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<h2>HL Paper 2</h2><div class="specification">
<p>There is a proposal to place a satellite in orbit around planet Mars.</p>
</div>
<div class="specification">
<p>The satellite is to have an orbital time <em>T</em> equal to the length of a day on Mars. It can be shown that</p>
<p style="text-align: center;"><em>T</em><sup>2</sup> = <em>kR</em><sup>3</sup></p>
<p>where<em> R</em> is the orbital radius of the satellite and <em>k</em> is a constant.</p>
</div>
<div class="specification">
<p>The ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{distance of Mars from the Sun}}}}{{{\text{distance of Earth from the Sun}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>distance of Mars from the Sun</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>distance of Earth from the Sun</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> = 1.5.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by gravitational field strength at a point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting Mars.</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>Mars has a mass of 6.4 × 10<sup>23</sup> kg. Show that, for Mars, <em>k</em> is about 9 × 10<sup>–13 </sup>s<sup>2 </sup>m<sup>–3</sup>.</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 time taken for Mars to revolve on its axis is 8.9 × 10<sup>4</sup> s. Calculate, in m s<sup>–1</sup>, the orbital speed of the satellite.</p>
<p> </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>Show that the intensity of solar radiation at the orbit of Mars is about 600 W m<sup>–2</sup>.</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>Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The atmosphere of Mars is composed mainly of carbon dioxide and has a pressure less than 1 % of that on the Earth. Outline why the mean temperature of Earth is strongly affected by gases in its atmosphere but that of Mars is not.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force per unit mass ✔</p>
<p>acting on a small/test/point mass «placed at the point in the field» ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Mars is spherical/a sphere «and of uniform density so behaves as a point mass» ✔</p>
<p>satellite has a much smaller mass/diameter/size than Mars «so approximates to a point mass» ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r} = \frac{{GMm}}{{{r^2}}}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> hence» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{GM}}{R}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>R</mi>
</mfrac>
</msqrt>
</math></span>. Also <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \frac{{2\pi R}}{T}">
<mi>v</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mi>R</mi>
</mrow>
<mi>T</mi>
</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="m{\omega ^2}r = \frac{{GMm}}{{{r^2}}}">
<mi>m</mi>
<mrow>
<msup>
<mi>ω</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> hence <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\omega ^2} = \frac{{GM}}{{{R^3}}}">
<mrow>
<msup>
<mi>ω</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p>uses either of the above to get <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T^2} = \frac{{4{\pi ^2}}}{{GM}}{R^3}">
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
</mfrac>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>uses <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = \frac{{4{\pi ^2}}}{{GM}}">
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p><em>k</em> = 9.2 × 10<sup>−13</sup> / 9.3 × 10<sup>−13</sup></p>
<p> </p>
<p> </p>
<p><em>Unit not required</em></p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{R^3} = \frac{{{T^2}}}{k} = \frac{{{{\left( {8.9 \times {{10}^4}} \right)}^2}}}{{9.25 \times {{10}^{ - 13}}}}">
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>k</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>8.9</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>4</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>9.25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>13</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> <em>R</em> = 2.04 × 10<sup>7</sup> «m» ✔</p>
<p> </p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega r = \frac{{2\pi \times 2.04 \times {{10}^7}}}{{89000}} = ">
<mi>ω</mi>
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mo>×</mo>
<mn>2.04</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>7</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>89000</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 1.4 × 10<sup>3</sup> «m s<sup>–1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{GM}}{R}} = \sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.4 \times {{10}^{23}}}}{{2.04 \times {{10}^7}}}} = ">
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>R</mi>
</mfrac>
</msqrt>
<mo>=</mo>
<msqrt>
<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>6.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2.04</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>7</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
<mo>=</mo>
</math></span>» 1.4 × 10<sup>3</sup> «m s<sup>–1</sup>» ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="I \propto \frac{1}{{{r^2}}}">
<mi>I</mi>
<mo>∝</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> «1.36 × 10<sup>3</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{{1.5}^2}}}">
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mrow>
<mn>1.5</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>» ✔</p>
<p>604 «W m<sup>–2</sup>» ✔</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{600}}{4}">
<mfrac>
<mrow>
<mn>600</mn>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> for mean intensity ✔</p>
<p>temperature/K = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt[4]{{\frac{{600}}{{4 \times 5.67 \times {{10}^{ - 8}}}}}} = ">
<mroot>
<mrow>
<mfrac>
<mrow>
<mn>600</mn>
</mrow>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>5.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mn>4</mn>
</mroot>
<mo>=</mo>
</math></span>» 230 ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>reference to greenhouse gas/effect ✔</p>
<p>recognize the link between molecular density/concentration and pressure ✔</p>
<p>low pressure means too few molecules to produce a significant heating effect</p>
<p><em><strong>OR</strong></em></p>
<p>low pressure means too little radiation re-radiated back to Mars ✔</p>
<p> </p>
<p><em>The greenhouse effect can be described, it doesn’t have to be named</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is 4.0 Ω.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPoAAAERCAYAAABSGLrIAAAS3klEQVR4nO3df1SUdb4H8HccjytcDmcXO0FS/FgYvNyb0pLcFekqGWmDGUilFZbcBW7mLYGw09kAXRfs14aAGemKSRu26TUcMiFdUtwN2LsmLZlyLw9ckQRkr42FHqY8yXP/EFgUUBhmeOaZz/t1jucIzzPPfJj5vp/vM8/3+zxzk6qqKojIqbloXQAR2R+DTiQAg04kAINOJMAkLZ40yD9g4P/NradGXOYs6wy33FnXGe/rd+0yso2btDjrHuQfwDeUhmC7sB8euhMJoEmPTkQTiz06kQAMOpEADDqRAJoEfaShG5KN7cJ+2KMTCcCgEwnAoBMJwKATCcCgEwnAmXFEArBHJxKAQScSgBNmyGGwXdgPe3QiARh0IgEYdCIBGHQiAZwm6DyRQzQyTYLOGwDScNgu7MdpenQiGhmDTiQAJ8yQw2C7sB/26EQCMOhEAjDoRAIw6EQCMOhEAnDCDDkMtgv7YY9OJICooHOclqSapHUBesGdxFA81NYPTYIe5B+gy0aix5rtxR47Pr22Cz0QdehOJBWDTiQAg04kAINOJAAnzJDDYLuwnxHPujvrcJKz/l1a4GvpOG60k7zu8Jqe9rCjbXTW/k1s1EPpqX04s9G0TX5GJxKAt5Iih8F2YT/s0YkEYNCJBGDQiQRg0IkE0OTqNb0Oy/BkkX3ptV3oAa9HHyU2QtIzUYfuDCtJJSroRFJxwgw5DLYL+2GPTiQAg04kAINOJACDTiQAg04kAG8lRQ6D7cJ+2KMTCcCgEwnACTPkMNgu7MdpenR+viMamdMEnYhGxqATCcCgEwnAoBMJwAkz5DDYLuyHPTqRAAw6kQCcMEMOg+3CftijEwnAoBMJwKATCcCgEwnAoBMJwAkz5DDYLuyHPTqRAAw6kQAMOpEAnBlHDoPtwn7YoxMJMEmrJ+7fe197pnW4vbre1xmpp3LGdWz1+pFt3aSqqjrcgiD/AA53EOnAaLLKQ3ciARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiARh0IgEYdCIBGHQiASZpXQDZT3t7O9ra2vC3ri4AwNGjRwEAISEhcHd3xy1eXvD19YWPj4+WZdIEYNCdjKIo+KTqE+ze9T4AYE5kJMLDwwEAjyxdCjc3N5w8cQIA8Omf/oT6Y8fQ1dWFpcseRcScCISGhmpWO9kPg+4k6urqsKmgAADwwOLFeHfnzhF7aoPBcNXPZrMZ9fX1eOWllwAAq9PSEBERYd+CaULdpKqqOtyCIP8ANLeemuh6aIza29vxVlERWpqbbRLQhoYG/HbrVpi//hq/zs0dslMgxzOarPJknI5VVVVhXuTdCA8Px9slJTbphUNDQ/FmURGSUlLwVEoKdpaW2qBS0hoP3XVqy1tbsHvX+zhS86ldTqZFR0cjJCQEL23YgMbGRmRmZcHV1dXmz0MTgz26Dm15awuOH/8C+ysr7XrG3MfHB6/n5eH8+fNYk5EBi8Vit+ci+2LQdaY/5K/n5U1ID+vq6orX8/IAABtyc+3+fGQfDLqO1NXVYfeu95GTmzuhh9H9YT9//jw/s+sUg64TZrMZmb/8JbZu2wZPT88Jf35XV1e8mJmJ7cXFUBRlwp+fxodB14mNeXlISk7WdLjLx8cHL2ZlYW1WlmY1kHUYdB1QFAW1NTWIf+ghrUtBdHQ0PKdORV1dndal0Bgw6DrwTkkJUtPSHGZ4Ky09fWAWHukDg+7gzGYzamtqsGDhQq1LGdD/8aGhoUHjSmi0GHQHV1lRgaXLHnWY3rxfUkoKDh44oHUZNEoMuoOrra1FxJyxT23tVUqwxH8esqvPjbQGuqvXYeY/rUN1d++Ytx8WFobKiooxP460waA7MIvFggMVlVZdOupieACpy4Hyqi/RPewaZtRXVQPx9yDMY+zNwNPTE15eXmhvbx/zY2niMegO7MyZM1gYY7Ty0Z4Ii44Cyg6jfpgeu7fjU+wuux0ZK2bDw8pnCLvrLrS1tVn5aJpIwwa9fy/Nuc3aOnfuHPz9/a18tAs85j6ODEM1dh86g6uj/h1aDu7BQUM05gROsbq+4ODggbvXkGMbEvRykwnzIu8GACwyGhl2Df2tqwvBwcHWb8DFD3OW3I6DOw6hZXDSe0+jdm8XHkt/AIZxHtN1dp4d3wbIahaLBVmZmQCA+VFR1/0YNeTGE/OjotDWetq+FdKo5RXkIzYuzvoNdFcje3YxgsqLscJwpffuVUrwUOwppP55HaKs+HzeT1EUGO9bYH1tZFMLY4x4s6ho2GU3vB59S/E2REdH27wourFyk2n8G/G4A/fGd6Gw5jSeMEyHC75DS80RXEpZhVnjCHm/RxMeR+6GDeOvk8as3GRCRlr6wM+NJ0+OuO6Qd3rDyy8P/H9hjBGRkZE2Lo8m1s2YuyIB2Ft35fD94nHs3wUsfWAG3Me55ZMnTiAkJMQWRZIVZoWHw9ffb+DnpOTkEdcdEvSIiAgcb7yyZ3izqMjhJmpIcouXF5qamsa9HZfACMThCGpbetD92Uco9Y/FfeM4CTeYu/t4dxdkLR8fH+wpKwMAfFBuQsLy5SOuO+yxG8PtGG6++Wa0traOf0MuBixJ/yk+qvkMn1V9CeOyuzHNBgOrTU1NuMXLa/wbIqv1X7J8o7kWHEd3YAaDAQcqKm0w8uECj7B/xT/uegV5x6OwZJZtrmevP3YMvr6+NtkW2ReD7uAWxhhtcvgOj9l4cpkXJi9ZgDvdx/+2t7e3o6uri9/yohMMuoNbEh+PulpbXPs9BYbEHdibON0mb3r14cNYuuxRG2yJJgKD7uDCwsLw+quvOtzEpY/27cO90fdqXQaNEoPu4Dw9PfHUqqcd6pLQ/rvL8Ftc9INB14G4JUtQWFDgML36poICrE5L07oMGgMGXQcMBgOMMTHY/MYbWpeCcpMJnlOn8ksYdYZB14lnnn0WlRUVmt6+qb29HRlp6Xix70IK0g8GXSdcXV2RX1iI9NRUTW72YLFYsOa557CleBuH1HSIQdeR0NBQpKal4YmEhAkNu8ViwZqMDMyLuocXOOkUg64zsXFxWLrs0QkLe3/IZ8yYiZVPr7T785F9MOg6tPLplQM9uz0/syuKgkVGI0PuBPj96DoVGxcH/4AApKemwhgTg2eefdZmFyNZLBYcPHAAhQUFeDEri4frToA9uo6FhoZif2UlgCu3/So3mcY11m6xWFBXV4dFRiOOHj2KPWVlDLmTGHIrqX5B/gFobj010fWQlRRFgWnvXmwtegtrXngBEXMiEBwcPKpevqGhAXW1V76SeU5kJFYkJnLWm46MJqsMupMxm82or6/H3rIyHKioxMIYI/z9/YfcZLKz8yzOnPkK7+98DwtjjJgzZw6i7rmHQ2c6xKATFEXBuXPnhtyW+R/c3eHn54fbbruNNxrRudFklSfjnJzBYOBhOPFkHJEEDDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAAw6kQAMOpEADDqRAJO0LoCcRS+6q9fj7sTfoWeYpW7Rq5Gz6jEsDvNm76IBvuZkY5HI/kMjmltP/f3f/9bh7Zknkb38VezruKR1gSIx6COoqqrCztJSrctwDi7emPXMGmQYjqDk4Cn0al2PQAz6NcxmM7IyM7F92zb8y89/rnU5TuZ7tDR34qLWZQjEoA9SVVWFh+PjERISgrdLSmAwGLQuycn8CIFBt8Jd6zIE4sk4AO3t7XhpwwYAwNZt2xhwW+s9i882v448ZR5yFgSwd9GA+KCXm0zISEtHXkE+YuPitC7HCdQg574Q5Fz1OzdMX/48NpXHI2raZI3qkk1s0Af34kdqPoWPj4/GFTmLSGT/oRgrDFMAdON/Sl7AI6/9gPtj78dcg4fWxYkl7ijKYrFgZ2kpnkhIwIIFC/BmURFDbjcemJ74MkpSzCh85D+wqf4brQsSS1TQFUXBLxIT0djYiD1lZTxUnxA/RlhqPvKMHdic+S7qL3JwTQsigt7fiz+VkoKklBTkbtgAT09PrcuSw8UXi7NfwILTW5C97RiH1zTg9EFvaGjALxIT0dHRgT1lZYiOjta6JJFcpsUg66UF+KrwFRTzEH7C3aSqqjrcgiD/ADS3nproemzGYrFg8xtvoLKiAvmFhQgNDdW6JCK7GE1WnbJHb2howCKjEQCwv7KSISfxnGp4zWw2Y3txMeqPHWMvTjSI0/To/dNXp02bhrdLShhyokF036ObzWZszMtDS3Mzp6/2CfIP0LoEh6Tnc07jpeugl5tMKCwoQFJyMjKzsuDq6qp1SQ5DcqMejvSdny6DPnj66rs7d3JmG9EN6O4zernJhHmRd3P6KtEY6KZHVxQFBfn5AHgRCtFYOXzQLRYLyj74ANuLi/FiVhZnthFZwaGDrigK1mZlITAoCHvKyjg/nchKDhv0naWl7MWJbOS6Qdd6SOIv9cc07cW1/vvJtiS/nyMGneOw+n0NJDfo69Hr+2kLuhteI6KxY9CJBGDQiQRg0IkEcJKgd0OpLkG28Z8R5B9w5Z8xC+9UK7w/GREceBx99L5BfX4SEk/ch7d3fI4c78kAenFR+RCvrl6GZZ9vxa70cHFfA8Qz7zTYiPeM043uamTPXgcUfYCcqJsHLej7vu5VwKY/r0OUh5McvBBZQfc9em9XK77sAe4YssQFHlHr8cVJDYoicjC67+ZcAucj0XgJv09MQnaJCdVKt9YlETkc/R+6A+g9exTvbc7Fr0q/6PuNN+anpmHRz8Jwb5RB3Odzoms5RdAHXFRQXXUC50/tx7rCKvTADdNXbML2dffCW/fHLtrp7TDhmeh8TB1yHuRa3VA+eQe/eXYjDvUAwEw89qt0PPnwXBjcR3gDes+ifv8R/LG8AJurzg782i16NdbHzkPEojC+d7agOqvLnerRwmR1hl+CWtJk0boa/bp8WjWtnK0G+s1Vsw7/3/VXbdqhxoUkq5v+0qleVlVVvfClWpI0W52ReVj9drj1O2vVTUmz1UC/2WrKxr3qsc7vryy40KR+sjFZneHnrwbev1Y1NQ33aBoL591XunhjVmICYt0+h6nmNPjVfta4hI4P85HT+hME3nDd79BSU4WW+ASsCPe+cvLHPQRLli8Ayg6jvvuad6C3DfvWP4fCKmD+r4qxMT0OYd59353ubsD89DfxcUEc3Bp/h4zV7/DLGcdJ50H/DkrJcgTFlkAZsR38DHGRfnr/QzXR21GB3PVA5poH4XbDlU+jdu9JBAbdOuiciAvcfQIQ2NOC012XBq+M7j9uR3blWSDkcax8OGSY8yiTMe3BlcgIdQMatyBnj8Kd9TjovP1PgeHhVDxzaRPS1pZcfcb9ooJD23fhy0f+DQsDp2hXol71tmFfzm+BdelY7Gv96+fi5Y873L5Cc/vgOYo9aP78KHoAuN01A0EjfX538cGMKD8APWhp7uQsx3HQ/Tg63MOR9p+7cOfBj/BebCiSe/p+H5KA7FUpeIsnc6zQd8iOf8eHD/rCpWUUD7nYiWbl+zE/0+SpHtc5WpiCaQFBABrRc/Yb9ADwGPMzEOAMQQcAdwOi4tMRFZ+udSVOof+QPXt/DKa5wCEOmd28f3zjjw80IvZ1dLXBh+zTJo/+ce63Isjwo1Gu7IbgeUZMB3Dp6270jLjeN/jvzxoA+CI2+g725uPAoNNVelsOoaSyEQfT5iG470rA4PvW4zja8PvEcMzMqsZY5h5emaJ8O4J8Bp9uc4H7nQ/h+RUz0VNWjsMdl4Z/bMen2F3WBjdjOp6ee73xe7ohrcf3yPFdbtqhxt1wHN2iNu1IuGbM/LL67eG16oyQterhby8Ps+G+uQ5DxsovqxeaDqr5SXPVmMy9atOFYR5LY8IenWxkCgIjoxFYmo+N1R3oBdB79r/wTmk1bk95ALMGXz34Qz3eSDehA96YtXob/rpjLj5fvQ7lZ3/oW/5XFD9Zhp88vw/7c+NgcO9Gff6rf19OY+YcJ+NIA99BKUmG8bVAFPddBuxiiMdr2y/gN6siEdwDXLnm4NcoSLlryDj55ep0zP3p4JOnkQi48APgPQk414aTnR/j0MKPkTOwfDHyHpuAP8tJOddcdyIaFg/diQRg0IkEYNCJBGDQiQT4f2UkTSUZF0GDAAAAAElFTkSuQmCC"></p>
<p>When S is open the reading on the voltmeter is 12 V. When S is closed the voltmeter reads 8.0 V.</p>
</div>
<div class="specification">
<p>Electricity can be generated using renewable resources.</p>
</div>
<div class="specification">
<p>The voltmeter is used in another circuit that contains two secondary cells.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPkAAAE8CAYAAAACHRcjAAAdV0lEQVR4nO3dfViUZaI/8G9z9esAESVxwkJlcGZkJUBjZRPtKCZavsWLZquSsgmm7laYltfJUdfUShNB7Zyzpa24aYYpL+XLL0KcXIHyhV8e0F0dJkAD4bdINXLAZfOZ8wcvy9vwMjMwM/fz/VyX11XzvMw9M/f3ee7nvu/n4S6TyWQCEQlLYe8CEFH/YsiJBMeQy51Rh7UBjyI69QokSDDq1iNYGYt9+ts9bFgDnXYi1L1al+yJISeLSJVncOhYCH732ztI2vc1jPYuEJnFkJMFbsOQfRhnZszEnNARQPopFBolexeKzGDInV2dHrnJCQhW+kGt9ENw/C7k6tueV43Qn9yFJQFNy9XTtNhfWAWrIimVIz/jMlTqIXgkZBIiocPJwlorPwj1F4bcmUnXkPXaQiRemohPiw0o+S4PO31ysCQyCTqjBKARlZnrMXtbDWZkXURJmQHfpvwCp2N/i52FP1r+toYCZF4MQNR4Xyg8AjE5BsjKKWaT3UEx5E5MMuQi9YQKK1fPgb+7AlA8gvANWSi5vAHhHgrAmI//eqMQkatfQqTGA4AC7v5z8NrrrnhvQyb0Fp3Ob8OQl4OiUREYp3IB4ImQiHA22R0YQ+60msPmpoKv9z1dLJdgLDyFrPqhUPu4t3n9HngrVXC7mIN8gwW94nVFOJZWjXkrZkKjAAAFPEImIRKHsSNdb91lAPWLu+1dAOpvedg4ZSQ2dnp9vAX7kmA8fxR//EsJ6uNCcbDj4owCGBb6N4efHAVD7uzqDSivbgQ8XLpe7rYQe75e39R870qfLqRrUZijA2L3onBTODzaLJH0qZg9JQf5hl9DozFTFrILHnOdlgtU4yMQZHZ5SzO6Y89384SXgPXNnXN9YCzGyXQvvBAzul3AAUChCkPUqMvIzCtnk93BMOROTKF6EnHTDEjachhX6pp606t0mzGjZRaax2hEJ3jh4JZdyNIbAUio03+Gd7fo8MRbizHB3Nm9S83X+JpZmDH6gS4K44tx0QEoSsvGt3WMuSNhyJ2ZYhgi3/0TUh79Cs8GqqBW+mPqfjcsSd+G5zUuAB5AyIq9OLHKC8ciR0GtVGF05DE8uGoPtkYN69uPL32PU2k6qKLDoOpyQxeops7B1PLDyDjPMXNHchdvNSUSG8/kRIJjyIkEx5ATCU7W4+RqpV/rf5eUlXb5eluOtE7b5aKuY6/vuGM5nZ2sO97USj/hflCyjoh1gs11IsEx5ESCk3VznUgOeCYnEhxDTiQ4WYfc3NAKyZeIdULWISeSA4acSHAMOZHgGHIiwTHkRILjZBgiwfFMTiQ4hpxIcLIOuYgTH8g6ItYJWYecSA4YciLBMeREgmPIiQTHkNuYiB035NxkHXLRHthH1hOxTsg65ERywJATCY4hJxKcrEPOTjLqSMQ6IeuQE8kBQ04kOIacSHAMOZHgZB1yESc+kHVErBOyDjmRHDDkdiDiMA05rrvtXQDqPR4cOhOxeW1rsg65WunndJXE2crbn/rjoOeMdaInbK4TCY4hJxIcQ04kOIacSHCyDrloHSxkPRHrhKxDTiQHNhtC4xhu3/D7sg1+j026a4HYdJxcxKZOX/W20lnyXbFCd8Y613O9kHVznaGhjkSsE7IOOZEcMOREgmPIiQTHkBMJTtZ3oTkjETuGqH/JOuTONvzibOV1RiJ+x2yuEwmOIbcDEc8W5LhkHXJe31JHItYJWYdcrqTKTCx/bD10RqmnNVGn/xIp8WFQK/2gVj6KGdpU6PTG7reqKsTR9GQsCfBr3s4PamUYliSn4WhhFXp6V7IthlxmpKqTeHPxGmT/vTcr63Fk1SZcDt6OM9+VoqSsANvV3+DlyCQzB4hGVJ37A5Y+ORuJ2ssIeOtI83YGfPvlmwi4lILEmMmYpc2Evo5RHygMuWwYoT/5H1j/QT3Cn32sV1tIhgJk6sMxP+5xDFYAgAf8Y55DJHQ4WVjbef3K43hz0Rbk4mmszUhCYlRI83YKuGumIPGDNCRN88CV/WuQuPsC6mz58cgshlwWJBh1SZh38H7EvjoZPr361W/DkJeDIo0ffNzbbOD+MNSaWyguu9mh2V2D0/+ZjOx6N/gnvIDZ/h6dd6kYhlmvvogg1OPKjh04or9t1aei3mHIZUEB94BlOP5BLPzdrfzJFQ/CN+g+GEputD8T/3wN3x67BsALIY/5wd3c5n7BmDgIAK6jpILn8oEg65DLaShL8dBgPNSnX7sOFSXXLXine/Ggh4v5xXc/BL9fDgJwC9U/Ot6ZXMQ6IeuQkz3dB+8HujkYkM0w5GSGO3zUQ3u/+t3DMWFhCID/wU1jN2doYwnO5/8AuIVjcoin1aWknsk65CJOfOh30k2UF92CSv1wh+vuBzB63nLEjqxBVtoZVHY5QtaIytwsZNUPxtS3FmOCh+NVPxHrhON9y05OnGs6F6jGRyBIX4qKtmPadTdQor8PgcoHO1UexeDJWLd3DxL+kYyEdR3Hwo3Qn3wfv3/jO0SmpGJr1DBWvgHC75nMUqjCEKX5HO8mnUKVBECqwvnUA8jynYPoMe2b2j8X/gGvZl4DBofhpT1f4sOIS0hM/AxVrcs/RNzBQVh5NgMbo/zhXncOKdrPW5dT/2HIqZWkT0W0ciLW6mqaXlBoMHvbFkyp0OKJ4X5QDw/DC/8djJSdixDSaSiuAacTJ2KE0g9qpT+eiNuDK3/7EbckAPgZNddKUZ2zFjMCVU3TXAPn4r2qOwP8CeXpLpPJZLLFjpzxT746Y5mpfzljneipzDyTW8DsDR51euQmJyC45aaMaVrs0+k7TN+8DX1qLNQB3d0gUgOddiKCtTp0fysIUc9kHXJLjtjmb/C4Df3hDUi89Ev88esrTTdlpPwCecvjsaWl+QsAcIEmJh7zzMz/BgAYi3EyHYiMCEQXk0OpHznbWbw3ZB3yvunhBg+pHPkZ1YiMnYMxg+8BoIC7/9OYHwNk5RS3PyN7BGJyV68DaB1m0vwGCyd49deHIRlhyHul5xs8JEMBMi96Q+3TdvS4aUJJfVEZqtu1zL0wYdFvoErPwqnKxg47KsWXe7+CKjoMKv46ZAOsRr1i6Q0e98BbqYJbx7FmtAxPfYXU7NJ2d3M13d45C6/EaPjjkE3Iuh71ZXZT9zd4SKirKIWhL2+u0CB6xSwYMgpgaE150+2dhphJCHHA2WBywBlvZEMKeIRMQqQ+B/mG5rneUjnyM+7ghZjR7HAjm2HIbUIBdx8/qPq6mcdYLHz9/yAzrxwSJNR9m41DeAozRj/QH4UkmWLI+1UjqssMqO/4dJVWLlCNnwhkFMAg1eJ8eg58f/MkO9zIplidbEShCkPUqOoOTztpevCCW5AS3ma+aYVmJl4JKkT+hbM4eWw05j45hD8K2ZSs65NNJz4ofDEu2hsHt7wPXVUjmp5cehgfp3v1cI3tiZCIf8Whde+heOFMjGGHm12JOBlG1n8LzbZcoJmzHh/8sBUvj/VHPQC4ReB3u95BfEh319gKeEyYi7nJ3wEzg8w+G43IUrK+QYVIBLxBhUjmZB1yESc+kHVErBOyDjmRHMi+463lyN32msbc0dyR1ul4DSbiOvb+jkXBjjciJ8eONyKZY8iJBMeQEwmOIScSHENOJDiGnEhwDDmR4BhyIsEx5ESCY8iJBMeQEwmOIScSHENOJDiGnEhwDDmR4BhyIsEx5ESCY8iJBMeQEwmOIScSHENOJDiGnEhwDDmR4BhyIsEx5ESCY8iJBMeQEwmOIScSHENOJDiGnEhwDDmR4BhyIsEx5ESCY8iJBMeQEwmOIScSHENOJDiGnEhwDDmR4O62dwFoYOn1ely+dAnnzp3DDz/8gC+On2i3PPTxX0GlVmPkyJEIDArCiBEj4OrqaqfSki3cZTKZTLbYkVrph5KyUlvsimystrYWJ44fx4d79sDb2xszZ83CcJUKXl5e0Gg07datqKhATU0NykpLkZ2djS+On8CLy5chKjq607rkGHrKHkMusNraWhxKO4RtW7Zg1erVmPXMLPj4+PR5H38+fRqfHDwIlVqNRXFxDLuD6Sl7vCYXVE5ODubExAAAzhZewNJlS/sccADw9PREZFQUDqalIXzSJLyYkIB3t25FQ0ODrYtM/YQhF0xDQwO0a9bgw9278f7u3Vi6bCk8PT1tsu+IiAgcO9F0Df9CXBwqKipssl/qXwy5QBoaGrBq5Urcf//9+GNqar80q11dXfHa669jcUICnl+wgEF3AuxdF0RLwIOCgrF02dJ+f7+IiAjce++9eH7BAnx04IBFlwI0MHgmF8RABrxFWFgYNr/9Ns/oDo4hF8CB/fsBYEAD3iIsLAyL4+Px1ubN7IxzUAy5k9Pr9fhwzx5s3LTJbmVYEBuLQYMGIfuLL+xWBjKPIXdy67RavKHV2qwH3VKvrlyJlYkrUFtba9dyUGcMuRMrKCgA0NQJZm+enp7YsGkjDqUdsndRqAOG3IntTEnBy4mJ9i5Gq2nTp2Pbli08mzsYhtxJtfRmh4WF2bkk/+Tp6YlVq1fjz6dP27so1AZD7qR0p05h5qxZ9i5GJ2HjwvDJwYP2Lga1wZA7qfz8fPzq8cf7vJ2kT0W0ciLW6mrMrQGjbj2CA9ZDZ5T6vP9Ro0bh3Ddn2WR3IAy5E2poaMAXx09YNG1VoZmJV2KBrJxiGLtcoxaFOTogZhJCPCyrHr9eMB/Xr1+3aFuyPYbcCX3//fd4avo0C7f2REhEOJB+CoVdnKmlyjM4lD4UKxeNhYeF7xAaGoqyUt527ChsEvKWoZycnBxb7I56UF9fj0GDBlm4tQIeE+ZjpUaHQ7nfo33Mb8OQfRjZmgiMU7lYXL573d1x40aVxdtT77VkrrvsWR3ynJwcPD9vPgBgaXwCsjIzrd0l9aCstBShoaGW70Dhi3HRQ5G9NxeGtimXypGfUY15K2ZCY0XN8PX1xfffs7ne37IyM7E0PgFA99mz+skw2jVr8MmBj63ZBVnIqifxGHVYO3YP1Fl7sEjTdNaW9KmYHVmKV75ej3ALr8eBpqm206ZMtbxsZJFfL5iPTZs3d3rd6ltNQ0ND24V81erVdrlRQk5s0lryCMTkmGrsyCvH8xp/KHAbhryv0JiwHGOsCHgLcxWObCcrMxMrE1e0/v+QIUO7XM/qX3PqU09h1erVAJoCvihukbW7pB485O2Nq1evWrkXL0xYtADIKGhqstcV4VgaMHdmENyt3HNNTQ3uv/9+K/dCPelt9qwOuaura+uZe+mypXx87wDw8vLCTz/9ZPV+FKowROEr5BvqYTx/FPuVkZhiRYdbi/9fXY0RI0ZYvR/qXm+zxyE0JzRkyBDb9IMoNIheMRxH887jfE4xpj33BB6xQY24evUqHvL2tn5HZBMMuRNydXVF6OO/ssHTWBTwCPk3/CLtHSQVhSN6jG1uVz1x/DiGDRtmk32R9RhyJzUxfBLOnztn/Y48xmLhc964J3oqRrtbXx0qKirg7e3NZ745EIbcSdnuRhAXaOL2IiPO3yaVwVFvnJEzhtxJjRo1CkDTmLSjaGhowId79iB80iR7F4XaYMid2K/nzcO+1FR7F6NV9hdfYNz48WyqOxiG3IlNfeop5Ofl4eLFi/YuChoaGrAjJQWL4uLsXRTqgCF3Yq6urtj89tt456237P445Pd27cK06dP5xxAdEEPu5MLCwqBSq/Herl12K0NBQQFOHD+O3730kt3KQOYx5AJYo9Wi8MIFu9wBWFFRgefnzcf7u3dztqODYsgF4Orqim3bt2NHSkrrvf0DoaKioulvoR38mM10B8aQC8LHxwcfHTiANf/+761/Nqk/Xbx4Ec8vWIDNb7/tUE+Mpc4YcoG0BD0/Px/aNWv6rTMuKzMTK155hQF3Egy5YHx8fLAtKQlDhgzFjGnTbPpILr1ej98uX47s7Gx8dOAAA+4krH4yTAu10s+6J5WQzen1eqzTagEALycmYvTo0RZ1jl28eBGfHjqE/Lw8vKHVOsSfZaJ/6il7DLkMFBQU4NjRo/jkwMd4cfkyPBYSgpEjR5qdmVZbW4vr16+jIL8Ah9I+gbe3NxYnJGD8+PHsQXdADDm1qq2tRWFhIf5fYSEKL1zAuW/OYpjSF+PGjwcAGEpK2r0WGhqKMaGhnKbq4Bhy6lZtbS1u3rwJAHBzc2OgnVBP2bP6QY7k3Dw9Pe3+t82pf7F3nUhwDDmR4BhyIsEx5ESCY8iJBMeQEwmOIScSHENOJDiGnEhwDDmR4BhyIsEx5ESCY8iJBMeQEwmOIScSHENOJDiGnEhwDDmR4BhyIsEx5ESCY8iJBMeQy5lRh7UBjyI69QokSDDq1iNYGYt9+ttdri7pUxGt9IO647+ABKRkFqJKGuDyU68w5NRHwzAv9RxKykqb/xnwbdYM3Hw/Hsv+dAXMueNhyMlKCrhrnsbC5wJQlFEAA1PucBhyZ1anR25yAoKbm83B8buQqzeaWf4oZmg/RmFVY78Vxy1ICW/WKIfDn8RZSdeQ9dpCJF6aiE+LDSj5Lg87fXKwJDIJOqPUvDweSTdn4EixASVlBdiu/jPifvM+CutsebqVUKf/v/jTmSDs/N04eNhwz2Qb/DNJTkoy5CL1hAorv5wDf3cFgEcQviELJRsAQIJR9yHWfhWOnV8/A427AoAH/BcmYmXGPGw8PBVH4vwtPMJfw8G4UBzs+PLIhRhz6zYw+B6rPhfZHs/kTuk2DHk5KHJTwde7q1DVojBHh3qNH3zc2/zEigfhG3SfldfOHTveSnH164/xik82Vr68z8atBLIFnslFdnEDpg3f0Pn1UbZ9G8XgMPx29YvInbIXGefnISTcy7ZvQFZhyJ1ZvQHl1Y2Ah0uXi91i9+LMpvABuU5WeCsR6DYAb0R9xua6U3KBanwEgswu90RIRDiQfgqFxrbN5xrotBMRrNXBaHZby0jVZSiuHwq1j7uN90zWYsidlEL1JOKmGZC05TCu1EkAGlGl24wZyljs0zfCY8xMvOD7Od7d+hn0dRIAI/SZu/Buegg2LrdxL3jdJXy05X0YYuMRrem6VUH2w+a6s1IMQ+S7f8J9u7fi2cC1qAfgFvEyNqZvwyyNC4BQJH6ahuDdWzE7cEXz8leRkrUSTz5iTQ94V73rwZi3cSeyF4RyCM0B3WUymUy22JFa6YeSslJb7IqI+qCn7LG5TiQ4hpxIcAw5keAYciLBybp3Xa30a/3vth0XbV9vy5HW6djRIuI69vqORetAlnXvujOWmfqXM9YJ9q4TyZysQ+5sR2zqfyLWCVmHnEgOGHIiwTHkRIKTdcjNDa2QfIlYJ2QdciI5YMiJBMeQEwmOIScSHENOJDhZh1zE2U1kHRHrhKxDTiQHDDmR4GQdchEnPpB1RKwTsg45kRww5ESCY8iJBMeQEwmOIbcxETtuyLnJOuQiTnwg64hYJ2QdciI5YMiJBCfrkPP6mToSsU7IOuREcsCQEwmOIScSHENOJDiGnEhwsg65iBMfyDoi1glZh5xIDhhyOxBxLJYc1932LgD1Hg8OnYnYvLY1WYdcrfRzukribOXtT/1x0HPGOtETNteJBMeQEwmOIScSHENOJDhZh1y0Dhaynoh1wqa96xzi6T1+V7bB77FnNgu5iEdAS/S20lnyfbFCd8Z61zNZN9eJ5EDWIeeZkToSsU7IOuREcsCQEwmOIScSHENOJDhZ34XmjMMvInYMORJnrBM9kXXInY2IFZD6H5vrdsCw0kBiyIkEJ+uQ8/qWOhKxTsg65ERywJDLRZ0euckJCFb6Qa30g3qaFvt0etR1u5GEOv2XSIkPa9pG+ShmaFOh0xu736qqEEfTk7EkoPm9lH5QK8OwJDkNRwurINnyc1GPGHI5kK4h67V4JN2cgSPFBpSUXcGZN4cgb/lCvJ55zXzoJD2OrNqEy8Hbcea7UpSUFWC7+hu8HJkEnbGrrRpRde4PWPrkbCRqLyPgrSPN2xnw7ZdvIuBSChJjJmOWNhP6OkZ9wJhkTOWrdIp9WuvO1b2mKN8FptSrDW1ebTBd3bvApHpmr+nqnW62G7nOdOqnNiv8dMqkHTnBpD31t87rV2SYlo1UmlQjl5pS//pTFzssN2UuHWtS+QaYpm8/a7pl3cfqF474+1mLZ3IZUGjikFG2H4s0Lp0X6ktR0eVZ9TYMeTko0vjBx71NNXF/GGrNLRSX3ezQAqjB6f9MRna9G/wTXsBsf48uCjIMs159EUGox5UdO3BEf9u6D0a9IuuQy3u8ug4VJdeBjiHuieJB+AbdB0PJjfbX8z9fw7fHrgHwQshjfnA3t7lfMCYOAoDrKKnovkfAHkSsE7IOuZxJlWdwKB2Yt2ImNF3WguaDQJ/diwc9umgxtLj7Ifj9chCAW6j+kWfygcBprXIkXcPnG5NRnrANW8O97FSI++D9QDcHA7IZWZ/JRZz40COpEroNL2EtVmD3K6Fmm9WAO3zUQ3u/37uHY8LCEAD/g5vGbs7QxhKcz/8BcAvH5BDP3u9/gIhYJ2Qd8v7g0Nd0dVeQtW4ZXq54Fp+++wweseTXl26ivOgWVOqHOxwgHsDoecsRO7IGWWlnUNnlCFkjKnOzkFU/GFPfWowJHqx+A4HfskxIVSfx+2djsLbqWXyaMh/+PXa2uUA1PgJBHXvf626gRH8fApUPdqo8isGTsW7vHiT8IxkJ6zqOhRuhP/k+fv/Gd4hMScXWqGGsfAPF3mN49iTimGiXbp01JT8dYFI9vdN04ZaZQfGu3PmrKfWZx0zT1+WYbtwxmUx3bpjO7Yg3BXWxn39c+C/TioxyU9OrfzfdOLXJNH1xhulG6/LtpnGLPzL9tWW7W2dNyWs+a13uKESsEzyY9oFUmYnlAROxVlfTw5pG6E/uajOtMxJrU3WdZnlJ+lREK7vbnwSjbj2CA9abmWHWG7ehP7wD7/2lHvjLdswNVLWZauoHtTIW+5rHqzuVR6HB7G1bMKVCiyeG+0E9PAwv/HcwUnYuQkinlkADTidOxAilH9RKfzwRtwdX/vYjbkkA8DNqrpWiOmctZrS8f+BcvFd1x8LPRH1i76OMPfXpqN06W6vr2V7tVr261xQ1Mt608+yNpjPbrWJT6uKxpqA1p0zt54H9zXRqzYQuXu/tcrI1nskF0/tOskZUfpaMjWWDoOpx3aaZYoaYBVgUOrjputN9JKJjpwLpp1DY7ozsiZCI8C5eb9I0lj0UKxeNRRfzx6gfOHTHqYVkHfLekiqPY9MGYM2qZ+DW48rlyM+43KH3WQF3Hz+o6g0or25ss7ICHhPmY6VGh0O533eYJnobhuzDyNZEYJyK48lkOYa8J9I1fL7xA2D9CswaZnnYFN5KBLp1MZVT4Ytx0UORvTcXhrYpl8qRn1HdzYw0ot6RdfXpeeJDczMdS6B9ppdDPnU3UKL/ex9K4QJNTDzm6XOQb/jnJBLJUIBM/TiHnDAiMk6GkZmWZvratdMtmzjSWx6BmBxTjcy88uYm+20Y8r5CY8JMjOGEEbISa5A5bZvpj9zT++3cH4Za8y99fDMvTFi0AMgoaGqy1xXhWBowd2ZQN9NOiXqHN6iYIRlykXriLyg6MREjEtsvK4oLRVbsXpzZFN7rXm+pugzF9UMR5dN1bBWqMEThHeQb5sK74ij2KyPxGTvcyAYYcjOaHrQQ1+41SZ+K2VP2IjD1CDaau3tL4Ytx0QFIKrmBOvg3HwQk1FWUwuCmgq+3mVaBQoPoFcOxOO88hpYUY9pzL/XvJQLJBquRzTXN+VbtT8Z2XSUkAFLVN9i3X4eh3V5jK+AR8m/4Rdo7SCoKR/QYdriRbcg65DaZ+CBdwb7IRxGs1aHlGaYKTQy2fhiByuXjMULphxFjX0XRo1qkJPyy+2tsj7FY+Jw37omeitF9eVoL2YyIk2HuMplMJnsXgoj6D08XRIJjyIkEJ+uQizi7iawjYp2QdciJ5ED24+QtR+62varmjuaOtE7HXmAR17H3dywK9q4TCY7NdSLBMeREgmPIiQTHkBMJjiEnEhxDTiQ4hpxIcP8LAa9eLW55w1kAAAAASUVORK5CYII="></p>
<p>Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.</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>State the emf of the cell.</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>Deduce the internal resistance of the cell.</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>Calculate the reading on the voltmeter.</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>Comment on the implications of your answer to (c)(i) for cell B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why electricity is a secondary energy source.</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>Some fuel sources are renewable. Outline what is meant by renewable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.</p>
<p>The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m<sup>−2</sup>.</p>
<p>The overall efficiency of the re-charging process is 18 %.</p>
<p>Calculate the minimum time required to re-charge the cell fully.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why research into solar cell technology is important to society.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>« conservation of » charge ✓</p>
<p>« conservation of » energy ✓</p>
<p> </p>
<p><em>Allow <strong>[1]</strong> max if they explicitly refer to Kirchhoff’ laws linking them to the conservation laws incorrectly.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>12 V ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>I</em> = 2.0 A <em><strong>OR</strong> </em>12 = <em>I</em> (<em>r</em> + 4) <em><strong>OR</strong> </em>4 = <em>Ir <strong>OR</strong> </em>8 = 4<em>I</em> ✓</p>
<p>«Correct working to get » <em>r</em> = 2.0 «Ω» ✓</p>
<p> </p>
<p><em>Allow any valid method.</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>Loop equation showing <em><strong>EITHER</strong> </em>correct voltages, i.e., 10 – 4 on one side or both emf’s positive on different sides of the equation <em><strong>OR</strong> </em>correct resistances, i.e. I (1 + 2) ✓</p>
<p>10−4 = I (1 + 2) <em><strong>OR</strong> </em>I = 2.0 «A» seen ✓</p>
<p><em>V</em> = 8.0 «V» ✓</p>
<p> </p>
<p><em>Allow any valid method</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Charge is being driven through the 4.0 V cell <em><strong>OR</strong> </em>it is being (re-)charged ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>is generated from primary/other sources ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«a fuel » that can be replenished/replaced within a reasonable time span</p>
<p><em><strong>OR</strong></em></p>
<p>«a fuel» that can be replaced faster than the rate at which it is consumed</p>
<p><em><strong>OR</strong></em></p>
<p>renewables are limitless/never run out</p>
<p><em><strong>OR</strong></em></p>
<p>«a fuel» produced from renewable sources</p>
<p><em><strong>OR</strong></em></p>
<p>gives an example of a renewable (biofuel, hydrogen, wood, wind, solar, tidal, hydro etc..) ✓</p>
<p> </p>
<p><em><strong>OWTTE</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE</strong> <strong>1</strong></em></p>
<p>«energy output of the panel =» <em>Vlt <strong>OR</strong> </em>6 x 5 x 0.25 x 3600 <em><strong>OR</strong> </em>27000 «J» ✓</p>
<p>«available power =» 380 x 0.4 x 0.15 x 0.18 <em><strong>OR</strong> </em>4.1 «W» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>27000</mn><mrow><mn>4</mn><mo>.</mo><mn>1</mn></mrow></mfrac></math>=» 6600 «s» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>«energy needed from Sun =» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>v</mi><mi>l</mi><mi>t</mi></mrow><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>×</mo><mn>5</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><mn>3600</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>18</mn></mrow></mfrac></math> </strong><strong>OR</strong> </em>150000 «J» ✓</p>
<p>« incident power=» 380 x 0.4 x 0.15 <em><strong>OR</strong> </em>22.8 «W» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>150000</mn><mrow><mn>22</mn><mo>.</mo><mn>8</mn></mrow></mfrac></math>=» 6600 «s» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong></em></p>
<p><em>Accept final answer in minutes (110) or hours (1.8).</em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>coherent reason ✓</p>
<p>e.g., to improve efficiency, is non-polluting, is renewable, does not produce greenhouse gases, reduce use of fossil fuels</p>
<p> </p>
<p><em>Do <strong>not</strong> allow economic reasons</em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>a) Most just stated Kirchhoff's laws rather than the underlying laws of conservation of energy and charge, basically describing the equations from the data booklet. When it came to guesses, energy and momentum were often the two, although even a baryon and lepton number conservation was found. It cannot be emphasised enough the importance of correctly identifying the command verb used to introduce the question. In this case, identify, with the specific reference to conservation laws, seem to have been explicit tips not picked up by some candidates.</p>
<p>bi) This was probably the easiest question on the paper and almost everybody got it right. 12V. Some calculations were seen, though, that contradict the command verb used. State a value somehow implies that the value is right in front to be read or interpreted suitably.</p>
<p>bii) In the end a lot of the answers here were correct. Some obtained 2 ohms and were able to provide an explanation that worked. A very few negative answers were found, suggesting that some candidates work mechanically without properly reflecting in the nature of the value obtained.</p>
<p>ci) A lot of candidates figured out they had to do some sort of loop here but most had large currents in the voltmeter. Currents of 2 A and 10 A simultaneously were common. Some very good and concise work was seen though, leading to correct steps to show a reading of 8V.</p>
<p>cii) This question was cancelled due to an internal reference error. The paper total was adjusted in grade award. This is corrected for publication and future teaching use.</p>
<p>di) The vast majority of candidates could explain why electricity was a secondary energy source.</p>
<p>dii) An ideal answer was that renewable fuels can be replenished faster than they are consumed. However, many imaginative alternatives were accepted.</p>
<p>ei) This question was often very difficult to mark. Working was often scattered all over the answer box. Full marks were not that common, most candidates achieved partial marks. The commonest problem was determining the energy required to charge the battery. It was also common to see a final calculation involving a power divided by a power to calculate the time.</p>
<p>eii) Almost everybody could give a valid reason why research into solar cells was important. Most answers stated that solar is renewable. There were very few that didn't get a mark due to discussing economic reasons.</p>
<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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>One possible fission reaction of uranium-235 (U-235) is</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">U</mi><mprescripts></mprescripts><mn>92</mn><mn>235</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi mathvariant="normal">n</mi><mprescripts></mprescripts><mn>0</mn><mn>1</mn></mmultiscripts><mo>→</mo><mmultiscripts><mi>Xe</mi><mprescripts></mprescripts><mn>54</mn><mn>140</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>Sr</mi><mprescripts></mprescripts><mn>38</mn><mn>94</mn></mmultiscripts><mo>+</mo><mn>2</mn><mmultiscripts><mi mathvariant="normal">n</mi><mprescripts></mprescripts><mn>0</mn><mn>1</mn></mmultiscripts></math></p>
<p style="text-align: left;">Mass of one atom of U-235 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>235</mn><mo> </mo><mi mathvariant="normal">u</mi></math><br>Binding energy per nucleon for U-235 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>7</mn><mo>.</mo><mn>59</mn><mo> </mo><mi>MeV</mi></math><br>Binding energy per nucleon for Xe-140 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>29</mn><mo> </mo><mi>MeV</mi></math><br>Binding energy per nucleon for Sr-94 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>59</mn><mo> </mo><mi>MeV</mi></math></p>
</div>
<div class="specification">
<p>A nuclear power station uses U-235 as fuel. Assume that every fission reaction of U-235 gives rise to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mo> </mo><mi>MeV</mi></math> of energy.</p>
</div>
<div class="specification">
<p>A sample of waste produced by the reactor contains <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>kg</mi></math> of strontium-94 (Sr-94). Sr-94 is radioactive and undergoes beta-minus (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">β</mi><mo>-</mo></msup></math>) decay into a daughter nuclide X. The reaction for this decay is</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>Sr</mi><mprescripts></mprescripts><mn>38</mn><mn>94</mn></mmultiscripts><mo>→</mo><mi mathvariant="normal">X</mi><mo>+</mo><msub><mover><mi mathvariant="normal">v</mi><mo>¯</mo></mover><mi>e</mi></msub><mo>+</mo><mi>e</mi></math>.</p>
<p> </p>
</div>
<div class="specification">
<p>The graph shows the variation with time of the mass of Sr-94 remaining in the sample.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="576" height="367"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by 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>Outline why quantities such as atomic mass and nuclear binding energy are often expressed in non-SI units.</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>Show that the energy released in the reaction is about <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mo> </mo><mi>MeV</mi></math>.</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>Estimate, in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, the specific energy of U-235.</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 power station has a useful power output of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo> </mo><mi>GW</mi></math> and an efficiency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn><mo> </mo><mo>%</mo></math>. Determine the mass of U-235 that undergoes fission in one day.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The specific energy of fossil fuel is typically <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mtext>MJ</mtext><mo> </mo><msup><mtext>kg</mtext><mrow><mo>–</mo><mn>1</mn></mrow></msup></math>. Suggest, with reference to your answer to (b)(i), <strong>one</strong> advantage of U-235 compared with fossil fuels in a power station.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the proton number of nuclide X.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the half-life of Sr-94.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mass of Sr-94 remaining in the sample after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(iii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">energy required to </span><span class="fontstyle2">«</span><span class="fontstyle0">completely</span><span class="fontstyle2">» </span><span class="fontstyle0">separate the nucleons<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle0">energy released when a nucleus is formed from its constituent nucleons </span><span class="fontstyle4">✓</span></p>
<p><em><span class="fontstyle5"><br>Allow protons </span><span class="fontstyle3"><strong>AND</strong> </span><span class="fontstyle5">neutrons.</span></em></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the values </span><span class="fontstyle2">«</span><span class="fontstyle0">in SI units</span><span class="fontstyle2">» </span><span class="fontstyle0">would be very small </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>29</mn><mo>+</mo><mn>94</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>59</mn><mo>-</mo><mn>235</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>59</mn></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>184</mn><mo> </mo><mo>«</mo><mi>MeV</mi><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle3">see <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mi>energy</mi><mo>=</mo><mo>»</mo><mo> </mo><mn>180</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>60</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></math> <em><strong>AND</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mi>mass</mi><mo>=</mo><mo>»</mo><mo> </mo><mn>235</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>66</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>27</mn></mrow></msup></math> ✓</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>13</mn></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">energy produced in one day<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>36</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>14</mn></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> ✓</span></p>
<p><span class="fontstyle0">mass<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>14</mn></msup></mrow><mrow><mn>7</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>13</mn></msup></mrow></mfrac><mo>=</mo><mn>3</mn><mo>.</mo><mn>9</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«specific energy of uranium is much greater than that of coal, hence» more energy can be produced from the same mass of fuel / per <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>kg</mtext></math><br><em><strong>OR</strong></em><br>less fuel can be used to create the same amount of energy ✓</p>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>39</mn></math> </span><span class="fontstyle2">✓</span></p>
<p><em><span class="fontstyle3"><br>Do not allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi mathvariant="normal">X</mi><mprescripts></mprescripts><mn>39</mn><mn>94</mn></mmultiscripts></math> unless the proton number is indicated.</span></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"><mn>75</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">s</mi><mo>»</mo></math> <span class="fontstyle3">✓</span></p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mi>min</mi></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo> </mo><msub><mi>t</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></math> ✓</span></p>
<p><span class="fontstyle0">mass remaining<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>8</mn></msup><mo>=</mo><mn>3</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>«</mo><mi>kg</mi><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><span class="fontstyle0">decay constant<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>=</mo><mo>«</mo><mfrac><mrow><mi>ln</mi><mn>2</mn></mrow><mn>75</mn></mfrac><mo>=</mo><mo>»</mo><mn>9</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>
<p><span class="fontstyle0">mass remaining<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mi>e</mi><mrow><mo>-</mo><mn>9</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>×</mo><mn>600</mn></mrow></msup><mo>=</mo><mn>3</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">c(iii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Generally, well answered but candidates did miss the mark by discussing the constituents of a nucleus rather than the nucleons, or protons and neutrons. There seemed to be fewer comments than usual about 'the energy required to bind the nucleus together'. </p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Well answered with some candidates describing the values as too large or small.</p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Well answered.</p>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This caused problems for some with mass often correctly calculated but energy causing more difficulty with the eV conversion either being inaccurate or omitted. Candidates were allowed error carried forward for the second mark as long as they were dividing an energy by a mass.</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates had the right idea, but common problems included forgetting the efficiency or not converting to days.</p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>HL only. This was well answered.</p>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates answered this correctly.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates answered this correctly.</p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered well with most candidates (even at HL) going down the number of half-lives route rather than the exponential calculation route.</p>
<div class="question_part_label">c(iii).</div>
</div>
<br><hr><br><div class="specification">
<p>A buoy, floating in a vertical tube, generates energy from the movement of water waves on the surface of the sea. When the buoy moves up, a cable turns a generator on the sea bed producing power. When the buoy moves down, the cable is wound in by a mechanism in the generator and no power is produced.</p>
<p style="text-align: center;"><img 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"></p>
<p>The motion of the buoy can be assumed to be simple harmonic.</p>
</div>
<div class="specification">
<p>Water can be used in other ways to generate energy.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the conditions necessary for simple harmonic motion (SHM) to occur.</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>A wave of amplitude 4.3 m and wavelength 35 m, moves with a speed of 3.4 m s<sup>–1</sup>. Calculate the maximum vertical speed of the buoy.</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>Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.</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 water in a particular pumped storage hydroelectric system falls a vertical distance of 270 m to the turbines. Calculate the speed at which water arrives at the turbines. Assume that there is no energy loss in the system.</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>The hydroelectric system has four 250 MW generators. Determine the maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x 10<sup>10</sup> kg of water passes through the turbines.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Not all the stored energy can be retrieved because of energy losses in the system. Explain <strong>two</strong> such losses.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxQAAAD4CAYAAAB17aD1AAAVQElEQVR4Ae3dP4hldxUH8POLi1pEqyDkRcRC/FMIARcsTGFiMSgRJJHVQlC2ElRCIGFgsVJBA4tpVKweEYOFoAZtDOIjthFBiMX4imAKs81U4xYbwXflDXnLkuxls3venb33ns/CZnbuvvO7v/P5nZc3330D07qu68IvAgQIECBAgAABAgQI3IHAPXdQo4QAAQIECBAgQIAAAQKnAud2Dq213R99JECAAAECBAgQIECAwE0F3voNTtcDxfYvtqHirQ+46SouEiBAgAABAgQIECBQSqAvK/iWp1JjoFkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xUQKPbraTUCBAgQIECAAAECpQQEilLHrVkCBAgQIECAAAEC+xWYV6C4+nJcfvgzcbg63q+S1QgQIECAAAECBAgQuKnAfALF1X/EL77/w/jdS2/ctFEXCRAgQIAAAQIECBDYv8AMAsV/48rffhmH31rFJy58Ie7dv5EVCRAgQIAAAQIECBDoEZh8oNisn49vPPVqHPzom3H+fe/qadNlAgQIECBAgAABAgSGEDg3xKJnueY9i0fjuT/cF/ffe09s/nOWd3YvAgQIECBAgAABAgQmHyji3g/E/c6RAAECBAgQIECAAIG7IjD5b3m6K2puSoAAAQIECBAgQIDAqYBAYRAIECBAgAABAgQIELhjAYHijukUEiBAgAABAgQIECAgUJgBAgQIECBAgAABAgTuWECguGM6hQQIECBAgAABAgQIlAgUm/UyDlqLxeEqTkZ55tdivbwQrZ2Pw9Vx7w7fUR+bo1geLKItLsXqZNOz1lnfL2K6ez9rK/fbDq152SKM8bk89/k0e6cvGmYvIuY+6/ob7WtNz1duY7/cuq7rdptsrcUNn+4u+0iAAAECBAgQIECAQHGBvqxQ4h2K4mevfQIECBAgQIAAAQKDCQgUg9FamAABAgQIECBAgMD8BQSK+Z+xDgkQIECAAAECBAgMJiBQDEZrYQIECBAgQIAAAQLzFxAo5n/GOiRAgAABAgQIECAwmIBAMRithQkQIECAAAECBAjMX0CgmP8Z65AAAQIECBAgQIDAYAICxWC0FiZAgAABAgQIECAwfwGBYv5nrEMCBAgQIECAAAECgwkIFIPRWpgAAQIECBAgQIDA/AUEivmfsQ4JECBAgAABAgQIDCYgUAxGa2ECBAgQIECAAAEC8xcQKOZ/xjokQIAAAQIECBAgMJiAQDEYrYUJECBAgAABAgQIzF9AoJj/GeuQAAECBAgQIECAwGACAsVgtBYmQIAAAQIECBAgMH8BgWL+Z6xDAgQIECBAgAABAoMJCBSD0VqYAAECBAgQIECAwPwFBIr5n7EOCRAgQIAAAQIECAwmIFAMRmthAgQIECBAgAABAvMXECjmf8Y6JECAAAECBAgQIDCYgEAxGK2FCRAgQIAAAQIECMxfQKCY/xnrkAABAgQIECBAgMBgAgLFYLQWJkCAAAECBAgQIDB/AYFi/mesQwIECBAgQIAAAQKDCQgUg9FamAABAgQIECBAgMD8BQSK+Z+xDgkQIECAAAECBAgMJiBQDEZrYQIECBAgQIAAAQLzFxAo5n/GOiRAgAABAgQIECAwmIBAMRjt7Sx8LdbLC9Ha+ThcHfcWbtbLOGgtFoerOOl71OYolgeLaItLsTrZ9DzqrO8XMd29n7WV+22H1rxsEcb4XJ77fJq90xcNsxcRc591/Y32tabnK7exX25d13W7TbbW4oZPd5d9JECAAAECBAgQIECguEBfVvAORfHB0D4BAgQIECBAgACBjIBAkdFTS4AAAQIECBAgQKC4gEBRfAC0T4AAAQIECBAgQCAjIFBk9NQSIECAAAECBAgQKC4gUBQfAO0TIECAAAECBAgQyAgIFBk9tQQIECBAgAABAgSKCwgUxQdA+wQIECBAgAABAgQyAgJFRk8tAQIECBAgQIAAgeICAkXxAdA+AQIECBAgQIAAgYyAQJHRU0uAAAECBAgQIECguIBAUXwAtE+AAAECBAgQIEAgIyBQZPTUEiBAgAABAgQIECguIFAUHwDtEyBAgAABAgQIEMgICBQZPbUECBAgQIAAAQIEigsIFMUHQPsECBAgQIAAAQIEMgICRUZPLQECBAgQIECAAIHiAgJF8QHQPgECBAgQIECAAIGMgECR0VNLgAABAgQIECBAoLiAQFF8ALRPgAABAgQIECBAICMgUGT01BIgQIAAAQIECBAoLiBQFB8A7RMgQIAAAQIECBDICAgUGT21BAgQIECAAAECBIoLCBTFB0D7BAgQIECAAAECBDICAkVGTy0BAgQIECBAgACB4gICRfEB0D4BAgQIECBAgACBjIBAkdFTS4AAAQIECBAgQKC4gEBRfAC0T4AAAQIECBAgQCAjIFBk9NQSIECAAAECBAgQKC4gUBQfAO0TIECAAAECBAgQyAgIFBm9vdVei/XyQrR2Pg5Xx72rbtbLOGgtFoerOOl71OYolgeLaItLsTrZ9DzqrO8XMd29n7WV+22H1rxsEcb4XJ77fJq90xcNsxcRc591/Y32tabnK7exX25d13W7TbbW4oZPd5d9JECAAAECBAgQIECguEBfVvAORfHB0D4BAgQIECBAgACBjIBAkdFTS4AAAQIECBAgQKC4gEBRfAC0T4AAAQIECBAgQCAjIFBk9NQSIECAAAECBAgQKC4gUBQfAO0TIECAAAECBAgQyAgIFBk9tQQIECBAgAABAgSKCwgUxQdA+wQIECBAgAABAgQyAgJFRk8tAQIECBAgQIAAgeICAkXxAdA+AQIECBAgQIAAgYyAQJHRU0uAAAECBAgQIECguIBAUXwAtE+AAAECBAgQIEAgIyBQZPTUEiBAgAABAgQIECguIFAUHwDtEyBAgAABAgQIEMgICBQZPbUECBAgQIAAAQIEigsIFMUHQPsECBAgQIAAAQIEMgICRUZPLQECBAgQIECAAIHiAgJF8QHQPgECBAgQIECAAIGMgECR0VNLgAABAgQIECBAoLiAQFF8ALRPgAABAgQIECBAICMgUGT01BIgQIAAAQIECBAoLiBQFB8A7RMgQIAAAQIECBDICAgUGT21BAgQIECAAAECBIoLCBTFB0D7BAgQIECAAAECBDICAkVGTy0BAgQIECBAgACB4gICRfEB0D4BAgQIECBAgACBjIBAkdFTS4AAAQIECBAgQKC4gEBRfAC0T4AAAQIECBAgQCAjIFBk9NQSIECAAAECBAgQKC4gUBQfAO0TIECAAAECBAgQyAgIFBk9tQQIECBAgAABAgSKCwgUxQdA+wQIECBAgAABAgQyAgJFRk8tAQIECBAgQIAAgeICAkXxAdA+AQIECBAgQIAAgYyAQJHRU0uAAAECBAgQIECguIBAUXwAtE+AAAECBAgQIEAgIyBQZPTUEiBAgAABAgQIECguIFAUHwDtEyBAgAABAgQIEMgICBQZPbUECBAgQIAAAQIEigtMP1BcXcdqeRgPtxbt9Pcn4+uXX4z11U3xo9U+AQIECBAgQIAAgeEFph0oNq/Fb594PL72lw/FM6+/EV3Xxf9e/3k8+MpT8dknXoh/yxTDT5A7ECBAgAABAgQIlBZo3far8Dd/bf+F/4ZPd5dH+3GzXsbnP/azePDPf4xnHrnv+j77rl9/gD8QIECAAAECBAgQIHBbAn1Z4dxtrTKyB9/z0YvxYnexZ1evx9//dRybuC+m/TZMT3suEyBAgAABAgQIEBiBwIy/1n4ovvLQh4WJEQyZLRAgQIAAAQIECMxXYH6BYvNavPDMs/HKxa/GwUfeO9+T0xkBAgQIECBAgACBEQhM+lue3u53EkfPfS++/eqX4/lfPRoPzC8uvb1lVwgQIECAAAECBAjcRYEZBYqTOFo+GY98N+IHqyfjkfvffRdZ3ZoAAQIECBAgQIBADYF5/Bv+5kq8/Ox33gwTz8bFj7+/xunpkgABAgQIECBAgMBdFph8oNhc+VNc+tyn4tO/fyB+8pIwcZfnye0JECBAgAABAgSKCUz651DE1Zfj8he/FE//87H4zV9/HI894Nucis2vdgkQIECAAAECBM5IoO/nUEz4HYprsf715Xj6pSsRV34aj3/wPbFt8sbfi8NVnETE9gfdHbQWu8/PyPw2bnMt1ssL0dr5OFwd99a9oz42R7E8WERbXIrVSd+PCj/r+73DMxjl3s/ayv22T4Dpzrrzm/b5mb3TFyD/L44Iz+VpP5cnfH6nT8Lp/Wfa71BMz9uOCRAgQIAAAQIECExSYIbvUEzyHGyaAAECBAgQIECAwKwEJvwtT7M6B80QIECAAAECBAgQmKSAQDHJY7NpAgQIECBAgAABAuMQECjGcQ52QYAAAQIECBAgQGCSAgLFJI/NpgkQIECAAAECBAiMQ0CgGMc52AUBAgQIECBAgACBSQoIFJM8NpsmQIAAAQIECBAgMA4BgWIc52AXBAgQIECAAAECBCYpIFBM8thsmgABAgQIECBAgMA4BASKcZyDXRAgQIAAAQIECBCYpIBAMcljs2kCBAgQIECAAAEC4xAQKMZxDnZBgAABAgQIECBAYJICAsUkj82mCRAgQIAAAQIECIxDQKAYxznYBQECBAgQIECAAIFJCggUkzw2myZAgAABAgQIECAwDgGBYhznYBcECBAgQIAAAQIEJikgUEzy2GyaAAECBAgQIECAwDgEBIpxnINdECBAgAABAgQIEJikgEAxyWOzaQIECBAgQIAAAQLjEBAoxnEOdkGAAAECBAgQIEBgkgICxSSPzaYJECBAgAABAgQIjENAoBjHOdgFAQIECBAgQIAAgUkKCBSTPDabJkCAAAECBAgQIDAOAYFiHOdgFwQIECBAgAABAgQmKSBQTPLYbJoAAQIECBAgQIDAOAQEinGcg10QIECAAAECBAgQmKSAQDHJY7NpAgQIECBAgAABAuMQECjGcQ52QYAAAQIECBAgQGCSAgLFJI/NpgkQIECAAAECBAiMQ0CgGMU5XIv18kK0dj4OV8e9O9qsl3HQWiwOV3HS96jNUSwPFtEWl2J1sul51FnfL2K6ez9rK/fbDq152SKM8bk89/k0e6cvGmYvIuY+6/ob7WtNz1duY7/cuq7rdptsrcUNn+4u+0iAAAECBAgQIECAQHGBvqzgHYrig6F9AgQIECBAgAABAhkBgSKjp5YAAQIECBAgQIBAcQGBovgAaJ8AAQIECBAgQIBARkCgyOipJUCAAAECBAgQIFBcQKAoPgDaJ0CAAAECBAgQIJARECgyemoJECBAgAABAgQIFBcQKIoPgPYJECBAgAABAgQIZAQEioyeWgIECBAgQIAAAQLFBQSK4gOgfQIECBAgQIAAAQIZAYEio6eWAAECBAgQIECAQHEBgaL4AGifAAECBAgQIECAQEZAoMjoqSVAgAABAgQIECBQXECgKD4A2idAgAABAgQIECCQERAoMnpqCRAgQIAAAQIECBQXECiKD4D2CRAgQIAAAQIECGQEBIqMnloCBAgQIECAAAECxQUEiuIDoH0CBAgQIECAAAECGQGBIqOnlgABAgQIECBAgEBxAYGi+ABonwABAgQIECBAgEBGQKDI6KklQIAAAQIECBAgUFxAoCg+ANonQIAAAQIECBAgkBEQKDJ6agkQIECAAAECBAgUFxAoig+A9gkQIECAAAECBAhkBASKjJ5aAgQIECBAgAABAsUFBIriA6B9AgQIECBAgAABAhkBgSKjp5YAAQIECBAgQIBAcQGBovgAaJ8AAQIECBAgQIBARkCgyOipJUCAAAECBAgQIFBcQKAoPgDaJ0CAAAECBAgQIJARECgyenurvRbr5YVo7Xwcro57V92sl3HQWiwOV3HS96jNUSwPFtEWl2J1sul51FnfL2K6ez9rK/fbDq152SKM8bk89/k0e6cvGmYvIuY+6/ob7WtNz1duY7/cuq7rdptsrcUNn+4u+0iAAAECBAgQIECAQHGBvqzgHYrig6F9AgQIECBAgAABAhkBgSKjp5YAAQIECBAgQIBAcQGBovgAaJ8AAQIECBAgQIBARkCgyOipJUCAAAECBAgQIFBcQKAoPgDaJ0CAAAECBAgQIJARECgyemoJECBAgAABAgQIFBcQKIoPgPYJECBAgAABAgQIZAQEioyeWgIECBAgQIAAAQLFBQSK4gOgfQIECBAgQIAAAQIZAYEio6eWAAECBAgQIECAQHEBgaL4AGifAAECBAgQIECAQEZAoMjoqSVAgAABAgQIECBQXECgKD4A2idAgAABAgQIECCQERAoMnpqCRAgQIAAAQIECBQXECiKD4D2CRAgQIAAAQIECGQEBIqMnloCBAgQIECAAAECxQUEiuIDoH0CBAgQIECAAAECGQGBIqOnlgABAgQIECBAgEBxAYGi+ABonwABAgQIECBAgEBGQKDI6KklQIAAAQIECBAgUFxAoCg+ANonQIAAAQIECBAgkBEQKDJ6agkQIECAAAECBAgUFxAoig+A9gkQIECAAAECBAhkBASKjJ5aAgQIECBAgAABAsUFBIriA6B9AgQIECBAgAABAhkBgSKjp5YAAQIECBAgQIBAcQGBovgAaJ8AAQIECBAgQIBARkCgyOipJUCAAAECBAgQIFBcQKAoPgDaJ0CAAAECBAgQIJARECgyemoJECBAgAABAgQIFBdoXdd1W4PWWnEK7RMgQIAAAQIECBAgcCuBN+PD9Yed2/3prX+xu+4jAQIECBAgQIAAAQIE+gR8y1OfjOsECBAgQIAAAQIECNxSQKC4JZEHECBAgAABAgQIECDQJyBQ9Mm4ToAAAQIECBAgQIDALQUEilsSeQABAgQIECBAgAABAn0CAkWfjOsECBAgQIAAAQIECNxS4P/K1Koua3MxBgAAAABJRU5ErkJggg=="></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force/acceleration proportional to displacement «from equilibrium position»</p>
<p>and directed towards equilibrium position/point<br><em><strong>OR</strong></em><br>and directed in opposite direction to the displacement from equilibrium position/point</p>
<p> </p>
<p><em>Do not award marks for stating the defining equation for SHM.</em><br><em>Award <strong>[1 max]</strong> for a ω–=<sup>2</sup>x with a and x defined.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>frequency of buoy movement <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{3.4}}{{35}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>3.4</mn>
</mrow>
<mrow>
<mn>35</mn>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> 0.097 «Hz»</p>
<p><em><strong>OR</strong></em></p>
<p>time period of buoy <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{35}}{{3.4}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>35</mn>
</mrow>
<mrow>
<mn>3.4</mn>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> 10.3 «s» <em><strong>or</strong></em> 10 «s»</p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi {x_0}}}{T}">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mrow>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
</mrow>
</mrow>
<mi>T</mi>
</mfrac>
</math></span> <em><strong>or </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi f{x_0}">
<mn>2</mn>
<mi>π</mi>
<mi>f</mi>
<mrow>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
</mrow>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\ = \frac{{2 \times \pi \times 4.3}}{{10.3}}">
<mtext> </mtext>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mi>π</mi>
<mo>×</mo>
<mn>4.3</mn>
</mrow>
<mrow>
<mn>10.3</mn>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2 \times \pi \times 0.097 \times 4.3">
<mn>2</mn>
<mo>×</mo>
<mi>π</mi>
<mo>×</mo>
<mn>0.097</mn>
<mo>×</mo>
<mn>4.3</mn>
</math></span></p>
<p>2.6 «m s<sup>–1</sup>»</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>peaks separated by gaps equal to width of each pulse «shape of peak roughly as shown»</p>
<p>one cycle taking 10 s shown on graph</p>
<p><img 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"></p>
<p><em>Judge by eye.</em><br><em>Do not accept cos<sub>2</sub> or sin<sub>2</sub> graph</em><br><em>At least two peaks needed.</em><br><em>Do not allow square waves or asymmetrical shapes.</em><br><em>Allow ECF from (b)(i) value of period if calculated.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>PE of water is converted to KE of moving water/turbine to electrical energy «in generator/turbine/dynamo»</p>
<p>idea of pumped storage, <em>ie:</em> pump water back during night/when energy cheap to buy/when energy not in demand/when there is a surplus of energy</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>specific energy available = «<em>gh</em> =» 9.81 x 270 «= 2650J kg<sup>–1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>mgh</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{1}{2}">
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup></p>
<p><em><strong>OR</strong></em></p>
<p><em>v</em><sup>2</sup> = 2gh</p>
<p><em>v</em> = 73 «ms<sup>–1</sup>»</p>
<p> </p>
<p><em>Do not allow 72 as round from 72.8</em></p>
<p> </p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total energy = «<em>mgh</em> = 1.5 x 10<sup>10</sup> x 9.81 x 270=» 4.0 x 10<sup>13</sup> «J»</p>
<p><em><strong>OR</strong></em></p>
<p>total energy = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}m{v^2} = \frac{1}{2} \times 1.5 \times {10^{10}} \times ">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>1.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
</math></span> (answer (c)(ii))<sup>2</sup> =» 4.0 x 10<sup>13</sup> «J»</p>
<p>time = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.0 \times {{10}^{13}}}}{{4 \times 2.5 \times {{10}^8}}}">
<mfrac>
<mrow>
<mn>4.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>13</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mn>2.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>» 11.1h <em><strong>or</strong> </em>4.0 x 10<sup>4</sup> s</p>
<p> </p>
<p><em>Use of 3.97 x 10<sup>13</sup> «J» gives 11 h.</em></p>
<p><em>For MP2 the unit <strong>must</strong> be present.</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>friction/resistive losses in pipe/fluid resistance/turbulence/turbine or generator «bearings»<br><em><strong>OR</strong></em><br>sound energy losses from turbine/water in pipe </p>
<p>thermal energy/heat losses in wires/components<br><br>water requires kinetic energy to leave system so not all can be transferred</p>
<p> </p>
<p><em>Must see “seat of friction” to award the mark.</em></p>
<p><em>Do not allow “friction” bald.</em></p>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iv.</div>
</div>
<br><hr><br><div class="specification">
<p>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>The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (<em>β–</em>) decay to form a stable boron (B) nuclide.</p>
</div>
<div class="specification">
<p>The initial number of nuclei in a pure sample of beryllium-10 is N<sub>0</sub>. The graph shows how the number of remaining <strong>beryllium </strong>nuclei in the sample varies with time.</p>
<p><img 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"></p>
</div>
<div class="specification">
<p>An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the missing information for this decay.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxAAAABtCAYAAAAxrYd/AAASaUlEQVR4Ae3dD2yU9R3H8c+VDlnSMiWSeIf/gk2LC41mJZjNGgtoi9tIXOu/6GhZG6eLOA2h7VR0ZpQZSocaZIimnZTEOLUXIhqlWOwSjJH0MjOM0qYSUOiRoa5CM5HRe5Zr79q73p1c7+557u65d5Om1989z+/3+75+T+7ue8/z/H4OwzAM8YMAAggggAACCCCAAAIIxCGQ79/G4XDEsSmbIIAAAggggAACCCCAQK4KBM87jCUQfoRgQa6CEDcCCCCAAAIIIIAAAghEFwg94ZAXfRNKEUAAAQQQQAABBBBAAIFIARKISBNKEEAAAQQQQAABBBBAIIYACUQMGIoRQAABBBBAAAEEEEAgUoAEItKEEgQQQAABBBBAAAEEEIghQAIRA4ZiBBBAAAEEEEAAAQQQiBQggYg0oQQBBBBAAAEEEEAAAQRiCJBAxIChGAEEEEAAAQQQQAABBCIFSCAiTShBAAEEEEAAAQQQQACBGAIkEDFgKEYAAQQQQAABBBBAAIFIARKISBNKEEAAAQQQQAABBBBAIIYACUQMGIoRQAABBBBAAAEEEEAgUoAEItKEEgQQQAABBBBAAAEEEIghQAIRA4ZiBBBAAAEEEEAAAQQQiBQggYg0oQQBBBBAAAEEEEAAAQRiCJBAxIChGAEEEEAAAQQQQAABBCIFSCAiTShBAAEEEEAAAQQQQACBGAIkEDFgKEYAAQQQQAABBBBAAIFIgfzIIkoQQAABBMwUcDgcZlYfUbdhGBFlVhVYHas/rnTGa5Ur7SCAAALpFCCBSKc+bSOAQM4KWPUhNx0f4KcOqlWx+tvNhHinxs//CCCAgN0EuITJbiNKPAgggAACCCCAAAIImChAAmEiLlUjgAACCCCAAAIIIGA3ARIIu40o8SCAAAIIIIAAAgggYKIACYSJuFSNAAIIIIAAAggggIDdBEgg7DaixIMAAggggAACCCCAgIkCJBAm4lI1AggggAACCCCAAAJ2EyCBsNuIEg8CCCCAAAIIIIAAAiYKkECYiEvVCCCAAAIIIIAAAgjYTYAEwm4jSjwIIIAAAggggAACCJgoQAJhIi5VI4AAAggggAACCCBgNwESCLuNKPEggAACCCCAAAIIIGCiAAmEibhUjQACCCCAAAIIIICA3QRIIOw2osSDAAIIIIAAAggggICJAiQQJuJSNQIIIIAAAggggAACdhMggbDbiBIPAggggAACCCCAAAImCpBAmIhL1QgggAACCCCAAAII2E2ABMJuI0o8CNhYwOfdq0eXVKnNMxIS5SkN7H1adS6HHA7/b6nq2tzyeM+GbMNDBFIpEP8xN35MBo9N8/+mMkrqQgABBGIJkEDEkqEcAQQySsDnfV/P/mGNnuoNTwx8A6/rwcoOqXG/hkYNjQ5t1ry3VmvFM/t1KqMioDN2EZjuMWcYhqz4tYsvcSCAQOYLkEBk/hjRQwRyXGD8297f3PCCRst/roowjTMa3P+Ouq+q0+8fvF7OPCnPeYNWrSyXd+e76jvlC9uafxBIXoBjLnlDakAAgWwXIIHI9hGk/wjYXuAbffzKZ7rxzS1a+8vrdHlYvCM61n9Yun6+XPnBJ2Zp/jWLdZV3UEdOhJ+tCG7BXwQSF+CYS9yOPRFAwC4CE2+5dgmIOBBAwG4Cl6m6/bnxoLxTY/tWwyeGpxYG/j+pr0+fi/EcxQgkKsAxl6gc+yGAgH0EOANhn7EkEgQQQAABBBBAAAEETBcggTCdmAYQQAABBBBAAAEEELCPAAmEfcaSSBDIQYGLdEXpZTHinqs5hVylGQOH4oQFOOYSpmNHBBCwjQAJhG2GkkAQyEWBfBXOmSvt7dOnEzMundPJo4P6zFmkKy+ZmYsoxGyqAMecqbxUjgACWSFAApEVw0QnEUAgusAsFZUvV6V3t3a8/on8y8v5vO9py5Y35Fx5kxbNzpN8h9RR5QosMjd1Ia8qNXfs08CI9dO9WrXAmN/NN9ChqrFF9qbG75BjSbM69g2M2UU3Tr7Uqlj97Zj/E8cxZ34naAEBBBBIqwAJRFr5aRwBBJIVyCu+TVu6VujzhlIVOhya4arTB4s3avfD5Zp93sq71dqwTBUP7dJxC3MIKxYVC23jexl6W9WwrEYPuY/KDILQflj1+HvjTcGTyR1zKegAVSCAAAJpFnAYhmH4v7Xxv7DzgwACCNhOwH8G4palalCL+t+uV3Ho1yYjh+Re/5BqWr9SU8872rj0YtuF7w/IfwbilpJ1Uvs+vV2/QJMEPo0M7NL6+1artX+Veg61aKn/rA0/KROw8v3VyrZSBkRFCCCQNQKhrzG8U2TNsNFRBBBIuUDBAlU/1qwmp0c79/xLp1LeQKZXmKeC4lv12OOr5PR2a0/f15neYfqHAAIIIJABAiQQGTAIdAEBBNIt4FRpiUsFod3weeVxt6nOFbxvoErNOw7Ia8Z1PqHtpu3xfJVcGiaQtp4k3vBZeT1utdWVBu55cWlJ8055vKxInrgpeyKAAAKRAiQQkSaUIIBArgj4L2HasFGt3nLdWX7l5KU9vqNy31upRTWN6pxY/bpbrauuU9m97iTulxiWp+1XWvLo3gxJRMYvYdqw/iV5K5ervGhWikb+C7nrFqnO/UWK6ounmrM67l6jskU1auz8OLCDV72ttVpUtkbu49NMIrxu1Tnul9vLaubx6LMNAgjklgAJRG6NN9EikLsC3Q0qmRE8mxD4W3i1alqlpq4/6Y7i4Ifnszq+a5NWd3yliqYu9Z8eHbtHzBgdUt9LTSrp+KOe2JXoDccXquy3D2rxS3W6+xG3xbM/edXdcLVmhM3GNEOFJTVq1Sp1bbkt/P6QLDtSfMff1BOrt8pb8Yi6+r8ZHzPjOw31daqpxK3VT7yZROKXZRh0FwEEEDBZgATCZGCqRwCBTBc4qAMffqKh4FSuvsPas90tb2WLtj9VreKCwMtknlNldY16vOkCdWzv0WCilzLNrtDjuxul1hpVPLBNBzLh8ppejz78eMjUqVzNPQrOaHDPK+rw3q727U+oujg4/9ZMOcvuGbvHQx2vaM/gGXO7Qe0IIIBAjgiQQOTIQBMmAjkvUNmu/lEj8M108O836u9u1OU7a1Sxvnf8JuqRIfUf9ErRzlg45mpZq0c6OKhjwYRj2rB5Kih7QC/3PKmSztW6zrVCze5DFnx4d6qy/VONGsHYA39P96t70yXaWfNrrd/35bSjyYwdRnSs/7Ck19RQ8sMpa37M0I+WPSWvDqv/mH+lEH4QQAABBJIVIIFIVpD9EUAgiwVmq/jm3+mxltvl3fmu+iZWsz5PSN5BHTkRuKb+nEdtRVMujQq7TCjacxfItexJ9Y41063Wmqt1bZtHabnavqBYN695RC2VQ4nPRDV2v0BonJerptOjzprLwz/M17k1cUvJeYhT//SQPjryZYy1Ls7J674/vK+uGnVqu2pcPwgpL7L4vo7UK1AjAgggkAoBEohUKFIHAghkv0AwKShwqaTUKUU9YxH89v5V1Qfvmcgv09rBYHm8f7/TUM+TqvCrOWu1qbtfH60tU36aFb0fHdGJRC7NclZrR9iZjc/VVVum2q7Pw8/47KiW05QYC3RpyXxJt6u9/9vwNif6NaQ9YWtghHYkX87q58P3G+pSre5T19D/QsoHtaP6stAdeYwAAgjkpAAJRE4OO0EjgMC4wCkN7N2mDetek4KzEOXNV9V91XJ2P60Nm/eE3OjsnyJ0p5qXuOSo6tBAIh+0xxr1acSzVXcve1L9tc/pQ8+LWntzcfgUstManhF52paEfEseOBNQ1CZPPKc0Rga0d/NTWtctVd75MxVl5bvCLBVV3aV652tat2Gb9g5Mrujh8x7QjuYqORx3qGOAeyCmdWixMQIIIBBDIN1feMXoFsUIIGAnAf/qlVb/GIYR3uTYPQ0N4WUT//1Cm3ZXB2Yhmql5lferpfYfamhcrs7GiY3GHzjr1b4viRmLRvr0/Nqt0iPd8rTcLGfSH9j/o6MHv5CzqUeHNi5V8PbhKb2WFJiFKRZBxWbtvqN4cirbyAoyuiRv3k1qbKnX2w1rVNm5ZkpfF6q2/S8hM21NeZp/EUAAAQSmJZD0W9e0WmNjBBDIWQH/B3qrfuNHdqqi6QXt6ntRa8ounNytYKHq/9atvq5Nqp245sa/bbt6ep9W/YLYH9MnK4n26IwGXn1Wb/10m15OSfIg6dy/dfj9/0YuhBet+ahllWpq362+lx9QWXDGqajbZXrhbC2o3yZPX5c21S6c7GxFk9p7urS1fmESZ3kmq+MRAggggIDkMAzD8H87GPFtHToIIIBAigSsfo2xur0UMSVUjW+gQ7eU/FXX9ryjjUsvTqgOdjJPwMpj0cq2zBOjZgQQyFSB0NcYzkBk6ijRLwQQQOC8Aj6NHBvUQQ3rwPrlgfsgXFrSvFOeTFhf4rz9z9YN/PfOPK06V3DmqVLVtbkxz9bhpN8IIDBtARKIaZOxAwIIIJApAmd14sigvFqgX7S9G7hE7JC2lfRqxd1b5Ul4rYpMiS8z++EbeF0PVnZIjfs1NGpodGiz5r21Wiue2T++lkhmdpteIYAAAikT4BKmlFFSEQIIxBIIPe0Za5tUllvdXir7noq6uKwpFYqx6jijgY5alfx5sfoOrVXZ2FQkgbJ1Reo51KKlsye/m7PyWLSyrVg6lCOAgH0FQl9jJl/l7BsvkSGAAAI5JZBXeKEu0bBODH+b9rj9bzhW/5obdGDV6+vnyzUxj+Eszb9msa4KriVibgeoHQEEEEi7AAlE2oeADiCAAAKJCnypfc2LItal8J0e1gn9RDcunJtoxSndz6rZt6yZDORbDZ8YjuFzUl+fjmfxjRi7U4wAAghkiQAJRJYMFN1EAAEEIgXmaPEd96ii2603/hn4UOs7rt6X/q6D9XepqmhW5C6UIIAAAgggkKQACUSSgOyOAAIIpE8gTwVlD+jlvjt1cu2Pxy8VmrFcO+asUe+zt2oer/DpGxpaRgABBGwsMHEFp41jJDQEEEDAxgIz5SxbqY3vrdRGG0eZOaFdpCtKL5MORuvRXM0p5G01mgxlCCBgLwG+n7LXeBINAggggICpAvkqnDNX2tunT0/5Ai2d08mjg/rMWaQrL5lpautUjgACCGSCAAlEJowCfUAAAQQQyBKBWSoqX65K727teP0TjUjyed/Tli1vyLnyJi0KmcI1SwKimwgggMC0BUggpk3GDggggAACuSyQV3ybtnSt0OcNpSp0ODTDVacPFm/U7ofLNTsKjFXT2EZpmiIEEEDAFAEWkjOFlUoRQCBUIHTxmdBysx5b3Z5ZcdihXqvHwur27DBGxIAAAgjEIxD6+soZiHjE2AYBBBBAAAEEEEAAAQTGBEggOBAQQAABBBBAAAEEEEAgbgESiLip2BABBBBAAAEEEEAAAQRIIDgGEEAAAQQQQAABBBBAIG4BEoi4qdgQAQQQQAABBBBAAAEESCA4BhBAAAEEEEAAAQQQQCBuARKIuKnYEAEEEEAAAQQQQAABBEggOAYQQAABBBBAAAEEEEAgbgESiLip2BABBBBAAAEEEEAAAQRIIDgGEEAAAQQQQAABBBBAIG4BEoi4qdgQAQQQQAABBBBAAAEESCA4BhBAAAEEEEAAAQQQQCBugfy4t2RDBBBAIAkBh8ORxN7sigACCCCAAAKZIkACkSkjQT8QsLGAYRg2jo7QEEAAAQQQyC0BLmHKrfEmWgQQQAABBBBAAAEEkhIggUiKj50RQAABBBBAAAEEEMgtARKI3BpvokUAAQQQQAABBBBAICkBEoik+NgZAQQQQAABBBBAAIHcEuAm6twab6JFAAEELBdgBi7LyWkQAQQQMFWABMJUXipHAAEEcluAGbhye/yJHgEE7CnAJUz2HFeiQgABBBBAAAEEEEDAFAESCFNYqRQBBBBAAAEEEEAAAXsKkEDYc1yJCgEEEEAAAQQQQAABUwRIIExhpVIEEEAAAQQQQAABBOwpQAJhz3ElKgQQQAABBBBAAAEETBEggTCFlUoRQAABBBBAAAEEELCnAAmEPceVqBBAAAEEEEAAAQQQMEWABMIUVipFAAEEEEAAAQQQQMCeAiQQ9hxXokIAAQQQQAABBBBAwBQBEghTWKkUAQQQQAABBBBAAAF7CpBA2HNciQoBBBBAAAEEEEAAAVMESCBMYaVSBBBAAAEEEEAAAQTsKUACYc9xJSoEEEAAAQQQQAABBEwRyA/W6nA4gg/5iwACCCCAAAIIIIAAAghEFRhLIAzDiPokhQgggAACCCCAAAIIIIBAqMD/AZms2klHLgpbAAAAAElFTkSuQmCC"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the graph, sketch how the number of <strong>boron </strong>nuclei in the sample varies with time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After 4.3 × 10<sup>6</sup> years,</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{{\text{number of produced boron nuclei}}}}{{{\text{number of remaining beryllium nuclei}}}} = 7.">
<mfrac>
<mrow>
<mrow>
<mtext>number of produced boron nuclei</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>number of remaining beryllium nuclei</mtext>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>7.</mn>
</math></span></p>
<p>Show that the half-life of beryllium-10 is 1.4 × 10<sup>6</sup> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10<sup>11</sup> atoms of beryllium-10. The present activity of the sample is 8.0 × 10<sup>−3</sup> Bq.</p>
<p>Determine, in years, the age of the sample.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by thermal radiation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The temperature in the laboratory is higher than the temperature of the ice sample. Describe <strong>one </strong>other energy transfer that occurs between the ice sample and the laboratory.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}} \to _{{\mkern 1mu} {\mkern 1mu} 5}^{10}{\text{B}} + _{ - 1}^{\,\,\,0}{\text{e}} + {\overline {\text{V}} _{\text{e}}}">
<msubsup>
<mi></mi>
<mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mn>4</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Be</mtext>
</mrow>
<msubsup>
<mo stretchy="false">→</mo>
<mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mn>5</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msubsup>
<mrow>
<mtext>B</mtext>
</mrow>
<msubsup>
<mo>+</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mrow>
</msubsup>
<mrow>
<mtext>e</mtext>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mover>
<mtext>V</mtext>
<mo accent="false">¯</mo>
</mover>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
</math></span></p>
<p>antineutrino <em><strong>AND</strong> </em>charge <em><strong>AND</strong> </em>mass number of electron <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{ - 1}^{\,\,\,0}{\text{e}}">
<msubsup>
<mi></mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mrow>
</msubsup>
<mrow>
<mtext>e</mtext>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overline {\text{V}} ">
<mover>
<mtext>V</mtext>
<mo accent="false">¯</mo>
</mover>
</math></span></p>
<p>conservation of mass number <strong><em>AND </em></strong>charge <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,5}^{10}{\text{B}}">
<msubsup>
<mi></mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>5</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msubsup>
<mrow>
<mtext>B</mtext>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}}">
<msubsup>
<mi></mi>
<mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mn>4</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Be</mtext>
</mrow>
</math></span></p>
<p> </p>
<p><em>Do not accept V.</em></p>
<p><em>Accept </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar V}">
<mrow>
<mrow>
<mover>
<mi>V</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span><em> without subscript e.</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct shape <em>ie </em>increasing from 0 to about 0.80 N<sub>0</sub></p>
<p>crosses given line at 0.50 N<sub>0</sub></p>
<p><img src="images/Schermafbeelding_2018-08-10_om_19.42.49.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/06.b.i/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>fraction of Be = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{8}">
<mfrac>
<mn>1</mn>
<mn>8</mn>
</mfrac>
</math></span>, 12.5%, or 0.125</p>
<p>therefore 3 half lives have elapsed</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{t_{\frac{1}{2}}} = \frac{{4.3 \times {{10}^6}}}{3} = 1.43 \times {10^6}">
<mrow>
<msub>
<mi>t</mi>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
<mn>3</mn>
</mfrac>
<mo>=</mo>
<mn>1.43</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>6</mn>
</msup>
</mrow>
</math></span> <strong>«</strong>≈ 1.4 × 10<sup>6</sup><strong>»</strong> <strong>«</strong>y<strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>fraction of Be = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{8}">
<mfrac>
<mn>1</mn>
<mn>8</mn>
</mfrac>
</math></span>, 12.5%, or 0.125</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{8} = {{\text{e}}^{ - \lambda }}(4.3 \times {10^6})">
<mfrac>
<mn>1</mn>
<mn>8</mn>
</mfrac>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>λ</mi>
</mrow>
</msup>
</mrow>
<mo stretchy="false">(</mo>
<mn>4.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>6</mn>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</math></span> leading to <em>λ</em> = 4.836 × 10<sup>–7</sup> <strong>«</strong>y<strong>»</strong><sup>–1</sup></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\ln 2}}{\lambda }">
<mfrac>
<mrow>
<mi>ln</mi>
<mo></mo>
<mn>2</mn>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span> = 1.43 × 10<sup>6</sup> <strong>«</strong>y<strong>»</strong></p>
<p> </p>
<p> </p>
<p><em>Must see at least one extra sig fig in final answer.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>λ</em> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\ln 2}}{{1.4 \times {{10}^6}}}">
<mfrac>
<mrow>
<mi>ln</mi>
<mo></mo>
<mn>2</mn>
</mrow>
<mrow>
<mn>1.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong> = 4.95 × 10<sup>–7</sup> <strong>«</strong>y<sup>–1</sup><strong>»</strong></p>
<p>rearranging of <em>A</em> = <em>λN</em><sub>0</sub>e<sup>–<em>λt</em></sup> to give –<em>λt</em> = ln <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{8.0 \times {{10}^{-3}} \times 365 \times 24 \times 60 \times 60}}{{4.95 \times {{10}^{-7}} \times 7.6 \times {{10}^{11}}}}">
<mfrac>
<mrow>
<mn>8.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>365</mn>
<mo>×</mo>
<mn>24</mn>
<mo>×</mo>
<mn>60</mn>
<mo>×</mo>
<mn>60</mn>
</mrow>
<mrow>
<mn>4.95</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>7.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>11</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> <strong>«</strong>= –0.400<strong>»</strong></p>
<p><em>t</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 0.400}}{{ - 4.95 \times {{10}^{ - 7}}}} = 8.1 \times {10^5}">
<mfrac>
<mrow>
<mo>−</mo>
<mn>0.400</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4.95</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>8.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>5</mn>
</msup>
</mrow>
</math></span> <strong>«</strong>y<strong>»</strong></p>
<p> </p>
<p> </p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>emission of (infrared) electromagnetic/infrared energy/waves/radiation.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the (peak) wavelength of emitted em waves depends on temperature of emitter/reference to Wein’s Law</p>
<p>so frequency/color depends on temperature</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda = \frac{{2.90 \times {{10}^{ - 3}}}}{{253}}">
<mi>λ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2.90</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>253</mn>
</mrow>
</mfrac>
</math></span></p>
<p>= 1.1 × 10<sup>–5</sup> <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from MP1 (incorrect temperature).</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>from the laboratory to the sample</p>
<p>conduction – contact between ice and lab surface.</p>
<p><strong><em>OR</em></strong></p>
<p>convection – movement of air currents</p>
<p> </p>
<p><em>Must clearly see direction of energy transfer for MP1.</em></p>
<p><em>Must see more than just words “conduction” or “convection” for MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iv.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The average temperature of ocean surface water is 289 K. Oceans behave as black bodies.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The intensity in (b) returned to the oceans is 330 W m<sup>-2</sup>. The intensity of the solar radiation incident on the oceans is 170 W m<sup>-2</sup>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that the intensity radiated by the oceans is about 400 W m<sup>-2</sup>.</span></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><span style="background-color:#ffffff;">Explain why some of this radiation is returned to the oceans from the atmosphere.</span></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><span style="background-color:#ffffff;">Calculate the additional intensity that must be lost by the oceans so that the water temperature remains constant.</span></p>
<div class="marks">[2]</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;">Suggest a mechanism by which the additional intensity can be lost.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">cii.</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;">5.67 <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>8</sup> × 289<sup>4</sup></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;">= 396«<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;">W m<sup>−</sup></span><sup>2</sup>» ✔<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 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> 400 <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;">W m<sup>−</sup></span><sup style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">2</sup>»</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;">«most of the radiation emitted by the oceans is in the» infrared ✔<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;">«this radiation is» absorbed by greenhouse gases/named greenhouse gas in the atmosphere ✔<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;">«the gases» reradiate/re-emit ✔<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;">partly back towards oceans/in all directions/awareness that radiation in other directions is also present ✔</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;">water loses 396 <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> 330/66 «<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;">W m</span><sup style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;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="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</sup>» ✔<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;">extra intensity that must be lost 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>170 <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> 66<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> = 104 <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> 100 «<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;">W m</span><sup style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;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="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</sup>» ✔<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;">absorbed by water 330 <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> 170/500 «<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;">W m</span><sup style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;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="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</sup>»✔<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;">extra intensity that must be lost 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>500 <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> 396<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> = 104 <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> 100 «<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;">W m</span><sup style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:11.6px;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="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</sup>» ✔</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;">conduction to the air above<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;">«mainly» evaporation<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;">melting ice at the poles<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;">reflection of sunlight off the surface of the ocean ✔</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;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Do not accept convection or radiation.</span></span></em></p>
<div class="question_part_label">cii.</div>
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<h2 style="margin-top: 1em">Examiners report</h2>
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<p>This was well answered with candidates scoring the mark for either a correct substitution or an answer given to at least one more sf than the show that value. Some candidates used 298 rather than 289.</p>
<div class="question_part_label">a.</div>
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<div class="question" style="padding-left: 20px;">
<p>For many this was a well-rehearsed answer which succinctly scored full marks. For others too many vague terms were used. There was much talk about energy being trapped or reflected and the ozone layer was often included. The word ‘albedo’ was often written down with no indication of what it means and ‘the albedo effect also featured.</p>
<div class="question_part_label">b.</div>
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<div class="question" style="padding-left: 20px;">
<p>This was well-answered, a very straightforward 2 marks.</p>
<div class="question_part_label">ci.</div>
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<div class="question" style="padding-left: 20px;">
<p>Many candidates didn’t understand this question and thought that the answer needed to be some form of human activity that would reduce global temperature rise.</p>
<div class="question_part_label">cii.</div>
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