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<h2>HL Paper 2</h2><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A particular K meson has a quark structure <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rm{\bar u}}">
<mrow>
<mrow>
<mrow>
<mover>
<mi mathvariant="normal">u</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</mrow>
</math></span>s. State the charge, strangeness and baryon number for this meson.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Feynman diagram shows the changes that occur during beta minus (β<sup>–</sup>) decay.</p>
<p><img 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"></p>
<p>Label the diagram by inserting the <strong>four</strong> missing particle symbols <strong>and</strong> the direction of the arrows for the decay particles.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>C-14 decay is used to estimate the age of an old dead tree. The activity of C-14 in the dead tree is determined to have <strong>fallen to</strong> 21% of its original value. C-14 has a half-life of 5700 years.</p>
<p>(i) Explain why the activity of C-14 in the dead tree decreases with time.</p>
<p>(ii) Calculate, in years, the age of the dead tree. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>charge:</em> –1«e» <em><strong>or</strong></em> negative <em><strong>or</strong> K</em><sup>−</sup></p>
<p><em>strangeness:</em> –1 </p>
<p><em>baryon number:</em> 0</p>
<p>Negative signs required.<br>Award <strong>[2]</strong> for three correct answers, <strong>[1 max]</strong> for two correct answer and <strong>[0]</strong> for one correct answer.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>correct symbols for both missing quarks</p>
<p>exchange particle and electron labelled W <em><strong>or</strong></em> W<sup>–</sup> and e <em><strong>or</strong></em> e<sup>–</sup></p>
<p><em>Do not allow W<sup>+</sup> <strong>or</strong> e<sup>+</sup> <strong>or</strong> β<sup>+</sup>. Allow β <strong>or</strong> β<sup>–</sup>.</em></p>
<p>arrows for both electron and anti-neutrino correct</p>
<p><em>Allow ECF from previous marking point.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i<br>number of C-14 atoms/nuclei are decreasing<br><em><strong>OR</strong></em><br>decreasing activity proportional to number of C-14 atoms/nuclei<br><em><strong>OR</strong></em><br><em>A </em>= <em>A</em><sub>0</sub>e<sup>–<em>λt</em></sup> so <em>A</em> decreases as <em>t</em> increases<br><em>Do not allow “particles”</em><br><em>Must see reference to atoms or nuclei or an equation, just “C-14 is decreasing” is not enough.</em></p>
<p><br>ii<br>0.21 = (0.5)<em><sup>n</sup></em><br><em><strong>OR</strong></em><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.21 = {e^{ - \left( {\frac{{\ln 2 \times t}}{{5700}}} \right)}}">
<mn>0.21</mn>
<mo>=</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mi>ln</mi>
<mo></mo>
<mn>2</mn>
<mo>×</mo>
<mi>t</mi>
</mrow>
<mrow>
<mn>5700</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
</math></span></p>
<p><em>n </em>= 2.252 half-lives or <em>t </em>=1 2834 «y»<br><em>Early rounding to 2.25 gives 12825 y</em></p>
<p>13000 y rounded correctly to two significant figures:<br><em>Both needed; answer must be in year for MP3.</em><br><em>Allow ECF from MP2.</em><br><em>Award <strong>[3]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).</p>
<p>The following data are available for binding energies per nucleon:</p>
<p style="padding-left: 30px;">plutonium 7.568 MeV</p>
<p style="padding-left: 30px;">uranium 7.600 MeV</p>
<p style="padding-left: 30px;">alpha particle 7.074 MeV</p>
</div>
<div class="specification">
<p>The energy in b(i) can be transferred into electrical energy to run the instruments of a spacecraft. A spacecraft carries 33 kg of pure plutonium-238 at launch. The decay constant of plutonium is 2.50 × 10<sup>−10</sup> s<sup>−1</sup>.</p>
</div>
<div class="specification">
<p>Solar radiation falls onto a metallic surface carried by the spacecraft causing the emission of photoelectrons. The radiation has passed through a filter so it is monochromatic. The spacecraft is moving away from the Sun.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the binding energy of a nucleus.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, a graph to show the variation with nucleon number <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> of the binding energy per nucleon, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>BE</mtext><mi>A</mi></mfrac></math>. Numbers are not required on the vertical axis.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some unstable nuclei have many more neutrons than protons. Suggest the likely decay for these nuclei.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy released in this decay is about 6 MeV.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The plutonium nucleus is at rest when it decays.</p>
<p>Calculate the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>kinetic energy of alpha particle</mtext><mtext>kinetic energy of uranium</mtext></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the power, in kW, that is available from the plutonium at launch.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spacecraft will take 7.2 years (2.3 × 10<sup>8</sup> s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> State and explain what happens to the kinetic energy of an emitted photoelectron.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> State and explain what happens to the rate at which charge leaves the metallic surface.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the energy needed to «completely» separate the nucleons of a nucleus</p>
<p><em><strong>OR</strong></em></p>
<p>the energy released when a nucleus is assembled from its constituent nucleons ✓</p>
<p> </p>
<p><em>Accept reference to protons and </em><em>neutrons.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>curve rising to a maximum between 50 and 100 ✓</p>
<p>curve continued and decreasing ✓</p>
<p> </p>
<p><em>Ignore starting point.<br></em></p>
<p><em>Ignore maximum at alpha particle.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>At a point on the peak of their graph ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>beta minus «decay» ✓</p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct mass numbers for uranium (234) and alpha (4) ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>234</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>600</mn><mo>+</mo><mn>4</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>074</mn><mo>-</mo><mn>238</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>568</mn></math> «MeV» ✓</p>
<p>energy released 5.51 «MeV» ✓</p>
<p> </p>
<p><em>Ignore any negative sign.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>K</mi><msub><mi>E</mi><mi>α</mi></msub></mrow><mrow><mi>K</mi><msub><mi>E</mi><mi>U</mi></msub></mrow></mfrac><mo>=</mo></math>»<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>α</mi></msub></mrow></mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>U</mi></msub></mrow></mfrac></mfrac></mstyle></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>m</mi><mi>U</mi></msub><msub><mi>m</mi><mi>α</mi></msub></mfrac></math> ✓</p>
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>234</mn><mn>4</mn></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn><mo>.</mo><mn>5</mn></math> ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>117</mn><mn>2</mn></mfrac></math> for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>number of nuclei present <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>33</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mn>238</mn></mfrac><mo>×</mo><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo>«</mo><mo>=</mo><mn>8</mn><mo>.</mo><mn>347</mn><mo>×</mo><msup><mn>10</mn><mn>25</mn></msup><mo>»</mo></math> ✓</p>
<p>initial activity is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>347</mn><mo>×</mo><msup><mn>10</mn><mn>25</mn></msup><mo>«</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>08</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup><mo> </mo><mtext>Bq</mtext><mo>»</mo></math> ✓</p>
<p>power is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>08</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup><mo>×</mo><mn>5</mn><mo>.</mo><mn>51</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>≈</mo><mn>18</mn></math> «kW» ✓</p>
<p> </p>
<p><em>Allow a final answer of 20 </em>kW<em> if 6 </em>MeV<em> used. </em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> and <strong>MP2</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>available power after time <em>t</em> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><msup><mi>e</mi><mrow><mo>−</mo><mn>2</mn><mo>.</mo><mn>50</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></msup><mo>=</mo><mn>17</mn><mo>.</mo><mn>0</mn></math> «kW» ✓</p>
<p> </p>
<p><em><strong>MP1</strong> may be implicit.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(c)(i)</strong>.</em></p>
<p><em>Allow 17.4 </em>kW<em> from unrounded power from <strong>(c)(i)</strong>.</em></p>
<p><em>Allow 18.8 </em>kW<em> from 6 </em>MeV<em>.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>stays the same ✓</p>
<p>as energy depends on the frequency of light ✓</p>
<p> </p>
<p><em>Allow reference to wavelength for <strong>MP2</strong>.</em></p>
<p><em>Award <strong>MP2</strong> only to answers stating that KE decreases due to Doppler effect.</em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreases ✓</p>
<p>as number of photons incident decreases ✓</p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>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>Radioactive uranium-238 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>U</mtext><mprescripts></mprescripts><mn>92</mn><mn>238</mn></mmultiscripts></mfenced></math> produces a series of decays ending with a stable nuclide of lead. The nuclides in the series decay by either alpha (α) or beta-minus (β<sup>−</sup>) processes.</p>
</div>
<div class="specification">
<p>The graph shows the variation with the nucleon number <em>A</em> of the binding energy per nucleon.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Uranium-238 decays into a nuclide of thorium-234 (Th).</p>
<p><br>Write down the complete equation for this radioactive decay.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Thallium-206 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>206</mn></mmultiscripts></mfenced></math> decays into lead-206 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>Pb</mtext><mprescripts></mprescripts><mn>82</mn><mn>206</mn></mmultiscripts></mfenced></math>.</p>
<p>Identify the quark changes for this decay.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The half-life of uranium-238 is about 4.5 × 10<sup>9</sup> years. The half-life of thallium-206 is about 4.2 minutes.</p>
<p>Compare and contrast the methods to measure these half-lives.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why high temperatures are required for fusion to occur.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to the graph, why energy is released both in fusion and in fission.</p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Uranium-235 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>U</mtext><mprescripts></mprescripts><mn>92</mn><mn>235</mn></mmultiscripts></mfenced></math> is used as a nuclear fuel. The fission of uranium-235 can produce krypton-89 and barium-144.</p>
<p>Determine, in MeV and using the graph, the energy released by this fission.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>U→«</mtext><mprescripts></mprescripts><mn>92</mn><mn>238</mn></mmultiscripts><mmultiscripts><mo>»</mo><mprescripts></mprescripts><mn>90</mn><mn>234</mn></mmultiscripts><mtext>Th+</mtext><mo>«</mo><mmultiscripts><mo>»</mo><mprescripts></mprescripts><mn>2</mn><mn>4</mn></mmultiscripts><mi>α</mi></math><strong> ✓</strong><strong> </strong></p>
<p><em>Allow He for alpha.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>udd→uud<strong><br><em>OR</em><br></strong>down quark changes to up quark <strong>✓</strong><strong> </strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>measure «radio»activity/«radioactive» decay/A for either<br><em><strong>OR</strong></em><br>take measurements with a Geiger counter. <strong>✓</strong></p>
<p>for Uranium measure number/N of radioactive atoms/<strong><em>OWTTE </em>✓</strong></p>
<p>for Thalium measure «rate of» change in activity over time. <strong>✓</strong></p>
<p>correct connection for either Uranium or Thalium to determine half life<strong> ✓</strong><strong> </strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>links temperature to kinetic energy/speed of particles <strong>✓</strong><strong> </strong></p>
<p>energy required to overcome «Coulomb» electrostatic repulsion <strong>✓</strong><strong> </strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«energy is released when» binding energy per nucleon increases</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>any use of (value from graph) x (number of nucleons) <strong>✓</strong></p>
<p>«235 × 7.6 – (89 × 8.6 + 144 × 8.2) =» 160 «MeV» <strong>✓</strong> </p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The first scientists to identify alpha particles by a direct method were Rutherford and Royds. They knew that radium-226 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{86}^{226}{\text{Ra}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>86</mn>
</mrow>
<mrow>
<mn>226</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Ra</mtext>
</mrow>
</math></span>) decays by alpha emission to form a nuclide known as radon (Rn).</p>
</div>
<div class="specification">
<p>At the start of the experiment, Rutherford and Royds put 6.2 x 10<sup>–4</sup> mol of pure radium-226 in a small closed cylinder A. Cylinder A is fixed in the centre of a larger closed cylinder B.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The experiment lasted for 6 days. The decay constant of radium-226 is 1.4 x 10<sup>–11</sup> s<sup>–1</sup>.</p>
</div>
<div class="specification">
<p>At the start of the experiment, all the air was removed from cylinder B. The alpha particles combined with electrons as they moved through the wall of cylinder A to form helium gas in cylinder B.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the nuclear equation for this decay.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that the activity of the radium-226 is almost constant during the experiment.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that about 3 x 10<sup>15</sup> alpha particles are emitted by the radium-226 in 6 days.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The wall of cylinder A is made from glass. Outline why this glass wall had to be very thin.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The experiment was carried out at a temperature of 18 °C. The volume of cylinder B was 1.3 x 10<sup>–5</sup> m<sup>3</sup> and the volume of cylinder A was negligible. Calculate the pressure of the helium gas that was collected in cylinder B over the 6 day period. Helium is a monatomic gas.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_2^4\alpha ">
<msubsup>
<mi></mi>
<mn>2</mn>
<mn>4</mn>
</msubsup>
<mi>α</mi>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_2^4{\text{He}}">
<msubsup>
<mrow>
</mrow>
<mn>2</mn>
<mn>4</mn>
</msubsup>
<mrow>
<mtext>He</mtext>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{86}^{222}{\text{Rn}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>86</mn>
</mrow>
<mrow>
<mn>222</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Rn</mtext>
</mrow>
</math></span></p>
<p> </p>
<p><em>These <strong>must</strong> be seen on the right-hand side of the equation.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>6 days is 5.18 x 10<sup>5</sup> s</p>
<p>activity after 6 days is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{A_0}{e^{ - 1.4 \times {{10}^{ - 11}} \times 5.8 \times {{10}^5}}} \approx {A_0}">
<mrow>
<msub>
<mi>A</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mn>1.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>5.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
</msup>
</mrow>
<mo>≈</mo>
<mrow>
<msub>
<mi>A</mi>
<mn>0</mn>
</msub>
</mrow>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>A = 0.9999927 <em>A</em><sub>0 </sub><em><strong>or</strong> </em>0.9999927 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span><em>N</em><sub>0</sub></p>
<p><em><strong>OR</strong></em></p>
<p>states that index of e is so small that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{A}{{{A_0}}}">
<mfrac>
<mi>A</mi>
<mrow>
<mrow>
<msub>
<mi>A</mi>
<mn>0</mn>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span> is ≈ 1</p>
<p><em><strong>OR</strong></em></p>
<p><em>A – A</em><sub>0</sub> ≈ 10<sup>–15</sup> «s<sup>–1</sup>»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>shows half-life of the order of 10<sup>11</sup> s or 5.0 x 10<sup>10</sup> s</p>
<p>converts this to year «1600 y» or days and states half-life much longer than experiment compared to experiment</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if calculations/substitutions have numerical slips but would lead to correct deduction.</em></p>
<p><em>eg: failure to convert 6 days to seconds but correct substitution into equation will give MP2.</em></p>
<p><em>Allow working in days, but for MP1 must see conversion of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span> or half-life to day<sup>–1</sup>.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1 </strong></em><br><br>use of <em>A</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span><em>N</em><sub>0</sub></p>
<p>conversion to number of molecules = <em>nN</em><sub>A</sub> = 3.7 x 10<sup>20</sup></p>
<p><em><strong>OR</strong></em></p>
<p>initial activity = 5.2 x 10<sup>9</sup> «s<sup>–1</sup>»</p>
<p>number emitted = (6 x 24 x 3600) x 1.4 x 10<sup>–11</sup> x 3.7 x 10<sup>20</sup> <em><strong>or</strong> </em>2.7 x 10<sup>15</sup> alpha particles</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>use of <em>N</em> = <em>N</em><sub>0</sub><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{ - \lambda t}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mi>λ</mi>
<mi>t</mi>
</mrow>
</msup>
</mrow>
</math></span></p>
<p><em>N</em><sub>0</sub> = <em>n</em> x <em>N</em><sub>A</sub> = 3.7 x 10<sup>20</sup></p>
<p>alpha particles emitted «= number of atoms disintegrated = <em>N</em> – <em>N</em><sub>0</sub> =» <em>N</em><sub>0</sub><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {1 - {e^{ - \lambda \times 6 \times 24 \times 3600}}} \right)">
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mi>λ</mi>
<mo>×</mo>
<mn>6</mn>
<mo>×</mo>
<mn>24</mn>
<mo>×</mo>
<mn>3600</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span> <em><strong>or</strong> </em>2.7 x 10<sup>15</sup> alpha particles </p>
<p> </p>
<p><em>Must see correct substitution or answer to 2+ sf for MP3</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>alpha particles highly ionizing<br><em><strong>OR</strong></em><br>alpha particles have a low penetration power<br><em><strong>OR</strong></em><br>thin glass increases probability of alpha crossing glass<br><em><strong>OR</strong></em><br>decreases probability of alpha striking atom/nucleus/molecule</p>
<p> </p>
<p><em>Do not allow reference to tunnelling.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>conversion of temperature to 291 K</p>
<p><em>p</em> = 4.5 x 10<sup>–9</sup> x 8.31 x «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}">
<mfrac>
<mrow>
<mn>291</mn>
</mrow>
<mrow>
<mn>1.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>p</em> = 2.7 x 10<sup>15</sup> x 1.3 x 10<sup>–23 </sup>x «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}">
<mfrac>
<mrow>
<mn>291</mn>
</mrow>
<mrow>
<mn>1.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>»<br><br>0.83 <em><strong>or</strong> </em>0.84 «Pa»</p>
<p> </p>
<p><em>Allow ECF for 2.7 x 10<sup>15</sup> from (b)(ii).</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Particles can be used in scattering experiments to estimate nuclear sizes.</p>
</div>
<div class="specification">
<p>Electron diffraction experiments indicate that the nuclear radius of carbon-12 is 2.7 x 10<sup>–15</sup> m. The graph shows the variation of nuclear radius with nucleon number. The nuclear radius of the carbon-12 is shown on the graph.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The Feynman diagram shows electron capture.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the nature of the particle labelled X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how these experiments are carried out.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the particles must be accelerated to high energies in scattering experiments.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain <strong>one</strong> example of a scientific analogy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot the position of magnesium-24 on the graph.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a line on the graph, to show the variation of nuclear radius with nucleon number.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«electron» neutrino</p>
<p>it has a lepton number of 1 «as lepton number is conserved»</p>
<p>it has a charge of zero/is neutral «as charge is conserved»<br><em><strong>OR</strong></em><br>it has a baryon number of 0 «as baryon number is conserved»</p>
<p><em>Do not allow antineutrino </em></p>
<p><em>Do not credit answers referring to energy</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«high energy particles incident on» thin sample</p>
<p>detect angle/position of deflected particles</p>
<p>reference to interference/diffraction/minimum/maximum/numbers of particles</p>
<p><em>Allow “foil” instead of thin</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>λ </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto \frac{1}{{\sqrt E }}">
<mo>∝</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mi>E</mi>
</msqrt>
</mrow>
</mfrac>
</math></span> <em><strong>OR</strong></em> <em>λ </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto \frac{1}{E}">
<mo>∝</mo>
<mfrac>
<mn>1</mn>
<mi>E</mi>
</mfrac>
</math></span></p>
<p>so high energy gives small <em>λ</em></p>
<p>to match the small nuclear size</p>
<p><strong><em>Alternative 2</em></strong></p>
<p><em>E = hf</em>/energy is proportional to frequency</p>
<p>frequency is inversely proportional to wavelength/<em>c = fλ</em></p>
<p>to match the small nuclear size</p>
<p><em><strong>Alternative 3</strong></em></p>
<p>higher energy means closer approach to nucleus</p>
<p>to overcome the repulsive force from the nucleus</p>
<p>so greater precision in measurement of the size of the nucleus</p>
<p><em>Accept inversely proportional</em></p>
<p><em>Only allow marks awarded from <strong>one</strong> alternative</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>two analogous situations stated</p>
<p>one element of the analogy equated to an element of physics</p>
<p><em>eg: moving away from Earth is like climbing a hill where the contours correspond to the equipotentials</em></p>
<p><em>Atoms in an ideal gas behave like pool balls</em></p>
<p><em>The forces between them only act during collisions</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correctly plotted</p>
<p><em>Allow ECF from (d)(i)</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>single smooth curve passing through both points with decreasing gradient</p>
<p>through origin</p>
<p><img 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"></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>During electron capture, an atomic electron is captured by a proton in the nucleus. The stable nuclide thallium-205 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>) can be formed when an unstable lead (Pb) nuclide captures an electron.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation to represent this decay.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The unstable lead nuclide has a half-life of 15 × 10<sup>6</sup> years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10<sup>6</sup> years later.</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The neutron number <em>N</em> and the proton number <em>Z</em> are not equal for the nuclide <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>. Explain, with reference to the forces acting within the nucleus, the reason for this.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Thallium-205 (<math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math>) can also form from successive alpha (α) and beta-minus (β<sup>−</sup>) decays of an unstable nuclide. The decays follow the sequence α β<sup>−</sup> β<sup>−</sup> α. The diagram shows the position of <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math> on a chart of neutron number against proton number.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Draw <strong>four</strong> arrows to show the sequence of changes to <em>N</em> and <em>Z</em> that occur as the <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Tl</mtext><mprescripts></mprescripts><mn>81</mn><mn>205</mn></mmultiscripts></math> forms from the unstable nuclide.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Pb</mtext><mprescripts></mprescripts><mn>82</mn><mn>205</mn></mmultiscripts></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>e </mtext><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mtext mathvariant="bold-italic">AND </mtext><mo> </mo><mmultiscripts><mi>ν</mi><mtext>e</mtext><none></none><mprescripts></mprescripts><mn>0</mn><mn>0</mn></mmultiscripts></math> <strong>✓</strong></p>
<p> </p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>calculates <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mo> </mo><mn>2</mn></mrow><mrow><mn>15</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo> </mo><mo>«</mo><mo>=</mo><mo> </mo><mn>4</mn><mo>.</mo><mn>62</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>8</mn></mrow></msup><msup><mtext> year</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p>calculates nuclei remaining <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>= </mtext><mn>0</mn><mo>.</mo><mn>50</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo> </mo><mo>«</mo><mo>=</mo><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>17</mn></msup><mo>»</mo></math> <strong>✓</strong></p>
<p>activity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>«</mo><mi>λ</mi><mo> </mo><mi>N</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>10</mn></msup><mo> </mo><mtext>nuclei per year</mtext><mo>»</mo><mo>=</mo><mn>440</mn><mo> </mo><mo>«</mo><mtext>nuclei per second</mtext><mo>»</mo></math><strong> ✓</strong></p>
<p><em><br>Accept conversion to seconds at any stage. </em></p>
<p><em>Award <strong>[3] marks</strong> for a bald correct answer. </em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> and <strong>MP2</strong> </em></p>
<p><em>Allow use of decay equation.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Reference to proton repulsion <em><strong>OR</strong> </em>nucleon attraction <strong>✓</strong></p>
<p>strong force is short range <em><strong>OR</strong> </em>electrostatic/electromagnetic force is long range <strong>✓</strong></p>
<p>more neutrons «than protons» needed «to hold nucleus together» <strong> ✓</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"></p>
<p>any α change correct <strong>✓</strong></p>
<p>any β change correct <strong>✓</strong></p>
<p>diagram fully correct<strong> ✓</strong></p>
<p><em><br>Award <strong>[2] max</strong> for a correct diagram without arrows drawn. </em></p>
<p><em>For <strong>MP1</strong> accept a (−2, −2 ) line with direction indicated, drawn at any position in the graph. </em></p>
<p><em>For <strong>MP2</strong> accept a (1, −1) line with direction indicated, drawn at any position in the graph. </em></p>
<p><em>Award <strong>[1] max</strong> for a correct diagram with all arrows in the opposite direction.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (<em>β–</em>) decay to form a stable boron (B) nuclide.</p>
</div>
<div class="specification">
<p>The initial number of nuclei in a pure sample of beryllium-10 is N<sub>0</sub>. The graph shows how the number of remaining <strong>beryllium </strong>nuclei in the sample varies with time.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxUAAAEsCAYAAAC1955GAAAgAElEQVR4AeydC3hVxbn3/4mKl8boQavugDfkSyifVDRAW6ElIE30VAonFLStgI03KuDtkEQQRRBQCAcrREH5SOVy2qM95EPtOZJoUjiFHqVJweJRkg+tSkysipVLQWmT9T2zs2dnZbLWngmZnWTt/NfzxDWXd973P7/ZkT1Za2aSHMdxwIsESIAESIAESIAESIAESIAETpBA8gm2YzMSIAESIAESIAESIAESIAESCBPgpIIfBBIgARIgARIgARIgARIggQ4R4KSiQ/jYmARIgARIgARIgARIgARI4GQVQVJSklrEPAmQAAmQAAmQAAmQAAmQAAlECajLsttMKoSlahRtzQQJkAAJkAAJkAAJkAAJkECPJuD1EIKvP/XojwQ7TwIkQAIkQAIkQAIkQAIdJ8BJRccZ0gMJkAAJkAAJkAAJkAAJ9GgCnFT06OFn50mABEiABEiABEiABEig4wQ4qeg4Q3ogARIgARIgARIgARIggR5NgJOKHj387DwJkAAJkAAJkAAJkAAJdJwAJxUdZ0gPJEACJEACJEACJEACJNCjCXBS0aOHn50nARIgARIgARIgARIggY4T4KSi4wzpgQRIgARIgARIgARIgAR6NAFOKnr08LPzJEACJEACJEACJEACJNBxApxUdJwhPZAACZAACZAACZAACZBAjybASUWPHv6gd/4L1JZMQlJOCWqbultfmnCkthSFo9IgjrLvco1Ne1GS0x85JXthjirCN20OKg+Zt+puI0E9JEACJEACJEAC8SdwcvxDMAIJ9EACTbV4fuYMbOhXjLqKXPQJ5PT9NKTnPQ8nrweOH7tMAiRAAiRAAiTQLgKB/KrTrh7SmAS6ksC5Z+NM/pZ15QgwNgmQAAmQAAmQQCcQ4NedToCcmCGacKhyDtKSJmFN5VasK8xpfs0naRCmLitD7ZHI6zKHKlGYloS0wkocioKQbYegsPJTAJ+isnAIknIeQ2nZ45ialtTsa1Qh1lV/iEO1ZVg2dVBzWdpUPL6zQXmF52O8+UpLu7Spj+OV2pZo4bBNDaheV4hR4lUk8TOqECWVtTgiNYV1pmFU4YporNaapaG4i1ebKlES7bNoV4LKSMym2hLknPQ13FLegIal1+CsJNlPtw8AkZg5a17BTpe21vojbNRXkLy4Kn1s7UeJHc4eR0P1hpZXtJJyUFhS2TJ24OtPXtRYRgIkQAIkQAIk0JYAJxVtmbCkXQR+hdsfKceZt/wKjuOgsX45+vzHdNyxuqrlC7upv/IVWFl5MR6obYTTWIeKb+3GzUP6YsCiffjOY9VwnIN4e+HJKBq/CJs/PN7itXw2ZvyiF6ZXfxm22TruEyzO+BGWVX/ebNP0Pkpvy8bYyouwpF7YNOLwqoHYdtME3F36vmuC0oCtG95A79k74DT+GVtvH4LUliiRVBOO7N2A6Vl3Y9sFD6G+0YHTWI0lF2zDTZGYyel5KGt8G2uzQwgVVOCgU4Ulo89t46m5oAHlty/DpjN/gpcc4asOG/tsQfYda1EtJ2Y+LVsVR/o45NmTMLPmYJhD5cg3MTVrDkrdrKKNjuPD0vuQOfZVXLCkGo0i9uF/Qca2u5F192Z8yCUUUVJMkAAJkAAJkAAJ6AlwUqFnRIuYBDJR8OB9yE1v/vqdHLoSY4adja2vvIn69n4xDd2MBx8Yj/SUZCA5hCFjMhHCRCx84BYMC/UCkIr0EcMxqOE1vF7jehIRmo7ixbe12OTehwcLPsLy5/+AQ2jCoa1PY0bJ11x+kpEyYDJWbhyLl2c8ja2uRcihyT/GDwakAsnnIf2ytlMK4DPs/PlKvHLdfCy+ezhC4jcoOYRh9/4LNhZ8hPw5pe1eNB4qKMQDuQOQIjjLfm/9b7xR75o4xRwDoGlfBZ4uOdU1FqkY8IMfYzJK8XTZu66JU8TRoe1YMaMUgxbOxt3DQgj/jyDlcuStfAKTX16MFVvFEyReJEACJEACJEACJGBGgJMKM060MiaQgr4Z/YA9+1DXnr+0G/v3MBx0FS4PTzpkXbOGhg2vourQp6gqK0dDqD8uuUBMTOSVjJS+/TGooRxlVZ/JQv390B9RtqEeg4YPbJ5QRFvY6ndEF95FTV305axoFO/EF9i3fQvK0Q8ZfcNTk2az1NFYUl+PsrwBzZOGaOMmHKp6FRsa0jD4knNb16WkIWNQPTaU/dH1ulq0IRMkQAIkQAIkQAIk4EmAuz95YmFhlxAY1B99xVOKeFwNj+Kasx718JyJwR6lfkVNH72H3Q1+tQAa9uG9j44D/WPYdJuqaiy95qtY6qEn1B4oHu1ZRAIkQAIkQAIk0LMIxOkbXM+CyN4GgED2WtSI9Q9i7UCrn1jrHdr2K/mCSzA41LY8WtLmiUi0phsmJmJtzTGFRzOf+iWjPdaTdMMuUBIJkAAJkAAJkEC3IMBJRbcYhgQWEX6dJta3cAt9b/Oq1RHU1byL0OQxGJJ6LobkZCO05w94s8G9RqEJR6ofx6ikSSip/cJcROrXkTM5DXt2vIWGVmtGmmPC+tOWyGtVMRWehv4jrkW2+spU+MC7NI+D95KROmQMJofexo43/9x6vcWRnVg2qr2H5MUUx0oSIAESIAESIIEeQICTih4wyF3axeRLMOKGEWjY8K/4971icbXYjnUzFj3yLGK9RdQuzQ3P4pFFmyNboR7C3pJC3LThmyi+awRSkYzUrDtQfN02zJizBjvDE4tmDY/MehIomoVJ6ae1I1xvDPvJTHz35XmY88SOyMQiEnPpBShanIt0q79VkQlDw0tY9+9vNe+odWQvShctwVIXwOT+OSicfQ6WPvIkKsN9PI6Grc9hQ/lV3ppSR+Cu4pF4ecZDeEJu0Sv8PvIg8jEdiyelt15r0Q5CNCUBEiABEiABEuh5BKx+/el5+NhjPYHTkD5pIcrv+zvmfu0sJCX1xdi1f8WEBx9Atr6xmUX2XZg5+n0sSj8JSUlnYfS2y7Fu62Lk9okszE6+GLlPbMLGkR+gMO1UJCWdhDOzXsBXZz6HX9w3rHnXJbNIYnum8M5RT259AiM/WoC0k8S5FwPw05rh2FjzC8zKPNvYk6lhcvoPsLI8D5g7CGeKMzbG/hyHJ8zCM9muJ0DJfTB64bOouvkoHgn38VSkPXIUN1etwX2emnqhT+5ibN04Eh8VZuIk4ffMiXjhq3eg6hfTkRmvtS2mnaYdCZAACZAACZBAoAgkOeIFc9clDgZTily1TJIACZAACZAACZAACZAACfRkAl7zBT6p6MmfCPadBEiABEiABEiABEiABCwQ4KTCAkS6IAESIAESIAESIAESIIGeTICTip48+uw7CZAACZAACZAACZAACVggwEmFBYh0QQIkQAIkQAIkQAIkQAI9mQAnFT159Nl3EiABEiABEiABEiABErBAgJMKCxDpggRIgARIgARIgARIgAR6MgFOKnry6LPvJEACJEACJEACJEACJGCBACcVFiDSBQmQAAmQAAmQAAmQAAn0ZAKcVPTk0WffSYAESIAESIAESIAESMACAU4qLECkCxIgARIgARIgARIgARLoyQQ4qejJo8++kwAJkAAJkAAJkAAJkIAFApxUWIBIFyRAAiRAAiRAAiRAAiTQkwlwUtGTR599JwESIAESIAESIAESIAELBDipsACRLkiABEiABEiABEiABEigJxM4uSd3nn0ngZ5EICkpKWZ3HccJ18+bNy9qN3/+fIh8KBRCQ0NDtNydUG1k3m0j09KPaiPzsl7au+/SRpapeVku7tKPaiPzst7dRqZVG5mX9e679KPaqHl3G5mWNn4+pJ24+9moPtxtZFq1kXlZ73VXbWRe6ojVRtrINl62fjayjaz3aittZJ2al+XiLv2oNjIv691tZFq1kXlZ775LP6qNmne3kWlp4+dD2om7n43qw91GplUbmZf1XnfVRualjlhtpI1s42XrZyPbyHqvttJG1ql5WS7u0o9qI/Oy3t1GplUbmZf17rv0E8tG2It6XiSQkAQc5QKglDBLAiSQ6AR0v/erVq3SIrBhY+LjoYce6rAWkzg2bGxoFZ3VadHVm/gQNjq9tuLo/OjqTbSa9Nkkjg0bHVcTrSY2NrSasLUVR+dHV2+itTO56fSafA6EXl4kEAQCXt8bkoRw92xJ/DVTKXJXM00CJJCABPh7n4CDyi6RAAmQAAmQQJwIeH1v4JqKOMGmWxJIJAKrV6/WdseGjYkP9+tZfqJ0fnT1wq8NGxtaTbTY0Cri6PTaiqPzo6s30dqZ3HR6dVxNtJrY6HSY+BA2Or224uj86OpNtJr02SSODRsdV6GVFwkEmQAnFUEePWonARIgARIgARIgARIggW5AgJOKbjAIlEACJEACJEACJEACJEACQSbANRVBHj1qJwFLBLzejbTkmm5IgARIgARIgAQSjIDX9wY+qUiwQWZ3SCAeBGy8Tyx06fzo6oUPk/eSdX509SZaTWxsaDWJY6s/Or224uj86Or5ORAE2l4m3Exs+DmID1sd17ZRWUICwSLAJxXBGi+qJYG4EBB/cVi1ahWmTZum/eKv2ujyQrDORq2P1UaclyH2g29PGwnNVhvpT95VvzIvtUo7913ayDI1L8vdd9VGzbttZVq1UfPSTtylXtVGzbvbyLRqo+alnfuu2qh5t61MSxs/rdLOfZdtZJmal+Xuu2qj5t22Mq3ayLzUKu3cd2kjy9S8LHffVRs177aVadVGzUs7cZd6VRs1724j06qNmpd27rtqo+bdtjItbfy0Sjv3XbaRZWpelrvvqo2ad9v6pWUboZVnVPhRYnnQCHg9qWhzKIXXvrNB2C+XGkmABE6cgO73Xrf/uohsw8bEh8le7zo/unpb/bGh1USLrf7o9NqKo/OjqxdMdFo7k5tOrw2tndkfnV5df020mtiYxNFptRXHRIvOxkSr0MuLBIJAwOt7A19/CtrUkHpJgARIgARIgARIgARIoJsR4KSimw0I5ZAACZAACZAACZAACZBA0AhwUhG0EaNeEiABEiABEiABEiABEuhmBDip6GYDQjkkQAIkQAIkQAIkQAIkEDQCnFQEbcSolwRIgARIgARIgARIgAS6GQFuKdvNBoRySKArCHhuDdcVQgxiir3eg7ItY5C0CvRB0kutBr8sJ2hCticIjs1IoAcR8PrewCcVPegDwK6SwIkSMDkwy4aNiQ+TPuj86OpFDFs2Or024tjwodNpk4lOr67eRKuJXpM4tmx0mm3EseFDp9OEqy0bk/7Y0GsSx4aNmKzxIoFEJsAnFYk8uuwbCRgS4OF3q6Ok5EFVskDNy3L3XbWReXkwl9tWpqWNX16Wu+/xbiP1xjuO7FNH4vhplb7d947EkX5UH7LcfVdtZF5qddvKtLTxy8ty9z3ebaTeeMeRfepIHD+t0rf73pE40o/qQ5bHuss2QmtQnrLG6g/rSEAQ8HpSwcPvgnDCCDWSQJwJeB1i4w6pO9RJ2NqwMfFhcoCUzo+u3lZ/bGg10WKrPzq9tuLo/OjqBROd1s7kptNrQ2tn9kenV9dfE60mNiZxdFptxTHRorMx0Sr08iKBIBDw+t7AJxWccJIACXj/xaGbcuH73vEbGLKND9sgcRUEgqQ3SFrj8+miVxLoGgJeTyq4pqJrxoJRSSBQBGy8Tyw6rPOjqzeFpvOjqzfRamqj02xDiw0fOp2m/bWhxcSHDb0mcWzZ6PTaiGPDh04nPwf+hHT8xQSIFwkkMgFOKhJ5dNk3EiABEiABEiABEiABEugEApxUdAJkhiABEiABEiABEiABEiCBRCbASUUijy77RgIkQAIkQAIkQAIkQAKdQICTik6AzBAkQAIkQAIkQAIkQAIkkMgEOKlI5NFl30iABEiABEiABEiABEigEwhwS9lOgMwQJNDdCfDwOx5+Jz6jfgeJycO7Yn2OVRs179VWtVHzsdr4aY3VRta1J46NNlKr9OW+q1rUvNtWplUbNS/t3HfVRs27baVe1UbNu9vItGqj5qWd+67aqHm3rUxLGz+t0s59l21kmZqX5e67aqPm3bZ+adlGaOXhd36UWB40Al5byvLwuyCcMEKNJBBnAl6H2LhD6g51ErY2bEx8mBwgpfOjq7fVHxtaTbTY6o9Or604Oj+6esFEp7Uzuen02tDamf3R6dX110SriY1JHJ1WW3FMtOhsTLQKvbxIIAgEvL438ElF0KaG1EsCcSDg+ReHOMShSxIgARIgARIggeAT8PrewDUVwR9X9oAE4k5Ad6iTEGDDxsSHyQFSOj+6elv9saHVRIut/uj02oqj86OrF0x0WjuTm06vDa2d2R+dXl1/TbSa2JjE0Wm1FcdEi87GRKvQy4sEgkqAk4qgjhx1kwAJkAAJkAAJkAAJkEA3IcBJRTcZCMogARIgARIgARIgARIggaAS4JqKoI4cdZOARQJe70ZadN/tXTXVluC6jC24oWY98tJP6156j+xF6SN3Y8LScgATsbY7avQk9gVqS6YgY25/VOxdiNGpZn/Dah6LpzC4YguWjD7X0zMLSYAESIAEupaA1/cGs//Ld61uRieBHkCgCYcq5yAtKQ2jlu3EkTY9lvWTUFL7RZvaeBfo3hUW8W3YmPgweS9Z50dXb6s/Hdf6BWqffwgTnv4Sm+q+hOM87znpsdUfnd72xTkN6XnPw6lf3GZCEctPcnoe/mnVrdoJhU6ryRjG0iF/p2zY2NDamf3R6bXBxFZ/dFptxbHRZxOt8nPHOwkEkQCfVARx1Kg5AQmIScNcDLjmUTTgeyiq2ohZmWe7+inr92FhHP5SLf7isGrVKsj91F2B2yRVG11eONDZqPWx2sTal171o8vLOKsWTEHxvP9B5vybsf6hma0mSKqPNkBi9E9qbU+b1rZ/w8e/exbzXjwP9zz8fTx+z0+taWsdpzkn9ap9VvNebVUbNW+7jZ9W23Gkv470R2qVvtx31a+ad9vKtGqj5qWd+67aqHm3rdSr2qh5dxuZVm3UvLRz31UbNe+2lWlp46dV2rnvso0sU/Oy3H1XbdS829YvLdsIrTynwo8Sy4NGwOtJBc+pCMJmwNTYAwg0OgcrZjshZDpZWZc5yFruVB1udPVb1k901tYcc5XbSXrtN+32rNt/XdiesM3BCqcgFHKynyl3CqdmO1mAI/SEpix3ymsORmR84lQUZDoIzXYmFz7YIi3cFk6ooMI56EhG453cO+5wiqZcHvYDZDsFz77u1B+sccqLpjihsP80Z8ry7U59BHFjzVonG+Odok2bWtqd9Q2nqLzGOdwSzXGcL536qvVOQVYo4nugU7C2wqmJjlVEZ1aB80zRFOdMESs026k46B5Ll8PDNc49k1v6jKwCZ21FJGbj287abBknwiTcT1f7cPIT557sixzRVsQM90/GbKx3qp4tiDJt5V+0leyLfuVskXoRcrIK1jtV9Z84NeXLnSkhOR7FTuFjK1uCC9+biqL1CLdb69wz//GIzTGnZu1EV/8jbLKLnXsKb25hGJrSirMYi4G4yCmo+MRxnJY2Fa+7uIemOGNumt56bA67x/dyZ0rRemdy9kBX/BbpMnXCn1npIHLX+TE5n0DnQ4TS2ejqTXwIG51eW3F0fnT1JlpN+mwSx4aNjqvQyosEgkLA63sDX38K2tSQehOcQD/8aM485NUUYdbqKo/XoBK1+w0ov30Zdp32LbzkOHAa67CxzxZk37EW1Uea2tnpzSj9zfvo98AOOM6XqK+4Gjtv/gbSBizCm995DHVOI34277tA0TTM3fw+WrxvRv6MF3DS9HI0Cpv7BuOTxf+IsdHX0Y7jw9L7kDn2VVywpBqNjoNVP5uAjG13I+vuzfiwxRGw9T+xvXc+pj/0AOq33oFhXusJjryJkukT8PPa3lhSL15t+hL1Sy7CtpuymmMmD0Be2buoWTsROOtaVBxsRP2S0Uj1oxGJWSv8iJgp+1F6WzbGVl4U9r9q1VM4vGogtt00AXeXuvvdgPL8NajsNxvTH3oIjfXr8K2dhRiSNgqL3hyGx+ocOIf3YCFWY/WLb0b6+Tmql9+GsS+cjunVQrsYs9/jwZOew8/+dUfsMStfhP/cdSpueamuuc8b++E/su/D6urP/XoGlC/CI5u+0qrN/9tY3tKm6X2U3j0BU/eMRuXhRjjODszuvRUvlr/l75M1JEACJEACVglwUmEVJ52RQMcJnHTxOCwozkVN/oKWL00dd9vtPYQKCnHd4AuQIpQmhzBkTCZCW/8bb9Qfb6f2TGT/4zXITRdfv3shNOTbGBYKIXvhbNw9LIRkJOPU8y/ByEEH8PLr77gmbpcjr3hBi815V+CBByehZvlm7DzUBBzajhUzSjEo6gfAqWnIW/kEJr+8GCu2ftqiMzQWU38wEL1wEkLpFzf3qaUWQBMO7fwF5r4yEjeOH45hoV7NWof9FCs33oya/GV4vr1rZyIxU0Sf0y9E09anMaPka1j4wC0R/0lIGTAZKzeOxcsznsZW0afIJdg/kDsAQkVy6EqMGZYGZN+LB+4ejpD4VyKlP0aM/BoO/s/7qBGTvEN/wPPLP8LkqTdEfIuGfZB18w0YWPtu7DEL3Yx/vO4KpKcIx3J8/oBX3vjINcGTyqTAm/HgA+Nbtelz5keRNk04JPr68kgUL/4hBoT9pmJA3hL8JPsixRGzJEACJEAC8SLASUW8yNIvCZwwgV7oMz4fxXnvI3/Wz2P/1feEY3T3hslI6dsfg/AuauraLluPj/qvYfjl56Plf4pJzRoaylFW9SkOVb2KDQ1pGHzJuS4b8YU7DRmD6rGh7I84ZCzsM1SVlaNh0FVIO+tkVytb/Y74D/XHJReIqYK8Iv7DffpMFrb/njoaS+qrsGTYZ6gsLUWp+CkpxDUZt6DdzwbC/IA9NfWuCZ5GUkoazjlPtmlheXl4cibbpuAfzufuUZIG7yRAAiQQbwIt/37GOxL9kwAJmBNIvhjjF8zvga9BmSPyt+yH8//hVP/qDtVUY+k1X4VYoCZ+fvrTnyLppK/hlvKG9nlt+hTv7a6P0aYeu9/71P8v9zFatqpqeBTXnHVSi9akJJyUcQvE5rQtVwiDMtI8nqa0WLRNHcLekluQdmYGrln5OsIvLp19HVZVPYOB+LQTJ4JtlbGEBEiABEigawhwUtE13BmVBLQEkvtc3yNfg9KC6VIDcU7EseY1BGJNxapV0XTM9Q6q5uRzccngNLXUlfd4IuKqNU5mr0VNoxPW6NbqOFXaLVtjxWiq/XfcfctOXLfpPTT+ZgnycnORm/sdpB38Ez6M1ZB1JEACJEACCUuAk4qEHVp2LPgE3K9BleD1zxuD36UT7kEK+mb0O+HWZg3VV60cHKnbhz2hbOQMORepQ8Zgcuht7Hjzz62fIBzZiWWj+iOnZG/r8phBe2NITjZCe/6A+oN/d1k2NcdEP2T0Da8ucdW1J9ni/80G95qUJhypfhyjkjpy3onUqL4u9ncc/tz8BbD29Ca2rezrPtS1WtR/BH/5s2udS2wnrCWBuBPgdrJxR8wAXUyAk4ouHgCGJ4GYBKKvQS3Hwyu3xzRN7MrT0H/EtchueAlvvPVJ87v34qTpRUuwtJ1vHvlzqsbSR5ajtFZ8MW7Clx+9jpk3vYTriu9Alti9KXUE7ioeiZdnPIQndjY0TyC+/AiljzyIfEzH4knprdda+AcSq5qROuxHWPjdbfi3zTuwM/zFvwlH9m7AzJueRUbRLEzq0MneyUjNugPF123DjDlrIv4dHKndjEdmPQl0yH9yZIK1HRue/S0awuu9j6Nh5xrMmfEkDsbsdzwqZV/L8ciizagNTywOobZ0Of6z/IN4BKRPEjghAjz87oSwsVGACPDwuwANFqUmMoFYh9s1b2U6dMKTaIB4/Wa956nKOjpiDUCs6yc/+QkuvPDCWCaedeKvb+5/LNW8V6NWNl/+CV+s34BVl07GnWMuhVwN4RzYhV88WYXzJ/8YYy49A/Pn/zNmTJ6I375Qjj8eBpBVgHGX1aNx6wvYdv543DnmEuBPv8FTGz5D1vTxuPKck8MHTc27fwpefWoz/pw1GbUvPon58+YBzqfY9YsN2Bpudyl6hWP9P1w66evIOe0t5K9/Ezjz6xgz7tv4vxuKUSTahK8vceBPb2HXf23F794XIs7D18dkoWT9Bry4ehGAo/jTq/+KDX+6GZOnnIxLT/VnHmYwewb+9D+78F8v/Q7vC/8XX42x37kS//vSc8I7MQF/x4Fdm/Hk1t6YfOcorH9sgQfr/OaYey4L27SKefwARv6vryDvlqXN/s/8OoqeLUHD7heRIqR9+acomx9deS6a1R7FyC9+g2s2pWH6j67EOUnA/PmzMeP7mVEdl57ahCMN/4PXyiuiHKYUrYCz99/xzvM7gPE/xo71jyhtjrXRGWbw0PToWNTtWI9lM77vGncYtfkXMT7HD+Ddqt/ihVf/iMORcRmAP+L5189FRd02bPuX+ZExFP1p/ZmNVrgSqo2ad5lGk6qNmo8auhKqjZp3mUaTqo2ajxq6EqqNmneZRpOqjZqPGroSqo2ad5lGk6qNmo8auhKqjZp3mUaTqo2ajxq6EqqNmneZ+ibdbUSaFwkkAgEefheUE0WoswcSkAe3+Rxu1/iesylPHOYm67906isedh1qNtvZFD0orv34xCE24mf79u2ejW0c/CQc6/zo6oUPkwOkdH509SZaTWxsaDWJY6s/Or224uj86OrNPgfHnPmTr4ocjChatL1M4tiw0XEVymzEseFDaNHptRVH50dXb6LVhK1JHBs2Oq5CKy8SCAoBHn6XCFND9iFBCSQjdfRi1DvPez+FSL4YuWv3wInW/xn/va4c/cRCWecvqPre23h6e3073ulvi3HlypUYMWIEduzY0baSJSTQbQmIp3xzkJZ2C0r2yjUd4nWstfjPF4/jvklX+R8Y2G37RGGJSIBPKRJxVNknNwGuqXDTYCI3jIYAACAASURBVJoEgkLg7x/j3R2D8L1v9RFv5+N/XfU17Nn2Fv7cAf0zZswAJxYdAMimXURArKmYiZeKv4Zto8+KbPd7KjKfPIbBd96E+zLP7iJdDEsCrQm4XxNtXcMcCSQGAU4qEmMc2YseTSAZZ5zVG2dYYMCJhQWIdNH5BJJDyMydhXX1zdvnOo6D+nWzMPiis9qxeL7zZTMiCZAACSQSAU4qEmk02RcSsEBATCzKysr4KpQFlnRBAiRAAiRAAj2FACcVPWWk2c/EInDyeeg3vAavvy3OMv4cb/xmBy4bORDnW+pldnY2tm/fHp5YrF+/3pJXuiEBEiABEiABEkhUApxUJOrIsl8JTuB8fGPc/8aGa76KpKR/wJDlfXBHTj+rr3oMHz48PLGYOnUqtm7dmuA82T0SIAESIAESIIGOEDi5I43ZlgRIoKsI9EKf3GLUO8VxFSAnFmJXKPEjXo3iRQIkQAIkQAIkQAIqAR5+pxJhngR6IAFxiM2qVaswbdo0rF69ug2Bd955B8uWLcMNN9yAf/u3f2tlo7ZR88KZWtYq73yEXps34l/Ovwkzrr4gcgCbf5uGhgaEQqE2PrVxPHTINqsWTEHxvP9B5vybsf6h27BgynDMq/7fmD/jajx0RxamDPomXuz7Ezz8Txk4rQ0dvVaPJm30t2Li1SCqfxW+/KASTz11BKs++A/U/uKZFmvnID54vRKb1pWjNlw6EAVrl+CkT97DRWc1/w0pVhw/trHayOCqjZoP2zkf4XfFT6E6887wWP9U+bx5tsHf8PHvnsW8F8/DPQ9/H4/f89Pw589Pq9Tjvqt+1bzbVqZVGzUv7dx31UbmpVa3rUxLG7+8LHff491G6o13HNmnjsTx0yp9u+8diSP9qD5keay7bCO0clvZWKRYFyQCPPwuKCeKUCcJdDIBr0Ns3BLEwU/79+93hg4d6uTn5ztHjx51V4fTJ3w4VOPbztrsy5zstW87T61a1cavWmBygJROi1rfWLPWyY4eLHjMqVk70cHAyU5Noxq9dV7107pWf4iYsNf5aG3T6Bx++1+dguxMB6HZTsXBZoHNPr506jZNd0JZBc6zVfWOqGms3+4sn3J5+AC4xy2wbZ9WlYYQ1DzWAyfPC+vzsAgXmcSJx+fAS4+JFp2NDa1Cmy6Ort7Eh7DR6bUVR+dHV2+i1aTPJnFs2Oi4Cq28SCAoBLy+N/BJRZCmhdRKAnEi4PkXB49YdXV1yM3NxRVXXIEVK1bg9NNP97BqZ1HTXpRcdz2eu+HXeDlvgNV1IaZKmmpLcF3GFtxQsx556UBtyRRkPHctal7OQ3p3WXnW1IDqDSux4pNs3NX7KQyZ2x8VexdidGpEoA/HcN+y9qHQbWsKxradj0bbYeiPBEiABEggvgS8vjd0l38u49tzeicBEugQAflKVN++fVFaWoo33ngDd911F44dOxb1K22iBR6JmDafvYl7JnwTaUlJSEoahKnLylB7pKmVl6aGnRg/vH/kgLM0jCosQWWtPEU5crJyUg5ybvonTE0Tfpp/0gorIa2Ew9WrV0VOYZ6DykOtY0QD1kUWp4svwjlpaPYhYwxBYeWnrtfAPkVl4RAkpUX8HapEYVoa+n93IsqWTY30SejdgOqGT1H7yuNRfWd/84fY2XA8GtYrsXr1StQ+Owuzakbhsfu+iTMVozDXI/Wo2XM2Bl9ybquJWfIFl2AwyrFk3nKlVSQb0Zqz5hXcOn44RklmUx/HK1G2kf6dfV1rXuG2SRE2zf5Wr1qC6nWFPn6abeq2/ptLy3E0VG9A4ai0yHjlIGfKva6x/wK1JZNa2EZamhwkFvPzFv4ctH3VzyUsnNT5EEY6GxtaTeLodJj4EDY6vbbi6Pzo6k20mvTZJI4NGx1XoZUXCQSZACcVQR49aieBLiAgJhZbtmwJR/7hD38I8fSi49dRlOfPx87kb6O60YFz+FcY98lyZIx9AtWRiUXTh6W4LfMW/CnlO6gXNs5erMrYgZuy5qD0Q/eX8nK8vu8szK5tRGN9DapK84ENpXi1lc1fUVVWDkwegyHyL/0d74TioQHvvLoLlf1mo9Zx0Fi/Dt/aWYghaaOw6M1heKxO9HMPvo//wvi5v8aHPnObZqcnI+26x/HS4u8i5PN/7aaP3sPuBkVCNFuPugNH4B+iAeW3L8Pbpw7GS44Dp7EOG/tsQfYda6P8o65iJZrex+6NKzDk2ZMws+YgHOcgKke+ialtxkg6OY4PS+9D5thXccGSajSK2If/BefXPo+suzdrmEgfvJMACZAACXQHAj7/PHUHadRAAiTQXQn07t07/PrTV7/61fDrUDYmFqG8+Rg/+rLmL80pA5D7QCEKav4Vz+/8DMCn2LpiMUoG3Ytvf+PCyBfrVAzIW4KNk1/DjBXbXU8iMvGNb12OASnJSA6lI/O7P8B9GVvwdNm7LV+qv/gQZRuAyTlfR2ocIZ959dV4IHcAUgAkh67EmGFpQPa9eODu4ZF+9kf/9AvQ8HIVapSnMq1lJSEldF7YT+tymXNwpG4f9sjsCdxDBYX49oBzm2MkhzBkTCZCW/8bb9S7J2yxHTftq8Bvf3cyCh68D7npgmwqBvzgx5iM0tb8pZtD27FiRikGLZyNu4eFmp+wpFyOq2+chMkvL8aKrZ9KS95JgARIgAS6OQFOKrr5AFEeCXQHAmL3EvUS6ynEuoqsrKzwxGL06NGqSZu8l59mozMwaPhAFPzUFSclDRmD6rGh7I84dOiPKNtQjdDgS7B4wXyX3xT0zeiHhg2vosr1GtPgsTe32KR8Hd+ffBXKn/sd9oX/VN+EH339dGxANnKG9G6xU1N9s9SSNnn//jSbpoxw6WjTurngxqzLfGpainVxpk27o8XYJ9U360afmpbiOfMl22Sk9O2PQXgXNXVHWgzOuLIl3Sb1BfZt34K38A1k9BXTqMiVOhpL6utR5lov06ylCYeqXsWGhrQ2r2xNu+uOlrGXfpS7yS46em6uz5viX2Z1PoSdzsaGVpM4Oh0mPoSNTq+tODo/unoTrSZ9Noljw0bHVWjlRQJBJsBJRZBHj9pJoJMI+L1PLCYWS5cuxZQpU5CRkYEdO3bEVOTnRzZ62mM7W1kn7g1Lr8FZkXf+m9dLnI6MW37lNgmnd7/0rKvsNPTPuRF5e57C2vBfvj/DvCXPI+O+8RgW69UnuabC5UlNxu5PCGe8vSnG04Vmb/+29Z2I28jagVb9m4SS2i+07+yvXv1MZBKgKmzJt17H0FLuTi2eN8+dbZs+uqttWZsS2Z82FdGC1lqqsTR8iGPLGpikk76GW8p93+UK+zF5Pz32+OjXQohAOh8mNja0msSxoVXE0em1FUfnR1dvorUzuen06rgKrbxIIMgEuPtTkEeP2knAEgHxBT3WORXuMOIvdu5/PGVenLr93HPPoaysDO+++667SewzGfzOqbjddT7EdWJC8Rx+PeZ2TLjUQZrnORUOfpS+Hxdd86/4xj0z8U8ZKa64R1Dzf1fiucE/R0HoJbz88H/h/PtuxtXnnRK2MT+nIh2oeREP/+ytaAzR0WnTfoB7czLxs9cHNp+lkJeBnIty8c53fox//sdBkbM3mjX8rG5k8/kXPxUcV0bPYKhQz5xoRbA508zap80XNfi/D5cCP2nuu2w+7UfpyLnoJ9FyOV6yHuF2P8Pr37gH076ZiksibJuZbEPfe2ai7PGbW/Uv47Sk5uauth+UPYqfifM9xGtl4fM+Zrb6nIQbtDqn4nz8ODxeZfj+/JaxcH+2moPwnIroWEUS6hiqedVe5FUbNe9u43f2Q6w2sr1qo+alnfuu2qh5t61MSxs/rdLOfZdtZJmal+Xuu2qj5t22fmnZhudU+BFieRAJeO3+BHU/XK99Z1Ub5kmABBKLgO733nSP9u3btzvC18qVKz0BefoJn10QanuWwsEKpyCU6RRUfOI4zidORUGmE8rb5Nz74EMu339xqoq+5yB7rVPT2OgcrJjthJDpZN9T5LIRyUbncNVyJyt0h/PMM3c7ZylnUMQ8p8Kl76DwFD7TollXS3+a9UXPjghrDzmXjb3TdR5DxCasVco75syffFWrMydkjfveEkeURs7RUM+pcJ334T5eQ/Zt8vwVbpct6bBWhPkXPtTC1t3PaMyzro2ejRF24Gor2QzERZExi4SI8AuP0d+UcyrC7S938ja95+LkOKt+VugUZTWfXdLo0V/h2WTP/9bcWrosU7p6YWfDxoZWEy02tIo4Or224uj86OpNtHYmN51eHVehlRcJBIWA1/cGvv4UxOkhNZNANyUwfPhwbN++HTNnzsTixYtbbTmrk9ywdAle3v0Rwm/wH3kTJTPvxobr5uCurHMBnIusu+bgupfnoeL1/WgIr404hNrSpZiVDxQtztWcJ5GMlCuvw+RBL+L2259Hn8x+6H+C//dL7n81bsiux4Z1/4GPvhRzKKFjOR5ZWq3rYnzrk/sh545rsWduEZ7d27yBblPDDjyx6HHsKZiGq847pQPxT0P/Eddi4ME/Yt2/vxUZo70oXbQES11vKSX3z0H2tSlY+siTqAxvk3scDVufw4byq7zHKHUE7ioeiZdnPIQndjY0L6Q/she7//Ml5GM6Fk9Kb7U9bgc6wKYkQAIkQAJxJnCC/6zGWRXdkwAJBJaAmFjs378fmzdvbnOWhX+nzkB20W3I+GQL0sWagjN/iG2DlmHrE+PRJ/J/qeQ+4/HE1idw8ZH/QtpJ4v37s5D1Qm/MrFqD+zLP9ncta8JfunMRwghk9j/nxL+sJqdj0sqf4z4sw/x77kRS0kSsPZyNB5+ZKCN10b0X+mTfhY0Lz8WGr50VPvPhpLRp2D1oPl66ZwRO66Cq5PQf4Ia7rgbmDsKZYozG/hyHJ8zCM9mhFs/JfZDx/SmouvkoHkk7FUlJpyLtkaO42XeMeqFP7mJs3TgSHxVm4qTw2E/E7pRvo+oX05GZwn+iWuAyRQIkQALdm8DJ3Vse1ZEACQSRgDwkb8aMGRBnWRQXF0OUeV7JA5BXtg954UWxn6J+02ueZkAyUtJH48oxP8aLO+QuRW7TZKSOXox6Z3Hbd/nDZk346+cfA3k3YuBXP3Y3RHJ6HsocoaD5Ss97HquOr448/RD66sP6mmuFjhzMWpeDlG+tDr+r3lyeBee2iAM073h02rx5rsnLuRi9pAri2UbLdRrOu/o2OOv1uxC52wh9LrktVSnpGJ23JPzTUtic+r1aIPPh3ZkcLAkv0N0mS9swEdvDnve1a/BQ/a+wLmoFoKwe0W6L8qSzkDm1EL+ZKjwqV2Ssj69e7eKSivTReVgifiLmYl1FZqhXJHcafPuruGeWBEiABEig6wjwz0Bdx56RSSChCYhJxC9/+UvIsyxqa2u7tL9NDb/Fsxv+hvvuHI2zI+uMu1QQg5MACZAACZBAAhHgpCKBBpNdIYHuRkCeZSG3nH3nHf12o9b70LQXJTlpOCltGRpnPoppJq9KWRdBhyRAAiRAAiSQ4ATUVeZeq7lVG+ZJgAQSi0Bn/N6vW7cuvDOUuHfkCtIOKkHSKsYkSHqptSO/RbHbkm1sPqwlARJwwv+eqxz4pCLBJ43sHgnYIND27IC2XnU24mnFrFmzMHXqVN+doXQ+2kb1LtH50dULr7ZsvBW2lNqIY8NHiyL/lK04Oj+6en+FrWt0fnT1wpstm9bK2uZsxLHho62ytiW24uj86OrbKvMu0fnR1QuvNmx4+J33+LA0cQjw8LvEGUv2hAROmICNw+9kcHnQk8yLu7vs448/xq9//Wv06tULN9xwA045pfkAOvUfbXcbt49Yh135tZFa1Hq3Xz8brzbSVt5VG5mXWqWd+y5tZJmal+Xuu2qj5t22Mq3aqHlpJ+5Sr2qj5t1tZFq1UfPSzn1XbdS821ampY2fVmnnvss2skzNy3L3XbVR825bmVZtZF5qlXbuu7SRZWpelrvvqo2ad9vKtGqj5qWduEu9qo2ad7eRadVGzUs79121UfNuW5mWNn5apZ37LtvIMjUvy9131UbNu2390rKN0Dp/vtcmE34tWU4C3ZcAD79Tn9MwTwIkECage/1Jd6iTcNIem/379zu33nqrM3ToUEek5WXiw+TVDJ0fXX17+yP1q3cbWk202OqPTq+tODo/unrBRKe1M7np9NrQ2pn90enV9ddEq4mNSRydVltxTLTobEy0Cr28SCAIBLy+N/BE7SCMHDWSQJwJeP3PIc4hnaNHjzr5+fnh9zLFSdymV5D+YQ6SVsE/SHqp1fQ3pv12ZNt+ZmxBAj2NgNf3Bq6p6L5PlqiMBLoNAfXVJC9h7bURO0MtXboU69atw4gRI7B+/Xqj95a9YqtlOi26euHPlo2qTc3biGPDh6rLK28rjs6Prt5Lm1eZzo+uXvi0ZeOlz11mI44NH25NfmlbcXR+dPV++tRynR9dvfBnw4ZrKtSRYT7RCHBSkWgjyv6QQMAIiAXc27dvDy/g3rJlC44dOxawHlAuCZAACZAACZAAJxX8DJAACXQ5geHDh2P//v3YvXs37rrrLtTV1XW5JgogARIgARIgARIwJ8BJhTkrWpIACcSRgDiB+5//+Z/DEXJzc8MTDK9wQdo9JUhaBesg6aVWr98OO2Vka4cjvZBATyPASUVPG3H2t5lAUwOq1xViVFISxLZoSUk5KCz5NaobjvsQasKhyjlIi9rLdi33tMJKHAq3/gK1JZMiflvqk5LSkFOyF02eEaT/NIxathNH2tjI+kkoqf2iTW2iFIjtZVesWAHxStSVV16J0tLSNl0L0nvJQdIqQAdJL7W2+dWwVkC21lDSEQn0KAKcVPSo4WZnmwkcx4ebF2Hss8DNVfVodBw01j+EC7bNxtifbY9MDFRWyUgdvRj1jiN2THP9/AVVRd8DspbjpQezkBpudgR1NR8ie+3bYd8t9vUoyxuA2L90DdiavwCrqz9XBfSYvFjAPWPGDJSVlWHChAm+B+X1GCDsKAmQAAmQAAkEgAAPvwvAIFGiZQJNe1Fy3fV47oZf42XXl/ym2hJcl7UPhXsXYnRq7K/+zYqacKT6CYwdUoHvVW3ErMyzm4sPVaJwQAGwcQuWjD7XULx4EjEXA64pR0bW59iK6ah66W5kpkgdsn4fFtasR176aYZ+zcw68/A7oUgeBiXVqXlp8+ijj+Lpp5/G2WefHT4wTxyaF+uwK9WPLi/juHd2MWkjdcu7XxupVdq5735t3DZqOt5tpN54x5H96kgcP63St/vekTjSj+pDlrvvqo3MS61uW5mWNn55We6+x7uN1BvvOLJPHYnjp1X6dt87Ekf6UX3I8lh32UZoDdKrZbH6xDoS4OF3PW0TYfbXm8DBCqcglOkUVHzSut6vvLVVS+7w605RVsgJFVQ4B1tKncaatU42Jjpra465SnXJRudgxWwnhInOM+XrnbxQyMkqet05HG3WUt8+v1EHMRNe+027G+gOdRK2Nmy8fIjzLORBeeI8C5M99L38dEV/bGg1Yavrr4kPYaPTayuOzo+u3kSrSZ9N4tiw0XE10WpiY0OrCVtbcXR+dPUmWjuTm06vyedA6OVFAkEg4PW9Qf4ZlFMuEugxBJo+eg+7G/y6W4/d733qs+7B3eY4Pixfj+U1uSi+a0TktSdR34QjdfuwJ3Q6Pi69I7oGI23qMpRWNxj4BU66eBwWFOeipoe/BiVpi9eh1qxZE34lSpxn8dWvflVWdft70P4qGSS91Bq/jz/ZxodtkLjGhwC9JjoBTioSfYTZP4VA5Eu/UtrubNO7KHu6FJicizF9ermaH8dH7+1DQ0Y/DJu6JrIGoxG1D/TD67PuxHKjtRK90Gd8Porz3kf+rJ+j+oj30m5X0B6RlOdZiFeibrvtNnz22Wfdvt9BWvAqYAZJL7XG7+NPtvFhGySu8SFAr4lOgJOKRB9h9i8uBJr2/Q7PlV+F+yZd5XpKIUKdhvS85+H8Zh5Gh+RkIxkp6d9BzrD9yJ9TilqTOULyxRi/YD7yaoowa3WVx25QcelWt3cqzrOYNGlSWOe1117ru+1st+8IBZIACZAACZBAghHgpCLBBpTd0RFIRkrf/hikM4tZ/wX2bd+C8uxcfP/KyOLsmPaiMgV9M/oBe/ahzvDJQ3Kf6/kalAfX1NRU7bazHs1YRAIkQAIkQAIkEEcC3P0pjnDpupsS8Nudya9c7UZ496jRmDt4I/YuGa08qVCNZV6cXTEFGXP7o8Jzdymf3Z2a3kfpbddjwrtTUT7zE0yd8Ke47f4ktr4N2rVjxw6IdRb5+fnhXVXE+gteJEACJEACJEAC8SXgtfsTn1TElzm9d0cCKWnIGPR5mwXZzQu4+yGjb0pM1c2vPqVhcs7X204oxIQjJw0tB+FJV+LsincRmjwGQ4y2q420i74GtRwPr9wunXX63b3lql9wGzYmPtzvJYvXofbv34/a2lqMHDky+jqUzo+uXvTRho1ba1dzM+mPTq+JDxs2Jj50Wk3G0CSODRsbWjuzPzq9NpjY6o9Oq604NvpsolXo5UUCQSXAJxVBHTnq7gCB4/iw9D4MnXEMCysfR96AVDQ17MAT909D0QVPaJ4++DxRiKqJnF0x9k1MjvgO7wi1dwOmX/97jNu2HLmtFnbLhrH8RvROeBINmIi1J3hOhfirQqzroYceilXtWyd2NHH/Y6nmvRqqNmq+vW3+/ve/47XXXkNlZSXGjRuHK664IuxC9avm2xvHy16UqX7VvFc71UbNs40XAbLm5635c6H+vqh5r0+PaqPmbbVR/bjjiDQvEkgEAl5PKsTJwK0ur31nWxkwQwKJQOBwjVOxtsDJAsQ7Pw5wuTOlaJNTVf9ltHfN501AOYfC5LyIL536qk1O0ZTLI75DTlbBWqeixn2aRTRMJKHx2/iesylP+JPnX3zp1Fc83KI/a7azKaZ/NV7rvO73Xrf/uvBmw8bER6y93sU5FkOHDnWGDx/uHDhwoHUnXTmTODZsYmmVcmzEseFD6NHptRVH50dXb6JV2Oj86OpNfJjY6Lia+DCxsdUfnV5bcXR+dPWCiU5rZ3LT6TXRKvTyIoEgEPD63nByIsyW2AcSaDeBlHSMzlsS/vFrm5yehzInT6lORuroxaiPufygF0KZuZi1TvwozX2zGr/JFyN37R44a6WD/fjvdeXot+k9VOSehV3LfoI52+sxPj0VPfmdRvE6VGlpKW688UaI3aGeeeYZDB48WELjnQRIgARIgARIIF4E1NmQ18xDtWGeBEigiwn8rcopuuwOZ1P93xzHiTzlmLLJqT9BWUH6vTf5a584hXvdunXhJ0UrV650RL4rLhOtXaHLL2aQ9FKr3yh2vJxsO87Qy0OQuHrpZxkJuAl4fW/oyX/UjNc8jX5JoJMJJOOMs3rjjDhGtbFIUcjT+dHVm3Zx3bp1EIfl7dq1C+vXr8cPf/hD1NXVRZubxLFlEw3qk7ARx4YPH3mtim3F0fnR1bcSFSOj86OrF65t2cSQGa6yEceGD51Om0x0enX1JlpN9JrEsWVjqpl2JBBEApxUBHHUqJkESMCIgHj1acuWLUhPT8eFF14YfjXKqCGNSIAESIAESIAE2kWAk4p24aIxCXQTAiefh37Da/D6258D+Bxv/GYHLhs5EOd3E3ndSUbv3r2xdOlSbNq0CRMmTEBBQQH++te/dieJ1EICJEACJEACwSfgfj9KpL3ekVJtmCcBEuhqAl86dZumOyG5e1VourOprmXnqvaqC9LvfUfeS96/f78zbty48A5Ru3btai+mdtt3RGu7g1loECS91GphwH1ckK0PGBaTAAlECXh9b+CTiuDPC9mDHkmgF/rkFqPeccS20HDqi33Ov7ADx9b7xDo/unrT3vj56du3L375y19i4MCBuPLKK7F48WIcO3bM062fD7exiY3b3itt4kNno6sXcU1svPS5y0x82LAx8eHW5ZfW+dHVC7+2bPw0ynIbcWz4kHpi3W3F0fnR1cfS6K7T+dHVC182bNzn+bj1MU0CiUKAh98lykiyHyTQAQLiEJtVq1Zh2rRp2n88VRtdXsjS2aj1sdo0NDQgFAq18RmrjUTjjiMWbm/cuBHnnXcerr/++vDdxIf05b67/bp9SK1uW5n2ayPrve7xbiP1xjuO7FtH4vhplb7d947EkX5UH7LcfVdtZF5qddvKtLTxy8ty9z3ebaTeeMeRfepIHD+t0rf73pE40o/qQ5bHuss2QisPv4tFinVBIsDD76IPbZggARJwE/B6jOmu1x3qJGxt2Jj4MHk1Q+dH1outZhctWhR+7VNsQeveelbauDmoaZ2NDa0mbHU6THwIG51eW3F0fnT1JlpN+mwSx4aNjquJVhMbG1pN2NqKo/OjqzfR2pncdHpNPgdCLy8SCAIBr+8NfFIRpGkhtZJAnAh4/sUhTrE66la8QmD7r327d+/G7bffjrS0tPCibrFblI0rHlpt6PLzESS91Oo3ih0vJ9uOM6QHEkh0Al7fG7imItFHnf0jAQsEbLxPLGTo/OjqTbui86PWu7eezcjICJ9tsXLlSm041Y+2gYeBiQ+dja5ehDWx8ZDXqsjEhw0bEx+thPlkdH509cKtLRsfidFiG3Fs+IgKipGwFUfnR1cfQ2KrKp0fXb1wZsNGTNZ4kUAiEzg5kTvHvpEACZCAKQG59eyYMWMwd+5cHD9+HDk5OeEzLkx90I4ESIAESIAEeioBPqnoqSPPfpMACXgSyM7ODh+YJxZwy6cWfjtEeTpgIQmQAAmQAAn0QAKcVPTAQWeXSSDIBGyvp/BiIZ5a5ObmoqysDMXFxfjhD3+I2tpaL9OYZZ2hNaaAdlYGSS+1tnNw22FOtu2ARVMSIIEoAU4qoiiYIAESCAKBznwvWT61EAu3T+SpRWdqtTF2QdJLrTZG3NsH2XpzYSkJkEBsApxUxObDWhIggR5OQK612LVrV/SpaLB5lgAAIABJREFUhdgtihcJkAAJkAAJkEALAW4p28KCKRLosQR64uF3crDlwVQm+b/97W+oqKjACy+8gHHjxuGaa67BKaec0uYgPulTHswlfbvv0kaWqXlZ7r6rNmrebSvTqo2al3biLvWqNmre3UamVRs1L+3cd9VGzbttZVra+GmVdu67bCPL1Lwsd99VGzXvtpVp1UbmpVZp575LG1mm5mW5+67aqHm3rUyrNmpe2om71KvaqHl3G5lWbdS8tHPfVRs177aVaWnjp1Xaue+yjSxT87LcfVdt1Lzb1i8t2witQXq1zK8/LCcBQcBrS1moB2x4HWah2jBPAiSQWAR0v/e6Q50EDRs2Jj5MDpDS+dHV6/qza9cuZ9y4cc7FF1/slJWV+X4YbGjVaTGpN7XR6e0oNwlK50dXL/zotJr02SSODRsbWjuzPzq9NpjY6o9Oq604NvpsolXo5UUCQSDg9b2BTyo44SQBEvD+iwO5xCQgdoT61a9+halTpyI/Px/3338/xKtSvEiABEiABEgg0Ql4PangmopEH3X2jwQsELBx8JOQofOjqxc+TBaR6vzo6k20nn766Th69Cj279+Pv/zlLzjnnHNQWlrairYNrSZabPTHhK2tODo/unoTrZ3JTaeXnwMxGm0vHTddvfBog61JHBs2JlrbUmIJCQSHACcVwRkrKiUBEuiGBPr27Ys1a9aEt5997LHHMH78+BPafrYbdo2SSIAESIAESMCYACcVxqhoSAIkQAL+BOT2s8OGDQtvP7t48WLw0Dx/XqwhARIgARJILAJcU5FY48nekMAJEfB6N/KEHLFRmIDYcvbhhx9GfX09Fi5cCDHh4EUCJEACJEACiULA63sDn1QkyuiyHyQQRwI23icW8nR+dPXCh8l7yTo/unoTrbFsBg8ejF/+8pe49NJLkZOTg9tuu833lSgbWmz4MGFrK47Oj67eRGus8RF14jKJY8PGxmfWRK8NrSKOTq+tODo/unoTrZ3JTadXx1Vo5UUCQSbAJxVBHj1qJwFLBMRfHFatWtXmvAUv93LPdVmnyws7nY1aH6tNrH3pVT+6fKw4fv2T5e67XxyhNTU1Nbze4pVXXsENN9yAoUOH4itf+YqWidu/TPvFkfVe9/a08WOr+uhoHNle9avmpZ37Lm38tLptZVq28cvLcvfdZhup1e1fpm3GkT697u2JI/W2p42M2dlt/LRKPe57Z2lzxxRpGVdo5TkVKh3mg0rA60kFz6kIwmbA1EgCcSbgtd+0O6SNPdqFP50fXb3wYbLXu86Prt5Eq4mNW6s822Lo0KHOpk2bRPPwZUOLDR9CjFtvRF6rm604Oj+6ehOtwkbnR1dv4sPERsfVxIeJja3+6PTaiqPzo6sXTHRaO5ObTq+JVqGXFwkEgYDX9wa+/hTUKSJ1kwAJBIqAfCVKnGfBXaICNXQUSwIkQAIkYECAkwoDSDQhARIgARsExNkWubm52LJlC+QuUeJsi88++8yGe/ogARIgARIggS4jwElFl6FnYBIggZ5KQJy8PWfOHNTU1IQP0BMH561fv55b0PbUDwT7TQIkQAIJQICTigQYRHaBBEggmATS09Nx0003hRdyFxcXY+TIkSgvLw9mZ6iaBEiABEigRxPgpKJHDz87TwIk0B0IiHMstm3bBrHeQmxBy1O5u8OoUAMJkAAJkEC7CKgrzL1Wc6s2zJMACSQWgSD93gdpB5UT0XrgwAFn0aJFjhiT/Px8Z//+/Z32YTsRvZ0mTglErQoQi1mytQiTrkggQQl4fW/gk4p2TcFonDAEmhpQva4Qo5KSIPZaTkrKQWHJr1HdcDx2F5v2oiQnLdJGthX3SSip/SLS9jgaqjegcJS0S8OowjV4oboBTb7em3Cocg7SktIwatlOHGljJ+vdcdoYxa1Ad6iTCGzDxsSHSSd1fnT1tvpzIlrd6y1E+wsvvBA33nhjzMXctvqj02srjs6Prl6nU9br/OjqhR9bNlKT391GHBs+/PS5y23F0fnR1bs1xUrr/OjqhW8bNjz8LtYosS4RCPDwu0QYRfahnQSO48PS+zB05Vfw6LJ7MDkzBDTswBP3T0PRBU9g75LRSPXzeKgShQNWI2PreuSln+Zp1fRhKW4b+jTOffQR3DN5GEJowM4n7sf4oj7YuHchRqd6zeXFpGEuBlzzKBrwPRRVbcSszLNd/mX9Piys8Y/tatCuJA+/Wx3lJQ+qkgVqXpa776qNzMuDudy2Mi1t/PKy/J133oE4OO+NN97Apk2b8OGHH+KUU04JV6s+ZBv3XbVR825bqVe1UfPuNjKt2qh5aee+qzZq3m0r09LGT6u0c99lG1mm5mW5+67aqHm3rUyrNjIvtUo7913ayDI1L8vdd9VGzbttZVq1UfPSTtylXtVGzbvbyLRqo+alnfuu2qh5t61MSxs/rdLOfZdtZJmal+Xuu2qj5t22fmnZRmjl4Xd+lFgeNAI8/C5BH0GxW+0k0Pi2szb7Mid77dtOo6tpY81aJzs026k46C51GTiNzsGK2U4ops0xp2btRAfZa50at5twzKudgopP3A5d6YhvZDpZWZc5yFruVB1u5aA5NiY6a2uOudrZSXo9xnR71h3qJGxt2Jj4MHk1Q+dHV2+rPza0Si3iwDxxcJ56eJ6sF/dYl0mfdXpNfNiwMfGh0ypY6Pzo6k18mNjY0GoSx1Z/dHptxdH50dULJjqtnclNp9dEq9DLiwSCQMDrewNP1A7CyFGjXQIHK5yCUGbbL/h+5dHoPhOGaL1IfOJUFGQ6oYIK56BRuTSSk4qJzjPl6528UMjJKnrdOSyr5YSmiyYVURndIBGkf5htaz169Gj4NG4xsRg3bpyzfft2qyNiW69VcYozalWAWMySrUWYdEUCCUrAa1Lh9R5G0J7AUC8JtItA00fvYXeDX5N67H7vU5+1D0dQV/MuQhfsR+lPBkXWVQzC1GWlLWsxmj7Fe7vr/ZyjYfd7+Mh/YUW43UkXj8OC4lzU5C/A6urPfX11ZoWN94mFXp0fXb1pn3V+dPUmWk1tdJrbo8V9eN6YMWMwYsSI8E5Rc+fO1YXRstc6MBg/Uya6PuvqTbSaaDGJY8tGp9lGHBs+dDpNuNqyMemPDb0mcWzYcE2FyWjRJsgEOKkI8uhR+wkQaMKRun3YcwItEZ4wfI6MPldj6s/3iKd8cJwdeKBfFWb96ElUH2kCjtSjZo/vjMUwai/0GZ+P4rz3kT/r581+DVvSrGcQEIu5Z8yYgQMHDkBMLhYtWoSCggLU1tb2DADsJQmQAAmQQLcjwElFtxsSCuq2BJIHIK9sH36z+LsIRX9zUpE+ZgyG1RRhzvO1Pk84TqBHyRdj/IL5yKspwqzVVR67QZ2ATzZJOAJycrF48eJw3zIyMji5SLhRZodIgARIICAE1Fe9vN6RUm2YJ4EgEwgvyIbfmopQmwXc2r6GF2GHmtdRuNOtGjavtWizgDtq07KmomUh9pdO3abpTgjfc4qqDnTpQu2oTCa6NYGamprw2Rbi/+PijAuR50UCJNA9CARprUr3IEYV3ZmA13wh+vfWgMyBKJMEOkwg+YJLMDjk5yYNgy85Fyf8i5F8Li4ZnObnHKHBl+ACY+fu16BK8Prnjb5+411h431ioVHnR1cvfJi8l6zzo6s30WpiY0OrSRzZn/T0dCxduhQ1NTWiGdxPLqRNuMLnPzq9Jj5s2Jj40GkVXdT50dWb+DCxsaHVJI6t/uj02oqj86OrF0x0WjuTm4leoYcXCSQqAeOvN4kKgP3qgQRS0pAx6PM2C7KbF3D3Q0bfFE8oTbUlyEkagsLKT1vXh9dRpGFyzteRihT0zejXdkF2ZD3GoIw0eHtv7TKai74GtRwPr9weLWaCBGIR8JpclJaWcs1FLGisIwESIAES6BABHn7XIXxsHEwCkcPvZhzDwsrHkTcgFU1Gh999juplN2HsnomofHIyBqSIOfkh7C25F9fv+B62rclFn2Sg+fC7efj7wl/iybzLkdLUnsPvvA63i+id8CQaMBFrw4ffJaOh8lH86JqHsVUMQtZsbHr6fuSm+x7bF96tKtZ4PfTQQ7GqfevEYU7uvxaqea+Gqo2aZxsvAggfnHUirMWi7l27duF3v/sd8vPzcfToUZxzzjneQXDicU5EG9vw90f9/VfzXh9U1UbNd2UbNbZbm0jzIoFEIMDD77rzy2nU1rkEDtc4FWsLnCzAEe8FApc7U4o2OVX1X0Z1NK+9QOszJxrrnapNRc6UkGyX7RSsrXBqWh1Ud9CpqVjrFGSFIr7hhKYUOZuq6lsdthcNFE54ralwWTS+52zKu9xB9JyKD5xNU6528ja95zQ6f3Gqisa3fy2Iy73Xu5Guau0hYsJWd/CTiY2JD5P3knV+dPUmWk1sbGg1iWPaH92aC51e0zhCc6xL50dXL3zrtAobnR9dvYkPExsbWk3i2OqPTq+tODo/unrBRKe1M7np9JpoFXp5kUAQCHh9b+CTikSYLrIPPY/A36uxbMAa9PttMXJDyThUORcD1g1B9bpc+C4XiUHJ8y8OMexZFWwCYuvZ//N//g+KiorCTy5uvfVWiFemeJEACZAACZCACQGv7w1cU2FCjjYk0K0JJOOMs3rjjDhqNFmAaMPGxIf7dRm/Luv86OqFXxs2NrSaaGmvVq81F+KcC/GaVKyrvXH8fOn86OqFXxtsTeLYsLGhVfRZp0VXb+LDhK2tODo/unoTrSZ9Noljw8bkcyD08iKBoBLgpCKoI0fdJEACJNBBAurk4sknnwyf0L1jx44OemZzEiABEiCBnkaAk4qeNuLsb2IQOPk89Bteg9ff/hzA53jjNztw2ciBOD8xesdedDIBObkQi7jFCd0jRozg5KKTx4DhSIAESCDoBLimIugjSP09lIB7RygAoenY9PvlyO3T64R4eL0beUKO2CghCHz22Wf4xS9+gZkzZ2Lo0KG4//77cd111+H0009PiP6xEyRAAiRAAh0j4PW9gU8qOsaUrUmgiwj0Qp/cYtQ7DhzxU198whMKkw7YeJ9YxNH50dULHybvJev86OpNtJrY2NBqEsdWf6Te3r17h9dXiK1nxYTisccew8iRI3HjjTdCTDhiXTa0mPiQWjuixSSODRsbWrvic+DH1gYTW/2xwbaz+mOi1Y85y0kgCAT4pCIIo0SNJBBnAuIvDqtWrcK0adO0X/xVG11eSNfZqPWx2jQ0NCAUCrXxGauNxNeeOLHayDp5V/3KvNQq7dx3aSPL1Lwsd99VGzXvtpVp1UbNSztxl3pVm6lTp4YnF9u2bcMbb7yBG264AQMHDsR5550Xba62UfNRQ1dCtVHzLtNoUtr4aY0auhKyjSxS87LcfVdt1LzbVqZVG5mXWqWd+y5tZJmal+Xuu2qj5t22Mq3aqHlpJ+5Sr2qj5t1tZFq1UfPSzn1XbdS821ampY2fVmnnvss2skzNy3L3XbVR825bv7RsI7TynAo/SiwPGgGvJxXir5ytLq99Z1sZMEMCJJBwBHS/97r91wUQGzYmPkz2etf50dXb6o8NrSZabPVHp1fE2b59u3PrrbeGz2DJz88P592/EDa0mPjQae1Mbjq9NrR2Zn90enX9NdFqYmMSR6fVVhwTLTobE61CLy8SCAIBr+8NfP0paFND6iUBEiCBLiQwfPhwrFmzBjU1NTj77LOji7rLy8tx7NixLlTG0CRAAiRAAl1JgJOKrqTP2CRAAiQQUAJix6g5c+bgwIED4R2j5s6dG1538dprr2nXXQS0y5RNAiRAAiQQgwAnFTHgsIoESIAESCA2AbmoW6y3WLhwIXbv3o1zzjkHixcvhji5mxcJkAAJkEDPIMBJRc8YZ/aSBEiABOJKQGw3m52dHV5Av2vXLnz++efIyMgIn3fBV6Piip7OSYAESKBbEOCkolsMA0WQAAmQQOIQGDx4MJYuXdrm1aji4mK+GpU4w8yekAAJkEBrAuoKc6/V3KoN8yRAAolFIEi/90HaQSVIWsUnOl56jx496pSVlTnjxo3z3TWqvb9R8dLaXh0m9kHSGs/PgQmr9toEjW17+0d7EuiuBLy+N/BJRes5FnMkQAIeBDrrcCiTOB7y2hTp/OjqhUNbNm3EKQU24tjwocjyzJ5oHPlq1ObNm8O7Rn3wwQfhXaOGDRuG9evXt3l6YRLHU6BSqPOjqxfubNko0tpkbcSx4aONMI8CW3F0fnT1HtI8i3R+dPXCqQ0bHn7nOTwsTCACPPwugQaTXSGBEyXAw+9WR9HJg6pkgZqX5e67aiPz8mAut61MSxu/vCx33+PdRuqNdxzRp7/+9a+49NJLsWDBgvCBet/97nfDp6Xv2bPH3eU2aanNT2ubBgaHL8a7jdQa7zhe/mWZ5OaXl+XiLvW2p41s39lt/LRKPe57Z2lzxxRpGVdo5eF3Kh3mg0qAh99112dI1EUCXUzA6zGmW5LuUCdha8PGxIfJ6w46P7p6W/2xodVEi63+6PTaiqP62bVrl7No0aLwq1FDhw51pk6d6hw4cMD9EWyT1mntTG5qf1SxNrR2Zn90enX9NdFqYmMSR6fVVhwTLTobE61CLy8SCAIBr+8NfFIR1CkidZOARQKef3Gw6J+uSMCEwGeffYatW7eGX4l64YUXkJ+fj3HjxuGqq66CeIWKFwmQAAmQQPcg4PW9gWsqusfYUAUJdGsCNt4nFh3U+dHVCx8m7yXr/OjqTbSa2NjQahLHVn90em3F8fMjzrzIzc3FtddeC7Et7UUXXRReezFy5EiInaPq6uoEjvCl0yqM/OJEXGjrTXyY2NjQahJH118TH8JGp9dWHJ0fXb2JVpM+m8SxYaPjKrTyIoEgE+CkIsijR+0kQAIkkKAExLa0M2bMwNGjR8OH6r3xxhu48MILee5Fgo43u0UCJBB8AicHvwvsAQmQAAmQQKISkDtHiYP1xF96xQ5Sc+fOxe9//3ucffbZEE8xhg8fnqjdZ79IgARIIDAE+KQiMENFoSRAAoJAkHZPCZLWILDt27dv+OnFzp07sX379vAvxIgRIyC2phWvR9XW1nbLXxJ+DuI3LEFjGz8S9EwCXU+Ak4quHwMqIAESaAeBIL2XHCStYgiCpLe8vBxz5sxp9XpURkZG+PUor7Mv2vERs24aJK5B+xwEja31DxcdkkA3IsBJRTcaDEohARIgARJoHwH5etSaNWtw4MCB8ELv0tJSnHPOOdi4cSPE5EPsKsWLBEiABEggvgS4pWx8+dI7CQSCAA+/4+F34oPqd5CYPLwr1odZtVHzXm1VGzUfq42fVtnm448/xltvvYXXXnsN77//PsTheldccUV4R6mZM2dqd35Stah5Gcd9V21kXmp128q0tPHLy3L3Pd5tpN54x5F96kgcP63St/vekTjSj+pDlse6yzZCK1/XikWKdUEi4LWlLNQDNrwOs1BtmCcBEkgsArrfe92hToKGDRsTHyYHSOn86Opt9ceGVhMttvqj02srjs6Prl4w0Wl1cxOH661cudIRB+uJz7o4aG/79u3OihUrhFnMy0SLzqY9WmOJ0cXR1QvfJjY6vSY+bNiY+NBpNemzSRwbNiZaY40/60igOxHw+t7AJxVBmhZSKwnEiYDnXxziFItuSaArCezYsQPbtm3DAw88EJaxaNGi8A5SPGCvK0eFsUmABIJGwOt7A9dUBG0UqZcEuoCAjYOfhGydH1298GGyMFPnR1dvotXExoZWkzi2+qPTayuOzo+uviOfA7H9rFzgPWvWLOEqfMDeGWecgcWLF0NMOo4dOxYuF/8x0aKz0XG1FUenwzSOTq+tODo/unrRH51Wkz6bxLFhY6JV6OVFAkElwElFUEeOukmABEiABE6YgFjgfdlll0UnGO4tat0TjL/97W8nHIMNSYAESKAnEeDhdz1ptNlXEiABEiCBNgTEBEM8wRA/9957L/7whz+EX5ESZ2CI6/DhwxgyZEj4p3fv3m3as4AESIAESADgmgp+CkiABOD1biSxkAAJALt37w4ftCfOvhCneN96662YOHEiBg4cCHEYHy8SIAES6IkEvL438PWnnvhJYJ+BpgZUryvEqKSk8BfqpKQcFJb8GtUNx2PTOVKLyhJ3u0GYuqwMtUeaXO2+QG3JpIhf6V/c05BTshduy5ZGTThUOQdpSWkYtWwnjrRURFKyfhJKar9oUxvvAhvvEwuNOj+6euHD5L1knR9dvYlWExsbWk3i2OqPTq+tODo/uvrO/ByILWlnzJgBcYr3rl278O1vfxtPPfUULrzwwuhBewsWLBCSfC8dV9HQpM86G129aRydXltxdH509aI/Oq0mfTaJY8PGRKvQy4sEgkqATyqCOnLU3QECx/Fh6X0YuvIreHTZPZicGQIaduCJ+6eh6IInsHfJaKR6eW96H6W3XY8Zf5+GzY/dhmGhXmiS7U6ej9+vyUWf8DT9U1QWjsOSjLV4OW8AzGbuYtIwFwOueRQN+B6KqjZiVubZLhWyfh8W1qxHXvpprrqOJ8VfHFatWgW5n3osj6qNLi986WzU+lhtYu1Lr/rR5WPFkQxUH7LcfVdtZF5qddvKtLTxy8ty9z3ebaTeeMeRfepIHD+t0rf73pE40o/q4y9/+Qtqamqwb9++8OLuiy++GGLhtzgT46KLLsIpp5wS/dxLrdKX+676VfNuW5lWbdS8tHPfVRs177aVelUbNe9uI9OqjZqXdu67aqPm3bYyLW38tEo79122kWVqXpa776qNmnfb+qVlG6GV51T4UWJ50Ah4PangORXdadNfaukcAo1vO2uzL3Oy177tNLoiNtasdbJDs52Kg+7SFoNwPTKdgopPWgodx2lTfrDCKQi1tWvVqE2m0TlYMdsJIdPJyrrMQdZyp+qwW4esn+isrTnWpnVHC7z2m3b7tLFHu/Cn86OrFz5M9nrX+dHVm2g1sbGh1SSOrf7o9NqKo/Ojq+9un4Nly5Y5ZWVl4fMvxO+S+MnPzw+X7d+/38pnlp8DQaDtpfvMiha6z5Ou3sSHiY2J1rY9ZAkJdE8CXt8bOKnonmNFVfEk4Pel369co6V5UhGKTlKa8+398t8yaXimfL2TFwo5WUWvO4ejsVvqu2JSEZXRDRJB+oc5SFrF0AZJb3fVevToUUcetjdu3LjwBCMjIyN8+J4oF/Xd/equbL24UasXFZaRQPwJeE0qzN7MCNozGeolgRgEmj56D7sb/Azqsfu9T33WPfi1EeUjcMOIS5CMJhyp24c9odPxcekdSIus2Uibugyl1Q1Gfk+6eBwWFOeiJn8BVld/Hitop9XZeJ9YiNX50dWbdljnR1dvotXURqfZhhYbPnQ6TftrQ4uJDxt6TeK010bsJDV48ODwOozNmzdj//79uOKKK/DGG2/gyiuvhNiutqCgAOXl5airq4t2o71xog1dCRs+XO58k7bi6Pzo6n0FKhU6P7p64c6WjSKNWRJIKAKcVCTUcLIzegKRL/16QzOLpvexecnj2JN3I3L6i3UOx/HRe/vQkNEPw6auQb3jwHEaUftAP7w+604sN5ok9EKf8fkoznsf+bN+jupWi8DNZNGKBEigexAQO0QNGDAAa9aswdGjR8M7SYk1F+7F3sXFxXjnnXdaHbrXPdRTBQmQAAmYE+CkwpwVLUlAIXAIe59dgBnv/gAbF14fWaR9GtLznofzm3kYHeoVsU9GSvp3kDNsP/LnlKLWe/un1r6TL8b4BfORV1OEWaurPHaDam3OHAmQQPcnIM/DELtJyacYd955Jz744AMsW7Ys/BTjtttug9i+tra2tvt3iApJgARIwEWAh9+5YDDZEwgkI6VvfwxCeQc7ewh7S+7F6LnAwsp7XRMIP7cp6JvRD9iwD3VHmpCeqp/PJ/e5HguKKzF0wgKsHrUet/u5ZjkJkEAgCYinGOInOzsb/fr1wze/+U388Y9/xG9/+1tMnTo13Kf8/HyMGTMmfC5GIDtJ0SRAAj2GACcVPWao2VFJIPmCSzA4JHPqPQ2DLzk39jawTQ3Y+cT9GF90MhZWPo68AZ4b0KqOTyAvX4O6HhNmleCKmY0n4INNSIAEgkJArMUQP1OmTMGKFSvCJ3uLszHEq1IvvPACxLa1n332Wfhkbx6+F5RRbdHJ7WRbWDCVmAT0fy5NzH6zVz2ZQEoaMgZ93mZBdvMC7n7I6JviS6ep4RXMuSYT33ixD4q3ekwomvaiJCcNaYWVONTKyxHU1byL0OQxGGLwlCLaNPoa1HI8vHJ7tJgJEiCBxCagvip14MCB8EneqampmDt3bvjwvWHDhmHx4sVtFn0nNpng9o6H3wV37KjcjAAPvzPjRKuEIhA5/G7GseiThughdrEOvzuyE8vGjkd+TS42/X45cvvINRNuOE04Uv0Exo59E5OjTzGacGTvBvz/9u4/xorrOuD42TWiCabYwT/CW+PGwnSXqGBVBVJFVM4GKkhUq0GL/F9sp4sju+lPW3RRgLpVBXbAVlNTV3ZULwqliuRGICr/QbBYYktBxTYoaWwFL0IRVvGuXbAcY6wGFHaq85azGe6bt/cu787bN/O+T0LzZubMued+5q395s2P+2f3vC5feaX+duOD32UNbnel3nX/IqNyrwxe4+B3OlDNZK/HHntsstV11+mvb+n/WbrzWRu6Me4822QJSHXgLKz5vOnfyyOPPCJnz54VHVDto48+ktdff126urqqN4VXKhW55ZZbRA9A7OX+jbnzFpeeujHufDrW3rsx7rzFpadujDufjrX3bow7b3HpqRvjzqdj7b0b485b3GTT9Db6nhcCZRBg8Lv8H9tLC0UR+Gg4GRocSHqvDFQlsji5/8m9ybGRixM9GB9vQpLKwFDyYfJ/yfDgvdVnztvgVu50PE43v5iMHNubPHn/4ivxlaR3YDAZGv5wInftG884FJdPJ3v7NZ+Nf3ExGRn6+1/X3/vNZO9QWAHPAAAS2ElEQVSk+WtbTC/Jet50en2zBocKaSfkufS+PL712vcYMTFqDaklRq3ajq/eWO348vjWh9TaTDdfvT7XkFp9MTrI3oYNG6rjYdj4GPp3rYPw7d27NxkeHtYUQZ9rX72+/oa248vjW6/t+GoNqSWknRgxIbVqvbwQKIJA1vcG7qkow+EifZi6wOxuWdm/vfqv3sad3f1yMOmfWD1Hn+r069mJ5bVvZkplaZ9s2K3/atdmL+mUOSsflxE9DMl6dX5G+gbfkGTQVv6P/Nful2TB3tMy1HeD/PipP5FNPxqRtd1zJr8fxDZnigACpRLQG77vvPNOefjhh6tjZOi9FydOnBC9J+PAgQOybt26an9XrFhRfcrUXXfdJfpo27lz55bKoZU7w1mKVt471BZDgHsqYiiSA4FmC/zqf+XnR5bIH33+NumUOfLbv/dZeeOVn8l7za6D9hBAoCUF9GBBDyD08bU2RoYeYCxevFjefPPN6kB8N910k6xdu3bivgweY5vvrkxfuphvS2RHYHoEOKiYHndaRSCiQKfMumGuzIqYkVQIIFAuARvpW58utWPHDkmSRIaHh0XHydCXPmGqp6dH9DrpQ4cOVcfKOHLkSPVpU+WSoDcIIJCXAJc/5SVLXgQQQAABBFpYoLu7W/SfjpOhL71kSgfie+KJJ6pnM2ysjOXLl0tvb291HA0dT+Pjjz9u4V5RGgIITJcABxXTJU+7CDQiMONWWbBiWF498Qvpq8yQ//7hEbnzC/fIpxvJWZBti3RdcpFq1d1fpHqpNf4frF4ypf9eeOGFanI9o3HmzBl5++23J+7NeP7556vrdIA+faTtokWLqpdU3X777aJnQ5r9KtLnoNk2tIdAswW4/KnZ4rSHQBSBT8vvf+V3ZM+qW6Sj41Oy7B9vk4fWLGiLm7SLdF1ykWrVj2WR6qXWKP8hyUySttUbwNP3ZuhlU/pFXi+b0kfW6k3getnUrFmzqvdnDAwMyL59+6oHI3rmI+9Xuta82yI/AghMLsCZisl9WItAiwrMlNv6npGR5JkWrY+yEECgrAK33npr9ZIpu2xKbwTXm7xPnz5dneqBhp7R2LZtm9ilU3qDuD6dSkcF1wMVXgggUD4BBr8r3z6lRwhMWUBvznz22Werj6N87rnnJt1eH1mZjvHNazJfjLt+sm10sC8d3Gsq21iHYm1j+Wzq5rV5q9Xi0lOLsWXuvC1PT90Ydz4da+/dGHfe4nRq9box7nx6G3vvxrjzFpeeujHufDrW3ltMvVotLj21bWyZO2/L01M3xp1Px9p7N8bmrVaLS08txpa587Y8PXVj3Pl0rL13Y9x5i9Op1evGuPPpbex9OuaDDz6Qu+++u/r0qZGRkeoBh15KpS89+6EHFzfeeKM8+uij8uKLL8r1119fXZfOYXndqcXUq9WN13nbxta587Y8PXVj3Pl0bL33to3WyuVa9ZRYXjQBBr8rwmgi1IjANAhkDWKTLiPGwE+az5fHt15zhAwg5cvjWx9Sa0hMjFpD2onVH1+9sdrx5fGt53OgArWvELeQmDw/B++//351ID4dkE8H6XvwwQcnBhVdvnx5dbC+3bt3JwcPHkx27txZ20lnia9WDff12bc+JEdITEitTveYRaBlBbK+N3CmomiHhtSLQA4Cmb845NAOKRFAAIEsAb186uzZs/Lee+/J0aNHq2c19u/fnxXKMgQQaAGBrO8N3KjdAjuGEhBodYH05U71ao0RE5Ij5MZMXx7feu1jjJgYtYbUEqNWbcdXb6x2fHl860Nqbaabr16fa0itITG+OkJyaIyv3ljtpPPoo231kqi+vr7qOBp6QJFer3VlvXy16ja+PL71ITlCYkJqzeojyxAoigAHFUXZU9SJAAIIIIAAAggggECLCnBQ0aI7hrIQQAABBBBAAAEEECiKAPdUFGVPUScCOQpkXRuZY3OkRgABBBBAAIECC2R9b+BMRYF3KKUj0CyBZl1zHNJOyHXJvjy+9eoaIyZGrSG1xKhV2/HVG6sdXx7f+pBam+nmq9fnGlJrSIyvjpAcGuOrN1Y7vjy+9SG1hvQ5pJ0YMT5XrZUXAkUW4ExFkfcetSMQSUB/cWCcinFMe6a80brztjw9dWNs3p6hn4619xZTb96Wp6d5b2P15t2O9amRdurVarnT00basTxuDluenroxNm+1pmPtvcXUm7fl6Wne21i9ebdjfWqknXq1Wu70tJF2LI+bw5ZPNrVttFbGqZhMinVFEsg6UyHuA3CznjvrxjCPAALlEvD93TfrOe4h7YQ8692Xx7de926MmBi1htQSo1Ztx1dvrHZ8eXzrQ2ptppuvXp9rSK0hMb46QnJojK/eWO348vjWh9Qa0ueQdmLE+Fy1Vl4IFEUg63sDZyqKdFhIrQjkJJD5i0NObTWaVi8hKMqvfUWqVfdLkeql1kb/kupvj219m0bWFMm1kX6ybXsIZH1v4J6K9tj39BKBhgRiXE+sBfjy+NaHdsKXx7c+pNbQGF/NMWqJkcNXZ2h/Y9QSkiNGvSHtxIrx1RujnRg5fHXyOagvFOJff2vWIFB8AQ4qir8P6QECCCCAAAIIIIAAAtMqwEHFtPLTOAIIIIAAAggggAACxRfgoKL4+5AeIIAAAggggAACCCAwrQLcqD2t/DSOQGsIZN1w1RqV1VZRpJsdi1SrShepXmqt/duItQTbWJLkQaC8AlnfGzhTUd79Tc8QiCYQcgNijJiQHCGd8uXxrdc2YsX46o3RTowcvjpjmvjq9a0PqTWk3pB2YsX4ao7RTowcvjpDXGPFhPQnRr0h7cSI0YM1XgiUWYAzFWXeu/QNgUAB/cWBwe/GsWygKqNz5215eurG2LwNzJWOtfcWU2/elqeneW9j9ebdjvWpkXbq1Wq509NG2rE8bg5bnp66MTZvtaZj7b3F1Ju35elp3ttYvXm3Y31qpJ16tVru9LSRdiyPm8OWTza1bbTWojwOe7L+sA4BFcg6U8Hgd0UZZYQ6EchRIGsQm3RzMQZ+0ny+PL71miNkAClfHt/6kFpDYmLUGtJOrP746o3Vji+Pbz2fAxWofYW4hcTwOcjH1uda2ypLEGhdgazvDZyp4IATAQSyf3HABQEEEEAAAQQQyBDIOlPBPRUZUCxCAIGrBWJcT6wZfXl86zVHyHXJvjy+9SG1hsTEqDWknVj98dUbqx1fHt96PgcqUPsKcQuJ4XOQj63PtbZVliBQLAEOKoq1v6gWAQQQQAABBBBAAIGWE+CgouV2CQUhgAACCCCAAAIIIFAsAe6pKNb+oloEchHIujYyl4ZIigACCLSpgF7+xNOf2nTnl7DbWd8bOFNRwh1NlxCILRByHXaMmJAcIdcl+/L41qtfjJgYtYbUEqNWbcdXb6x2fHl860Nqbaabr16fa0itITG+OkJyaIyv3ljt+PL41ofUGtLnkHZixWg9vBAoqwAHFWXds/QLAQQQQAABBBBAAIEmCXD5U5OgaQaBVhbQ05gMfje+h2ygKttf7rwtT0/dGJu3gbnSsfbeYurN2/L0NO9trN6827E+NdJOvVotd3raSDuWx81hy9NTN8bmrdZ0rL23mHrztjw9zXsbqzfvdqxPjbRTr1bLnZ420o7lcXPY8smmto3WyuVPk0mxrkgCWZc/Mfhd644rQmUI1AhcHnk1+e7A6kQHnan+6x1IBvcfS0Yu14ROaUHWIDbpBCEDZsWICckRMoCUL49vvfY9RkyMWkNqiVGrtuOrN1Y7vjy+9SG1NtPNV6/PNaTWkBhfHSE5NMZXb6x2fHl860NqDelzSDsxYnyuWisvBIoikPW9gcufinRYSK3tLTD2tuzf8g35rnxVjo1clCS5KCPbf0te+dOH5J9ePtc2NkX6pa9IteoHqEj1Umt+f/LY5mdLZgTKLMBBRZn3Ln0rlcDYqSH5zq4Fct/6e2VpZaaIzJTK59bL5q0LZM/Bn8r5UvW2fmd8N5HW37L5a4pUq+oUqV5qze/zjG1+tmRGoMwCHFSUee/StxIJjMmFM6fkjcpCuWOeHlDYa6bMu2OhyJ5Dcuz8mC1kigACCCCAAAIINFWAg4qmctMYAtcqcEnePX1KRuttPnpKTr97qd5aliOAAAIIIIAAArkK8PSnXHlJjkAsgXNyeOOXZNWe1TL01lZZOcd+DxiT84e3yKJVp2Tr8L9Jf/cnrqnBzKc4XFMmNkIAAQQQyBLQy8qKdL9KVh9YhoAJZH1vsG8mFsMUAQQQqBGINfCTL49vvRYWcr23L49vvbYTIyZGrSG1xKg1xDZWO748vvUhtTbTzVcvnwPdG7Uvn5tvvWaMYRvSTqyYWgWWIFAeAc5UlGdf0pNSC/xSTu66X3q2LLzmMxX6qwIvBBBAAIHpE0gSfRo4LwSKL5B1pmJG8btFDxBoB4HxG7Ir9bpacwN3beBk/zPL+o9DbYbWWEKt+e0HbPOxLZKrChSp3qLVms8njKwItIYAlz+1xn6gCgQ8Ap0ye/5CWVJzQ/aVG7iXLJT5s/lz9iCyGgEEEEAAAQRyEuBbSE6wpEUgtkDnwlXyUP8J2bLtBXnrgj4+9pKMvjYo27b8XAY2/rF089ccm5x8CCCAAAIIIBAowNeQQCjCEJh2gc7bZfXGp2XrvO/JZ3/zOuno+A3pWvuaLHnmO/LXvTdPe3kUgAACCCCAAALtK8CN2u277+k5AhMCRbsuebL7QyY61QJviuSqXEWql1rz+4Bjm49tkVzzESBrmQSyPs+cqSjTHqYvCCCAAAIIIIAAAghMgwAHFdOATpMIIIAAAggggAACCJRJgMufyrQ36QsCCCCAAAIIIIAAAjkLcPlTzsCkRwABBBBAAAEEEECgHQW4/Kkd9zp9RgABBBBAAAEEEEAgogAHFRExSYUAAggggAACCCCAQDsKcFDRjnudPiOAAAIIIIAAAgggEFGAg4qImKRCAAEEEEAAAQQQQKAdBTioaMe9Tp8RQAABBBBAoEkCY3Lh5EF5atP35OTYeJNjJ3fJmo5lsvHwuSbVQDMI5C/AI2XzN6YFBBBAAAEEEGhbgXNyeOOXZNVPviHDB/qlm59z2/aTUKaO80jZMu1N+oIAAggggAACCCCAQIsIcLzcIjuCMhBAAAEEEECgbAJXzlLsOC7y0nrpuW78kqerL3/SmGXSseZbsu/gt+WBrg7RX4E7vrhRdh9/R87rpVMPLBlf1vWAfPu1UblyFVUVa2z0Ndm9cc34+o4u+eLGXXL45PmyQdKfAghwUFGAnUSJCCCAAAIIIFBEgZtl5fYfyNDAUpHVgzJ8+ZhsX3lzdkde2in/fPgzsvnkZUkun5Ghz/9EvrZsvizadkru/tZxSZIP5cTWGfLk2m2y/51L1Rxj7+yTry9dL4fnPSYjlxNJkrfk2Z4j8tXeTbLvSkx2YyxFIL4ABxXxTcmIAAIIIIAAAghMTaDyNfnbzWule3anSGdFlv3hUqnIvbJ183r5XGWmiMyR7j9YIUtGj8qrw3om4py8vPNx2bXkEdn8VyukUv1GN0cW9W+Xf7/vqPz5zh8J5yumtguIbkyAg4rG/NgaAQQQQAABBBBovsD5n8rBPcel8rt3yLyrvs3Nlvk9C2R0zyE5dj59oVTzS6TF9hK46mPYXl2ntwgggAACCCCAQIsILFko8/UsxRRfoztWyQ16D8bEv09Kz/rvTzEL4Qg0LjCj8RRkQAABBBBAAAEEEGi+QEVWDx6WA/2LZOqHI82vlhbLLcBnsNz7l94hgAACCCCAQBkF5twla+7rkjeO/ExGr7rK6Rdy/Kl7pGPNronB9srYffrUegIcVLTePqEiBBBAAAEEECiNwPg9DuPd+aVcuPCrSD27WXr/cpN8+cDfyaanj1w5sDgvJ/ftkA1/I/Lk430MtBdJmjRhAhxUhDkRhQACCCCAAAIIXIPAJ2Thl78u37y0RXquWyDr/uPUVeNMXEPCiU06b1srT7/8tHzh3X+Qruv0voobpPc/58pfHPtXeXTpjRNxvEGgGQIdSZIk6Yayht1Or+c9AggggAACCCCAAAIItK9A1vECZyra9/NAzxFAAAEEEEAAAQQQiCLAQUUURpIggAACCCCAAAIIINC+AhxUtO++p+cIIIAAAggggAACCEQR4KAiCiNJEEAAAQQQQAABBBBoXwEOKtp339NzBBBAAAEEEEAAAQSiCHBQEYWRJAgggAACCCCAAAIItK8ABxXtu+/pOQIIIIAAAggggAACUQQ4qIjCSBIEEEAAAQQQQAABBNpXgIOK9t339BwBBBBAAAEEEEAAgSgCHFREYSQJAggggAACCCCAAALtK8BBRfvue3qOAAIIIIAAAggggEAUgRlZWTo6OrIWswwBBBBAAAEEEEAAAQQQqBGoOahIkqQmiAUIIIAAAggggAACCCCAQD0BLn+qJ8NyBBBAAAEEEEAAAQQQCBL4f/VtEHoxbCIpAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the missing information for this decay.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the graph, sketch how the number of <strong>boron </strong>nuclei in the sample varies with time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After 4.3 × 10<sup>6</sup> years,</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{{\text{number of produced boron nuclei}}}}{{{\text{number of remaining beryllium nuclei}}}} = 7.">
<mfrac>
<mrow>
<mrow>
<mtext>number of produced boron nuclei</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>number of remaining beryllium nuclei</mtext>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>7.</mn>
</math></span></p>
<p>Show that the half-life of beryllium-10 is 1.4 × 10<sup>6</sup> years.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10<sup>11</sup> atoms of beryllium-10. The present activity of the sample is 8.0 × 10<sup>−3</sup> Bq.</p>
<p>Determine, in years, the age of the sample.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by thermal radiation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The temperature in the laboratory is higher than the temperature of the ice sample. Describe <strong>one </strong>other energy transfer that occurs between the ice sample and the laboratory.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}} \to _{{\mkern 1mu} {\mkern 1mu} 5}^{10}{\text{B}} + _{ - 1}^{\,\,\,0}{\text{e}} + {\overline {\text{V}} _{\text{e}}}">
<msubsup>
<mi></mi>
<mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mn>4</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Be</mtext>
</mrow>
<msubsup>
<mo stretchy="false">→</mo>
<mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mrow>
<mspace width="0.056em"></mspace>
</mrow>
<mn>5</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msubsup>
<mrow>
<mtext>B</mtext>
</mrow>
<msubsup>
<mo>+</mo>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mrow>
</msubsup>
<mrow>
<mtext>e</mtext>
</mrow>
<mo>+</mo>
<mrow>
<msub>
<mover>
<mtext>V</mtext>
<mo accent="false">¯</mo>
</mover>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
</math></span></p>
<p>antineutrino <em><strong>AND</strong> </em>charge <em><strong>AND</strong> </em>mass number of electron <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{ - 1}^{\,\,\,0}{\text{e}}">
<msubsup>
<mi></mi>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>0</mn>
</mrow>
</msubsup>
<mrow>
<mtext>e</mtext>
</mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\overline {\text{V}} ">
<mover>
<mtext>V</mtext>
<mo accent="false">¯</mo>
</mover>
</math></span></p>
<p>conservation of mass number <strong><em>AND </em></strong>charge <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>The diagram shows the position of the principal lines in the visible spectrum of atomic hydrogen and some of the corresponding energy levels of the hydrogen atom.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A low-pressure hydrogen discharge lamp contains a small amount of deuterium gas in addition to the hydrogen gas. The deuterium spectrum contains a red line with a wavelength very close to that of the hydrogen red line. The wavelengths for the principal lines in the visible spectra of deuterium and hydrogen are given in the table.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">Light from the discharge lamp is normally incident on a diffraction grating.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a)(i).</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>Explain your answer to (a)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10<sup>–6 </sup>m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angle between the first-order line of the red light in the hydrogen spectrum and the second-order line of the violet light in the hydrogen spectrum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The light source is changed so that white light is incident on the diffraction grating. Outline the appearance of the diffraction pattern formed with white light.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies λ = 435 nm ✔</p>
<p><em>E</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{\lambda }">
<mfrac>
<mrow>
<mi>h</mi>
<mi>c</mi>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{4.35 \times {{10}^{ - 7}}}}">
<mfrac>
<mrow>
<mn>6.63</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>34</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4.35</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>4.6 ×10<sup>−19</sup> «J» ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>–0.605 <em><strong>OR</strong> </em>–0.870 <em><strong>OR</strong></em> –1.36 to –5.44 <em><strong>AND</strong></em> arrow pointing downwards ✔</p>
<p><em>Arrow <strong>MUST</strong> match calculation in (a)(i)</em></p>
<p><em>Allow ECF from (a)(i)</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Difference in energy levels is equal to the energy of the photon ✔</p>
<p>Downward arrow as energy is lost by hydrogen/energy is given out in the photon/the electron falls from a higher energy level to a lower one ✔</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{{2\Delta \lambda }} = \frac{{656.20}}{{0.181 \times 2}} = 1813">
<mfrac>
<mi>λ</mi>
<mrow>
<mn>2</mn>
<mi mathvariant="normal">Δ</mi>
<mi>λ</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>656.20</mn>
</mrow>
<mrow>
<mn>0.181</mn>
<mo>×</mo>
<mn>2</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1813</mn>
</math></span> «lines» ✔</p>
<p>so spacing is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.5 \times {{10}^{ - 3}}}}{{1813}}">
<mfrac>
<mrow>
<mn>3.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1813</mn>
</mrow>
</mfrac>
</math></span> «= 1.9 × 10<sup>−6</sup> m» ✔</p>
<p> </p>
<p><em>Allow use of either wavelength or the mean value</em></p>
<p><em>Must see at least 2 SF for a bald correct answer</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>2 × 4.1 × 10<sup>−7</sup> = 1.9 × 10<sup>−6</sup> sin <em>θ</em><sub>v</sub> seen</p>
<p><em><strong>OR</strong></em></p>
<p>6.6 × 10<sup>−7</sup> = 1.9 × 10<sup>−6</sup> sin <em>θ</em><sub>r</sub> seen ✔</p>
<p> </p>
<p><em>θ</em><sub>v</sub> = 24 − 26 «°»</p>
<p><em><strong>OR</strong></em></p>
<p><em>θ</em><sub>r</sub> = 19 − 20 «°» ✔</p>
<p> </p>
<p>Δ<em>θ</em> = 5 − 6 «°» ✔</p>
<p> </p>
<p><em>For MP3 answer must follow from answers in MP2</em></p>
<p><em>For MP3 do not allow ECF from incorrect angles</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>centre of pattern is white ✔</p>
<p>coloured fringes are formed ✔</p>
<p>blue/violet edge of order is closer to centre of pattern</p>
<p><em><strong>OR</strong></em></p>
<p>red edge of order is furthest from centre of pattern ✔</p>
<p>the greater the order the wider the pattern ✔</p>
<p>there are gaps between «first and second order» spectra ✔</p>
<div class="question_part_label">b.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">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> is formed when a nucleus of deuterium (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{1}^{2}{\text{H}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
</mrow>
</msubsup>
<mrow>
<mtext>H</mtext>
</mrow>
</math></span>) collides with a nucleus of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{31}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>31</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>. The radius of a deuterium nucleus is 1.5 fm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State how the density of a nucleus varies with the number of nucleons in the nucleus.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the nuclear radius of phosphorus-31 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{31}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>31</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>) is about 4 fm.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the maximum distance between the centres of the nuclei for which the production of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> is likely to occur.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>. Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> undergoes beta-minus (β<sup>–</sup>) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by decay constant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a fresh pure sample of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span> the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s<sup>–1</sup>, the decay constant of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{}_{15}^{32}{\text{P}}">
<msubsup>
<mrow>
</mrow>
<mrow>
<mn>15</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</msubsup>
<mrow>
<mtext>P</mtext>
</mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>it is constant ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>R</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{1}}{\text{.20}} \times {10^{ - 15}} \times {31^{\frac{1}{3}}} = 3.8 \times {10^{ - 15}}">
<mrow>
<mtext>1</mtext>
</mrow>
<mrow>
<mtext>.20</mtext>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>15</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>31</mn>
<mrow>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>3.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>15</mn>
</mrow>
</msup>
</mrow>
</math></span> «m» ✔</p>
<p><em>Must see working and answer to at least 2SF</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>separation for interaction = 5.3 <em><strong>or</strong></em> 5.5 «fm» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy required = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{15{e^2}}}{{4\pi {\varepsilon _0} \times 5.3 \times {{10}^{ - 15}}}}">
<mfrac>
<mrow>
<mn>15</mn>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mrow>
<msub>
<mi>ε</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>×</mo>
<mn>5.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>15</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>= 6.5 / 6.6 ×10<sup>−13</sup> <em><strong>OR</strong></em> 6.3 ×10<sup>−13 </sup>«J» ✔</p>
<p> </p>
<p><em>Allow ecf from (b)(i)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«electron» <span style="text-decoration: underline;">antineutrino</span> also emitted ✔</p>
<p>energy split between electron and «anti»neutrino ✔</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>probability of decay of a nucleus ✔</p>
<p><em><strong>OR</strong></em></p>
<p>the fraction of the number of nuclei that decay</p>
<p>in one/the next second</p>
<p><strong>OR</strong></p>
<p>per unit time ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1 week = 6.05 × 10<sup>5</sup> «s»</p>
<p>17 = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="24{{\text{e}}^{ - \lambda \times 6.1 \times {{10}^5}}}">
<mn>24</mn>
<mrow>
<msup>
<mrow>
<mtext>e</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mi>λ</mi>
<mo>×</mo>
<mn>6.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
</msup>
</mrow>
</math></span> ✔</p>
<p>5.7 × 10<sup>−7 </sup>«s<sup>–1</sup>» ✔<br><br></p>
<p><em>Award<strong> [2 max]</strong> if answer is not in seconds</em></p>
<p><em>If answer <strong>not</strong> in seconds and <strong>no</strong> unit quoted award<strong> [1 max]</strong> for correct substitution into equation (MP2)</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Potassium-40 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>K</mtext><mprescripts></mprescripts><mn>19</mn><mn>40</mn></mmultiscripts></mfenced></math> decays by two processes.</p>
<p>The first process is that of beta-minus (β<sup>−</sup>) decay to form a calcium (Ca) nuclide.</p>
</div>
<div class="specification">
<p>Potassium-40 decays by a second process to argon-40. This decay accounts for 11 % of the total decay of the potassium-40.</p>
<p>Rocks can be dated by measuring the quantity of argon-40 gas trapped in them. One rock sample contains 340 µmol of potassium-40 and 12 µmol of argon-40.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation for this decay.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the initial quantity of potassium-40 in the rock sample was about 450 µmol.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The half-life of potassium-40 is 1.3 × 10<sup>9</sup> years. Estimate the age of the rock sample.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>Ca</mtext><mprescripts></mprescripts><mn>20</mn><mn>40</mn></mmultiscripts></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mtext>e</mtext><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mo>+</mo></mrow><msub><mover><mi>ν</mi><mo>¯</mo></mover><mtext>e</mtext></msub></math> <strong><em>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>β</mi><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mo>+</mo><msub><mover><mi>ν</mi><mo>¯</mo></mover><mtext>e</mtext></msub></math> ✓</em></strong></p>
<p> </p>
<p><em>Full equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mtext>K</mtext><mprescripts></mprescripts><mn>19</mn><mn>40</mn></mmultiscripts><mo>→</mo><mmultiscripts><mtext>Ca</mtext><mprescripts></mprescripts><mn>20</mn><mn>40</mn></mmultiscripts><mo>+</mo><mrow><mmultiscripts><mtext>e</mtext><mprescripts></mprescripts><mrow><mo>-</mo><mn>1</mn></mrow><mn>0</mn></mmultiscripts><mo>+</mo></mrow><msub><mover><mi>ν</mi><mo>¯</mo></mover><mtext>e</mtext></msub></math></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total K-40 decayed = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>12 μmol</mtext><mrow><mn>0</mn><mo>.</mo><mn>11</mn></mrow></mfrac><mo>=</mo><mn>109</mn></math> «μmol» ✓</p>
<p>so total K-40 originally was 109 + 340 = 449 «μmol»✓ </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mtext>ln</mtext><mfenced><mn>2</mn></mfenced></mrow><msub><mi>t</mi><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></msub></mfrac></math> used to give 𝜆 = 5.3 x 10<sup>-10</sup> per year ✓</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>340</mn><mo>=</mo><mfenced><mn>449</mn></mfenced><mfenced><msup><mi>e</mi><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>×</mo><mi>t</mi></mrow></msup></mfenced></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mfrac><mn>340</mn><mn>449</mn></mfrac></mfenced><mo>=</mo><mo>-</mo><mn>5</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>×</mo><mi>t</mi></math> ✓</p>
<p><em><br>t </em>= 5.2 x 10<sup>8</sup> «years» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>340</mn><mn>449</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>76</mn></math> </strong></em>«remaining» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mi>ln</mi><mfenced><mi>p</mi></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>693</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>ln</mi><mfenced><mrow><mn>0</mn><mo>.</mo><mn>76</mn></mrow></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>693</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>40</mn></math> ✓</p>
<p><em>t</em> = 0.40 x 1.3 x 10<sup>9</sup> = 5.2 x 10<sup>8</sup> «years» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 3</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mn>340</mn><mn>449</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>76</mn></math> «remaining» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>76</mn><mo>=</mo><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mfrac><mi>t</mi><mrow><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></msup></math> ✓</p>
<p><em>t </em>= 0.40 x 1.3 x 10<sup>9 </sup>= 5.2 x 10<sup>8</sup> «years» ✓</p>
<p> </p>
<p><em>Allow 5.3 x 10<sup>8</sup> years for final answer.</em></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong> for an incorrect number of half-lives.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«use the mass of the sample to» determine number of potassium-40 atoms / nuclei in sample ✓</p>
<p>«use a counter to» determine (radio)activity / A of sample ✓</p>
<p>use <em>A = λN</em> «to determine the decay constant / <em>λ</em>» ✓</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was very well done by candidates. The majority were able to identify the correct nuclide of Calcium and many correctly included an electron/beta particle and a properly written antineutrino.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a "show that" question that was generally well done by candidates.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a more challenging question for candidates. Many were able to calculate the decay constant and recognized that the ratio of initial and final quantities of the potassium-40 was important. A very common error was mixing the two common half-life equations up and using the wrong values in the exponent (using half life instead of the decay constant, or using the decay constant instead of the half life). Examiners were generous with ECF for candidates who clearly showed an incorrect number of half-lives multiplied by the time for one half-life.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Describing methods of determining half-life continues to be a struggle for candidates with very few earning all three marks. Many candidates described a method more appropriate to measuring a short half- life, but even those descriptions fell far short of being acceptable.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Rhodium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,45}^{106}{\text{Rh}}">
<msubsup>
<mi></mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>45</mn>
</mrow>
<mrow>
<mn>106</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Rh</mtext>
</mrow>
</math></span>) decays into palladium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,46}^{106}{\text{Pd}}">
<msubsup>
<mi></mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>46</mn>
</mrow>
<mrow>
<mn>106</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Pd</mtext>
</mrow>
</math></span>) by beta minus (<em>β</em><sup>–</sup>) decay. The diagram shows some of the nuclear energy levels of rhodium-106 and palladium-106. The arrow represents the <em>β</em><sup>–</sup> decay.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.42.36.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/09.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Bohr modified the Rutherford model by introducing the condition <em>mvr </em>= <em>n</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
<mfrac>
<mi>h</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span>. Outline the reason for this modification.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed <em>v </em>of an electron in the hydrogen atom is related to the radius <em>r </em>of the orbit by the expression</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v = \sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p>where <em>k </em>is the Coulomb constant.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the answer in (b) and (c)(i), deduce that the radius <em>r </em>of the electron’s orbit in the ground state of hydrogen is given by the following expression.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="r = \frac{{{h^2}}}{{4{\pi ^2}k{m_{\text{e}}}{e^2}}}">
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>h</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>k</mi>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electron’s orbital radius in (c)(ii).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what may be deduced about the energy of the electron in the <em>β</em><sup>–</sup> decay.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest why the <em>β</em><sup>–</sup> decay is followed by the emission of a gamma ray photon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the gamma ray photon in (d)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the electrons accelerate and so radiate energy</p>
<p>they would therefore spiral into the nucleus/atoms would be unstable</p>
<p>electrons have discrete/only certain energy levels</p>
<p>the only orbits where electrons do not radiate are those that satisfy the Bohr condition <strong>«</strong><em>mvr</em> = <em>n</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
<mfrac>
<mi>h</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{m_{\text{e}}}{v^2}}}{r} = \frac{{k{e^2}}}{{{r^2}}}">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><strong><em>OR</em></strong></p>
<p>KE = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>PE hence <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>m</em><sub>e</sub><em>v</em><sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}\frac{{k{e^2}}}{r}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span></p>
<p><strong>«</strong>solving for <em>v </em>to get answer<strong>»</strong></p>
<p> </p>
<p><em>Answer given – look for correct working</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>combining <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} ">
<msqrt>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</msqrt>
</math></span> with <em>m</em><sub>e</sub><em>vr</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
<mfrac>
<mi>h</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span> using correct substitution</p>
<p><strong>«</strong><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{m_e}^2\frac{{k{e^2}}}{{{m_{\text{e}}}r}}{r^2} = \frac{{{h^2}}}{{4{\pi ^2}}}">
<msup>
<mrow>
<msub>
<mi>m</mi>
<mi>e</mi>
</msub>
</mrow>
<mn>2</mn>
</msup>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>h</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p>correct algebraic manipulation to gain the answer</p>
<p> </p>
<p><em>Answer given – look for correct working</em></p>
<p><em>Do not allow a bald statement of the answer for MP2. Some further working eg cancellation of m or r must be shown</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong> <em>r</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{(6.63 \times {{10}^{ - 34}})}^2}}}{{4{\pi ^2} \times 8.99 \times {{10}^9} \times 9.11 \times {{10}^{ - 31}} \times {{(1.6 \times {{10}^{ - 19}})}^2}}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>6.63</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>34</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>8.99</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>9</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>9.11</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>31</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>1.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p><em>r</em> = 5.3 × 10<sup>–11</sup> <strong>«</strong>m<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the energy released is 3.54 – 0.48 = 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p>this is shared by the electron and the antineutrino</p>
<p>so the electron’s energy varies from 0 to 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the palladium nucleus emits the photon when it decays into the ground state <strong>«</strong>from the excited state<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Photon energy</p>
<p><em>E</em> = 0.48 × 10<sup>6</sup> × 1.6 × 10<sup>–19</sup> = <strong>«</strong>7.68 × 10<sup>–14</sup> <em>J</em><strong>»</strong></p>
<p><em>λ</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{E} = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{7.68 \times {{10}^{ - 14}}}}">
<mfrac>
<mrow>
<mi>h</mi>
<mi>c</mi>
</mrow>
<mi>E</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.63</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>34</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>7.68</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>14</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> =<strong>»</strong> 2.6 × 10<sup>–12</sup><strong> «</strong>m<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow ECF from incorrect energy</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br>