAACCCCAQCwFSChiOax0CgEEEEAAAQQQQAABOwIkFHacaQUBBBBAAAEEEEAAgVgKkFDEcljpFAIIIIAAAggggAACdgRIKOw40woCCCCAAAIIIIAAArEUIKGI5bDSKQQQQAABBBBAAAEE7AiQUNhxphUEEEAAAQQQQAABBGIpQEIRy2GlUwgggAACCCCAAAII2BEgobDjTCsIIIAAAggggAACCMRSgIQilsNKpxBAAAEEEEAAAQQQsCNAQmHHmVYQQAABBBBAAAEEEIilAAlFLIeVTiGAAAIIIIAAAgggYEeAhMKOM60ggAACCCCAAAIIIBBLARKKWA4rnUIAAQQQQAABBBBAwI4ACYUdZ1pBAAEEEEAAAQQQQCCWAiQUsRxWOoUAAggggAACCCCAgB0BEgo7zrSCAAIIIIAAAggggEAsBUgoYjmsdAoBBBBAAAEEEEAAATsCJBR2nGkFAQQQQAABBBBAAIFYCpBQxHJY6RQCCCCAAAIIIIAAAnYESCjsONMKAggggAACCCCAAAKxFCChiOWw0ikEEEAAAQQQQAABBOwIkFDYcaYVBBBAAAEEEEAAAQRiKZBKp9Pptp6lUqm2p/xEAAEEEEAAAQQQQAABBAIFPCmE+npLeN/wvs5zBBBAAAEEEEAAAQQQQCBIgFOeglR4DQEEEEAAAQQQQAABBLISIKHIiolCCCCAAAIIIIAAAgggECTw/wHvsi8XfS/2/QAAAABJRU5ErkJggg=="></p>
<p>Sketch on the grid the equipotential surface corresponding to a gravitational potential of –2<em>V</em>.</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>A meteorite, very far from planet X begins to fall to the surface with a negligibly small initial speed. The mass of planet X is 3.1 × 10<sup>21</sup> kg and its radius is 1.2 × 10<sup>6</sup> m. The planet has no atmosphere. Calculate the speed at which the meteorite will hit the surface.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At the instant of impact the meteorite which is made of ice has a temperature of 0 °C. Assume that all the kinetic energy at impact gets transferred into internal energy in the meteorite. Calculate the percentage of the meteorite’s mass that melts. The specific latent heat of fusion of ice is 3.3 × 10<sup>5</sup> J kg<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the field lines/arrows are further apart at greater distances from the surface</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>circle centred on Planet X<br>three units from Planet X centre</p>
<p><img 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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>loss in gravitational potential = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6.67 \times {{10}^{ - 11}} \times 3.1 \times {{10}^{21}}}}{{1.2 \times {{10}^6}}}">
<mfrac>
<mrow>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>3.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>21</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>«= 1.72 × 10<sup>5</sup> JKg<sup>−1</sup>»</p>
<p>equate to <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>v</em><sup>2</sup></p>
<p>v = 590 «m s<sup>−1</sup>»</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>available energy to melt one kg 1.72 × 10<sup>5</sup> «J»</p>
<p>fraction that melts is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.72 \times {{10}^5}}}{{3.3 \times {{10}^5}}}">
<mfrac>
<mrow>
<mn>1.72</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>3.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = 0.52 <em><strong>OR</strong></em> 52%</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<p><em>Allow 53% from use of 590 ms<sup>-1</sup>.</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">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br>