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</div><h2>HL Paper 2</h2><div class="specification">
<p>In beta minus (<em>β</em><sup>−</sup>) decay a d quark decays into a u quark, an electron and an electron antineutrino.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that lepton number is conserved in this decay.</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>A nucleus of phosphorus-32 \(\left( {{}_{15}^{32}{\rm{P}}} \right)\) decays by beta minus (<em>β</em><sup>−</sup>) decay into a nucleus of sulfur-32 \(\left( {{}_{16}^{32}{\rm{S}}} \right)\). The binding energy per nucleon of \({}_{15}^{32}{\rm{P }}\) is 8.398 MeV and for \({}_{16}^{32}{\rm{S }}\) it is 8.450 MeV.</p>
<p>(i) State what is meant by the binding energy of a nucleus.</p>
<p>(ii) Determine the energy released in this decay.</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>Quarks were hypothesized long before their existence was experimentally verified. Discuss the reasons why physicists developed a theory that involved quarks.</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;">
<div class="page" title="Page 15">
<div class="section">
<div class="layoutArea">
<div class="column">
<p>«lepton number on» LHS = 0 and «lepton number on» RHS = 0 +1−1<br><em><strong>OR</strong></em><br>quarks have no/0/zero lepton number and the lepton number for electron and the antineutrino cancel</p>
</div>
</div>
</div>
</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i)<br>energy released when a nucleus forms from constituent nucleons<br><em><strong>OR</strong></em><br>minimum energy needed/work done to break a nucleus up into its constituent nucleons</p>
<div class="page" title="Page 15">
<div class="section">
<div class="layoutArea">
<div class="column">
<p><em>Do not allow reference to “atom”.</em></p>
<div class="page" title="Page 15">
<div class="section">
<div class="layoutArea">
<div class="column">
<p><em>Award <strong>[0]</strong> for “energy to assemble nucleus”.</em></p>
<div class="page" title="Page 15">
<div class="section">
<div class="layoutArea">
<div class="column">
<p><em>Do not allow “particles”, “constituents” or “components” for “nucleons”.</em></p>
<p>(ii)<br>«energy/mass difference =» 8.450 – 8.398 «= 0.052 MeV»</p>
<p><em>Q</em> = 1.7 <em><strong>or</strong></em> 1.66 <em><strong>or</strong></em> 1.664 MeV<br><em><strong>OR</strong></em><br>2.66 × 10<sup><sub>–13</sub></sup> J</p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 15">
<div class="section">
<div class="layoutArea">
<div class="column">
<p>quark theory is simpler <em><strong>OR</strong></em> Occam’s razor example <em><strong>OR</strong></em> simple model explains complex observations</p>
<p>quotes experiment that led to quark theory, eg deep inelastic scattering or electron scattering</p>
<p>model incorporates strong/weak interactions/forces between protons and neutrons</p>
<p>model incorporates conservation rules</p>
<p>model explains differences between neutrons and protons <em><strong>OR</strong></em> explains decay of neutron to proton</p>
</div>
</div>
</div>
</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Rhodium-106 (\(_{\,\,\,45}^{106}{\text{Rh}}\)) decays into palladium-106 (\(_{\,\,\,46}^{106}{\text{Pd}}\)) 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>\(\frac{h}{{2\pi }}\). 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>\[v = \sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} \]</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>\[r = \frac{{{h^2}}}{{4{\pi ^2}k{m_{\text{e}}}{e^2}}}\]</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><span class="Apple-converted-space"><em>mvr</em> = <em>n</em>\(\frac{h}{{2\pi }}\)</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>\(\frac{{{m_{\text{e}}}{v^2}}}{r} = \frac{{k{e^2}}}{{{r^2}}}\)</p>
<p><strong><em>OR</em></strong></p>
<p>KE = \(\frac{1}{2}\)PE hence \(\frac{1}{2}\)<em>m</em><sub>e</sub><em>v</em><sup>2</sup> = \(\frac{1}{2}\frac{{k{e^2}}}{r}\)</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> = \(\sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} \) with <em>m</em><sub>e</sub><em>vr</em> = \(\frac{h}{{2\pi }}\) using correct substitution</p>
<p><strong>«</strong><span class="Apple-converted-space"><em>eg</em> \({m_e}^2\frac{{k{e^2}}}{{{m_{\text{e}}}r}}{r^2} = \frac{{{h^2}}}{{4{\pi ^2}}}\)</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><span class="Apple-converted-space"> <em>r</em> = \(\frac{{{{(6.63 \times {{10}^{ - 34}})}^2}}}{{4{\pi ^2} \times 8.99 \times {{10}^9} \times 9.11 \times {{10}^{ - 31}} \times {{(1.6 \times {{10}^{ - 19}})}^2}}}\)</span><strong>»</strong></p>
<p><em>r</em> = 5.3 × 10<sup>–11</sup> <strong>«</strong><span class="Apple-converted-space">m</span><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><span class="Apple-converted-space">7.68 × 10<sup>–14</sup> <em>J</em></span><strong>»</strong></p>
<p><em>λ</em> = <strong>«</strong><span class="Apple-converted-space">\(\frac{{hc}}{E} = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{7.68 \times {{10}^{ - 14}}}}\) =</span><strong>»</strong> 2.6 × 10<sup>–12</sup><strong> «</strong><span class="Apple-converted-space">m</span><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><div class="specification">
<p class="p1">This question is about nuclear reactions.</p>
</div>
<div class="specification">
<p class="p1">A reaction that takes place in the core of a particular nuclear reactor is as shown.</p>
<p class="p1">\[_{\;92}^{235}{\text{U}} + {\text{X}} \to _{\;56}^{144}{\text{Ba}} + _{36}^{89}{\text{Kr}} + 3{\text{X}}\]</p>
</div>
<div class="specification">
<p class="p1">In the nuclear reactor, \(9.5 \times {10^{19}}\) fissions take place every second. Each fission gives rise to 200 MeV of energy that is available for conversion to electrical energy. The overall efficiency of the nuclear power station is 32%.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the nature of X.</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 class="p1">State <strong>one </strong>form of energy that is instantaneously released in the reaction.</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 class="p1">Determine the mass of U-235 that undergoes fission in the reactor every day.</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 class="p1">Calculate the power output of the nuclear power station.</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 class="p1">In addition to the U-235, the nuclear reactor contains graphite that acts as a moderator. Explain the function of the moderator.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Outline how energy released in the nuclear reactor is transformed to electrical energy.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">neutron / \(_{\text{0}}^{\text{1}}{\text{n}}\);</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">kinetic energy / gamma radiation / binding energy;</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">number of fissions in one day \( = 9.5 \times {10^{19}} \times 24 \times 3600{\text{ }}( = 8.2 \times {10^{24}})\);</p>
<p class="p1">mass of uranium atom \( = 235 \times 1.661 \times {10^{ - 27}}{\text{ }}( = 3.9 \times {10^{ - 25}}{\text{ kg}})\);</p>
<p class="p1">mass of uranium in one day \(( = 8.2 \times {10^{24}} \times 3.9 \times {10^{ - 25}}) = 3.2{\text{ kg}}\);</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">energy per fission \( = 200 \times {10^6} \times 1.6 \times {10^{ - 19}}{\text{ }}( = 3.2 \times {10^{ - 11}}{\text{ J}})\);</p>
<p class="p1">power output \( = (9.5 \times {10^{19}} \times 3.2 \times {10^{ - 11}} \times 0.32 = ){\text{ }}9.7 \times {10^8}{\text{ W}}\);</p>
<p class="p1"><em>Award </em><strong><em>[1] </em></strong><em>for an answer of </em>\(6.1 \times {10^{27}}{\text{ eV}}{{\text{s}}^{ - 1}}\)<em>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">neutrons have to be slowed down (before next fission);</p>
<p class="p1">because the probability of fission is (much) greater (with neutrons of thermal energy);</p>
<p class="p1">neutrons collide with/transfer energy to atoms/molecules (of the moderator);</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">kinetic energy of neutrons/thermal energy of core is transferred into thermal energy</p>
<p class="p1">of the coolant (and elsewhere);</p>
<p class="p1">(thermal energy) is converted into kinetic energy in moving steam;</p>
<p class="p1">(kinetic energy of steam) is transferred into (rotational) kinetic energy of turbine;</p>
<p class="p1">(kinetic energy of turbine) is transferred into electrical energy by dynamo/generator;</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">X is a neutron and almost all answers were correct. G2 comments suggested that the term “State the nature of X” was rather vague. This is a helpful comment, but on this occasion candidates did not seem to be affected by it.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Instantaneous energy release: Binding energy, (particle) kinetic energy, gamma radiation were all accepted. Heat energy was not accepted.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Quite a few candidates found the mass defect rather than the mass of U-235 fissioned. The mass of a Uranium atom was often incorrect – candidates were expected to determine it from the mass number. A few stated the mass as 235g. Another common error was to find mass per second, rather than per day. However many correct answers were seen.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Working was often unclear. The power station efficiency of 0.32 was often overlooked. Whilst many candidates were eventually able to determine the power output of the power station in W, there were also answers giving the energy output per day. Quite a few candidates used eV/s and this was accepted for 1 mark.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">There was some confusion between a moderator and control rods. However, most candidates knew that the graphite moderator slowed neutrons (due to inelastic collisions) to thermal energies to maximise the probability of further fission.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Outlining the energy transfers occurring in a nuclear power plant is a frequent question, but answers were often poorly organised. A simple flow diagram would suffice. Thermal energy of core > thermal energy of coolant > KE of steam > KE of turbine > Electrical energy from generator, or similar. Far too many candidates barely mentioned energy; “…heat up water to make steam which turns a turbine…” gained no marks.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is in <strong>two </strong>parts. <strong>Part 1 </strong>is about electric fields and radioactive decay. <strong>Part 2 </strong>is about waves.</p>
<p class="p1"><strong>Part 1 </strong>Electric fields and radioactive decay</p>
<p class="p1">An ionization chamber is a device which can be used to detect charged particles.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-08-29_om_17.26.23.png" alt="N15/4/PHYSI/HP2/ENG/TZ0/06"></p>
<p class="p1">The charged particles enter the chamber through a thin window. They then ionize the air between the parallel metal plates. A high potential difference across the plates creates an electric field that causes the ions to move towards the plates. Charge now flows around the circuit and a current is detected by the sensitive ammeter.</p>
</div>
<div class="specification">
<p class="p1">The separation of the plates <em>d </em>is 12 mm and the potential difference \(V\) between the plates is 5.2 kV. An ionized air molecule M with charge \( + 2e\) is produced when a charged particle collides with an air molecule.</p>
</div>
<div class="specification">
<p class="p1">Radium-226 \({\text{(}}_{\;{\text{88}}}^{{\text{226}}}{\text{Ra)}}\) decays into an isotope of radon (Rn) by the emission of an alpha particle and a gamma-ray photon. The alpha particle may be detected using the ionization chamber but the gamma-ray photon is unlikely to be detected.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On the diagram, draw the shape of the electric field between the plates.</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 class="p1">Calculate the electric field strength between the plates.</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 class="p1">Calculate the force on M.</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 class="p1">Determine the change in the electric potential energy of M as it moves from the positive to the negative plate.</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 class="p1">Construct the nuclear equation for the decay of radium-226.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-08-29_om_18.04.47.png" alt="N15/4/PHYSI/HP2/ENG/TZ0/06.c.ii"></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 class="p1">Radium-226 has a half-life of 1600 years. Determine the time, in years, it takes for the activity of radium-226 to fall to 5% of its original activity.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">minimum of three lines equally spaced and distributed, <span class="s1">perpendicular to the plates and downwards; </span>edge effect shown; } <em>(condone lines that do not touch plates)</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(4.3 \times {10^5}{\text{ (N}}{{\text{C}}^{ - 1}}{\text{)}}\)</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\((F = Eq = ){\text{ }}4.3 \times {10^5} \times 2 \times 1.6 \times {10^{ - 19}}\); <em>(allow ECF from (b)(i))</em></p>
<p class="p1">\(1.4 \times {10^{ - 13}}{\text{ (N)}}\);</p>
<p class="p1"><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\Delta {E_{\text{P}}} = q\Delta V\)\(\,\,\,\)<strong><em>or</em></strong>\(\,\,\,\)\(3.2 \times {10^{ - 19}} \times 5.2 \times {10^3}\);</p>
<p class="p1">\(1.7 \times {10^{ - 15}}{\text{ (J)}}\);</p>
<p class="p1">negative/loss;</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left( {_{\;88}^{226}{\text{Ra}} \to _{\;86}^{222}{\text{Rn}} + _2^4{\text{He}} + _0^0\gamma } \right)\)</p>
<p>\(_{\;86}^{222}{\text{Rn}}\)\(\,\,\,\)<strong><em>or</em></strong>\(\,\,\,\)\(_2^4{\text{He}}\);</p>
<p>numbers balance top and bottom on right-hand side;</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\lambda = \frac{{\ln 2}}{{1600}} = 4.33 \times {10^{ - 4}}{\text{ (y}}{{\text{r}}^{ - 1}}{\text{)}}\);</p>
<p>\(0.05 = {{\text{e}}^{ - \lambda t}}\);</p>
<p class="p1">6900 (years);</p>
<p class="p1"><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer.</em></p>
<p class="p1"><em>Award </em><strong><em>[2 max] </em></strong><em>for 2.18 </em>\( \times \)<em> 10<sup>11</sup> (s).</em></p>
<p class="p1"><em>Award </em><strong><em>[1 max] </em></strong><em>to a candidate who identifies time as about 4.3 half-lives but cannot get further or gives an approximate reasoned answer.</em></p>
<p class="p1"><em>However award </em><strong><em>[3] </em></strong><em>if number n of half-lives is calculated from 0.05 = 2<sup>–n</sup> (= 4.32 usually from use of log<sub>2</sub></em> <em>working) and time shown.</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Field patterns were often negligently drawn. Lines did not meet both plates, edge effects were ignored, and the (vital) equality of spacing between drawn lines was not considered. Candidates continue to show their inadequacy in responding to questions that demand a careful and accurate diagram.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This sequence of calculations was often undertaken well with appropriate figures carried through from part to part.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This sequence of calculations was often undertaken well with appropriate figures carried through from part to part.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This sequence of calculations was often undertaken well with appropriate figures carried through from part to part. The only common error was the omission of a consideration of the gain or loss of the energy change in part (iii).</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">As one of the easiest questions on the paper this was predictably well done.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In the past candidates have found calculation involving exponential change difficult. On this occasion, however examiners saw a large number of correct and well explained solutions from candidates.</p>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about nuclear processes.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe what is meant by</p>
<p>(i) radioactive decay.</p>
<p>(ii) nuclear fusion.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Tritium is a radioactive nuclide with a half-life of 4500 days. It decays to an isotope of helium.</p>
<p>Determine the time taken for 90% of a sample of tritium to decay.</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>A nuclide of deuterium \(\left( {{}_1^2{\rm{H}}} \right)\) and a nuclide of tritium \(\left( {{}_1^3{\rm{H}}} \right)\) undergo nuclear fusion. The reaction equation for this process is</p>
<p>\[{}_1^2{\rm{H + }}{}_1^3{\rm{H}} \to {}_2^4{\rm{He + X}}\]</p>
<p>Identify X.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) refers to unstable nucleus/isotope / refers to spontaneous/random process;<br>which emits named radiation (from nucleus) / forms different nucleus/isotope;</p>
<p>(ii) combination of two nuclei / <em>OWTTE</em>; <em>(do not allow “particles” or “atoms”)<br></em>to form new nuclide with greater mass/larger nucleus/greater number of nucleons;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\lambda = \frac{{\ln 2}}{{4500}}\left( { = 1.54 \times {{10}^{ - 4}}} \right)\);<br>\(0.1{N_0} = {N_0}{{\rm{e}}^{ - 1.54 \times {{10}^{ - 4}}t}}\);<br>1.5×10<sup>4</sup>(d) <em><strong>or</strong></em> 1.3×10<sup>9</sup>(s);<br><em>Award <strong>[2 max]</strong> if answer is time to lose 10% (680 d).</em><br><em>Allow answer to be expressed in any time units.</em><br><em>Award <strong>[3]</strong> for a bald correct answer.</em></p>
<p><em><strong>or</strong></em></p>
<p>\(\ln 0.1 = \frac{{ - 0.69t}}{{{t_{\frac{1}{2}}}}}\);<br><em>t</em>=3.3×4500;<br>1.5×10<sup>4</sup>(d);<br><em>Award <strong>[2 max]</strong> if answer is time to lose 10% (680 d).</em><br><em>Allow answer to be expressed in any time units.</em><br><em>Award <strong>[3]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({}_0^1n\)/neutron;</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about the Rutherford model of the atom.</p>
</div>
<div class="specification">
<p class="p1">The isotope gold-197 \(\left( {_{\;{\text{79}}}^{{\text{197}}}{\text{Au}}} \right)\) is stable but the isotope gold-199 \(_{\;{\text{79}}}^{{\text{199}}}{\text{Au}}\) is not.</p>
</div>
<div class="question">
<p class="p1">A nucleus of \(_{\;{\text{79}}}^{{\text{199}}}{\text{Au}}\) decays to a nucleus of \(_{\;{\text{80}}}^{{\text{199}}}{\text{Hg}}\). State the <strong>two </strong>particles, other than \(\gamma \)-photon, emitted in this decay.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">electron/beta (condone lack of sign);</p>
<p class="p1">anti neutrino / \(\bar v\);</p>
<p class="p1"><em>Allow undefined symbols if unambiguous.</em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">Most candidates could write with confidence about the repulsive nature of the proton-proton interaction and the attractive nature of the strong nuclear force. Few gave good accounts of the balance between these two forces or described the energy situation (a better way to answer). Weak candidates could not name the strong nuclear force adequately.</p>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about binding energy and mass defect.</p>
</div>
<div class="question">
<p class="p1">(i) <span class="Apple-converted-space"> </span>The nuclear mass of the nuclide helium-3 \(\left( {_2^3{\text{He}}} \right)\) is 3.014931 u. Show that the binding energy per nucleon for the nuclide is about 2.6 MeV.</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>The binding energy per nucleon for deuterium \(\left( {_1^2{\text{H}}} \right)\) is 1.11 MeV. Calculate the energy change in the following reaction.</p>
<p class="p2">\[_1^2{\text{H}} + _1^1{\text{H}} \to _2^3{\text{HE}} + \gamma \]</p>
<p class="p1">(iii) The cross on the grid shows the binding energy per nucleon and nucleon number <em>A</em> of the nuclide nickel-62.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-09-07_om_09.12.11.png" alt="M14/4/PHYSI/HP2/ENG/TZ2/03.b.iii"></p>
<p class="p1">On the grid, sketch a graph to show how the average binding energy per nucleon varies with nucleon number <em>A</em>.</p>
<p class="p1">(iv) State and explain, with reference to your sketch graph, whether energy is released <strong>or </strong>absorbed in the reaction in (b)(ii).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">(i) <span class="Apple-converted-space"> </span>mass defect \(\left( {[2 \times 1.007276 + 1.008665] - 3.014931 = } \right){\text{ }}0.008286{\text{ u}}\);</p>
<p class="p1">binding energy per nucleon \(\left( {\frac{{0.008286 \times 931.5}}{3} = } \right)\frac{{7.7}}{3}\)\(\,\,\,\)<strong><em>or</em></strong>\(\,\,\,\)\(2.58{\text{ (MeV)}}\);</p>
<p class="p2"><span class="s1">(ii) <span class="Apple-converted-space"> </span></span>binding energy of left-hand side \( = 1.11 \times 2\) <span style="text-decoration: underline;"><span class="s2">and</span></span> binding energy of right-hand side \( = 3 \times 2.6\); } <span class="s3"><em>(both needed) (allow ECF)</em></span></p>
<p class="p1">energy release \( = 5.58{\text{ (MeV)}}\); <em>(ignore sign)</em></p>
<p class="p1"><span class="s1">(iii) <span class="Apple-converted-space"> </span></span>line goes through Ni point and nickel is the maximum ±2 small squares horizontally; } <em>(allow Fe-56 as maximum – this is just outside the range allowed)</em></p>
<p class="p1">line starts at 0, downward trend for <em>A </em>after 62, trend after nickel less steep than before;</p>
<p class="p1"><em>Line must go through part of the X to award first marking point. </em></p>
<p class="p1"><em>Line must not flatten out to award second marking point. </em></p>
<p class="p1"><em>Allow smooth curve for low A. </em></p>
<p class="p1"><em>Allow incorrect variations at low A.</em></p>
<p class="p1"><span class="s1">(iv)<span class="Apple-converted-space"> </span></span>nucleus produced in the reaction is higher up the curve than the reactants / <em>OWTTE</em>; } <em>(must see reference to graph)</em></p>
<p class="p1">reference to binding energy/other valid reason results in energy release;</p>
<p class="p1"><em>Award </em><strong><em>[0] </em></strong><em>for a bald correct answer.</em></p>
<p class="p1"><em>Award </em><strong><em>[0] </em></strong><em>for any discussion of fission.</em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">(i) This relatively easy problem was not well done. There were many permutations of the numbers, and almost all were poorly explained. Completely correct solutions were rare and even these tended to have a poor level of explanation.</p>
<p class="p1">(iii) Candidates are required to be able to draw and annotate this plot. This question proved that very many do not appreciate the prominent features. There were mis-drawings on both sides of the maximum; the maximum itself was often misplaced by more than the specified tolerance (showing that candidates do not appreciate the minimum value of the binding energy per nucleon at the Fe-56 or Ni position). Other errors included inappropriate gradients on the right-hand side of the graph compared to the left and failures to begin the curve at the correct place.</p>
<p class="p1">(iv) Few candidates referred their knowledge to the graph and simply recalled – often correctly – some physics about the stability of the fusion product. However, this was rarely referred to the relative position of reactants and product on the graph.</p>
</div>
<br><hr><br><div class="specification">
<p><strong>Part 2</strong> Energy levels of the hydrogen atom</p>
</div>
<div class="question">
<p>The diagram represents the three principal spectral lines in the visible region of the spectrum of atomic hydrogen.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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" alt></p>
<p style="text-align: left;">The electron in the hydrogen atom can only occupy certain allowed energy levels.</p>
<p style="text-align: left;">(i) Outline how the spectral lines provide evidence for the existence of these energy levels.</p>
<p style="text-align: left;">(ii) Determine the difference in energy between the <strong>two</strong> levels from which electron transitions give rise to the H<sub>α</sub> and H<sub>γ</sub> spectral lines respectively.</p>
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<h2 style="margin-top: 1em">Markscheme</h2>
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<p>(i) spectral lines are discrete;<br>therefore energy of photon is discrete/quantized;<br>photon energy is equivalent to difference in energy that electron has in each (discrete) level / Δ<em>E</em> = <em>hf</em> / <em>OWTTE</em>;<br>(so electron levels are themselves discrete)</p>
<p> </p>
<p>(ii) difference in energy = \(hc\left[ {\frac{1}{{{\lambda _\gamma }}} - \frac{1}{{{\lambda _\alpha }}}} \right]\);<br>=6.6×10<sup>-34</sup>×3×10<sup>8</sup>×10<sup>7</sup>×0.0780=1.54×10<sup>-19</sup>J;</p>
<p><em><strong>or</strong></em></p>
<p>\({E_\alpha } = \left[ {\frac{{hc}}{{{\lambda _\alpha }}}} \right] = \frac{{6.6 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{6.56 \times {{10}^{ - 7}}}} = 3.02 \times {10^{ - 19}}{\rm{J}}\) <em><strong>or </strong></em>1.89eV<br>\({E_\gamma } = \left[ {\frac{{hc}}{{{\lambda _\gamma }}}} \right] = \frac{{6.6 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{4.34 \times {{10}^{ - 7}}}} = 4.56 \times {10^{ - 19}}{\rm{J}}\) <em><strong>or </strong></em>2.85eV {<em>(both needed for the mark)</em><br>difference in energy=1.54×10<sup>-19</sup>J <em><strong>or</strong></em> 0.963 eV;</p>
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<h2 style="margin-top: 1em">Examiners report</h2>
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<p>(i) Although a good chain of argument was seen from many, some candidates struggled to relate the diagram to the existence of energy levels. Sometimes this resulted in a description of photon release that was accurate but irrelevant.<br>(ii) Simple algebraic misconceptions prevented many from obtaining a correct solution. It was common to see a subtraction of the values of the two wavelengths rather than a subtraction of the reciprocals. Candidates who carried both energies through separately scored more highly than those who attempted early subtractions.</p>
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<br><hr><br><div class="specification">
<p><strong>Part 3</strong> Atomic energy levels</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how atomic emission spectra provide evidence for the quantization of energy in atoms.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
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<p>Consider an electron confined in a one-dimensional “box” of length <em>L</em>. The de Broglie waves associated with the electron are standing waves with wavelengths given by \(\frac{{2L}}{n}\), where <em>n</em>=1, 2, 3, …</p>
<p>Show that the energy <em>E</em><sub>n</sub> of the electron is given by</p>
<p>\[En = \frac{{{n^2}{h^2}}}{{8{m_e}{L^2}}}\]</p>
<p>where <em>h</em> is Planck’s constant and <em>m</em><sub>e</sub> is the mass of the electron.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An electron is confined in a “box” of length <em>L</em>=1.0×10<sup>–10</sup>m in the <em>n</em>=1 energy level. Its position as measured from one end of the box is (0.5±0.5)×10<sup>–10</sup>m. Determine</p>
<p>(i) the momentum of the electron.</p>
<p>(ii) the uncertainty in the momentum.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
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<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>all particles have an associated wavelength / <em>OWTTE;</em></p>
<p>wavelength is given by \(\lambda = \frac{h}{p}\), where <em>h</em> is Planck’s constant and <em>p</em> is momentum;</p>
<div class="question_part_label">b.</div>
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<div class="question" style="padding-left: 20px;">
<p>from de Broglie hypothesis, \({p_n} = \frac{h}{{{\lambda _n}}} = \frac{{nh}}{{2L}}\);<br>kinetic energy given by \({E_K} = \frac{{{p^2}}}{{2{m_e}}}\);<br>combined and manipulated to obtain result;</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \(\lambda = \frac{{2L}}{n} = \frac{{2 \times 1.0 \times {{10}^{ - 10}}}}{1} = 2.0 \times {10^{ - 10}}\);<br>\(p = \frac{h}{\lambda } = \frac{{6.6 \times {{10}^{ - 34}}}}{{2.0 \times {{10}^{ - 10}}}} = 3.3 \times {10^{ - 24}}{\rm{kgm}}{{\rm{s}}^{ - 1}}\);<br><em>Award <strong>[2]</strong> for alternative methods, e.g. calculating energy then momentum.</em></p>
<p>(ii) use of \(\Delta x\Delta p \ge \frac{h}{{4\pi }}\);<br>to get \(\Delta p \ge \frac{{6.6 \times {{10}^{ - 34}}}}{{4\pi \times 0.5 \times {{10}^{ - 10}}}} = 1.1 \times {10^{ - 24}}{\rm{kgm}}{{\rm{s}}^{ - 1}}\);</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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A particular K meson has a quark structure \({\rm{\bar u}}\)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>\(0.21 = {e^{ - \left( {\frac{{\ln 2 \times t}}{{5700}}} \right)}}\)</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>The first scientists to identify alpha particles by a direct method were Rutherford and Royds. They knew that radium-226 (\({}_{86}^{226}{\text{Ra}}\)) 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>\(_2^4\alpha \)</p>
<p><em><strong>OR</strong></em></p>
<p>\({}_2^4{\text{He}}\)</p>
<p>\({}_{86}^{222}{\text{Rn}}\)</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 \({A_0}{e^{ - 1.4 \times {{10}^{ - 11}} \times 5.8 \times {{10}^5}}} \approx {A_0}\)</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 \(\lambda \)<em>N</em><sub>0</sub></p>
<p><em><strong>OR</strong></em></p>
<p>states that index of e is so small that \(\frac{A}{{{A_0}}}\) 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 \(\lambda \) 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> = \(\lambda \)<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>\({e^{ - \lambda t}}\)</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>\(\left( {1 - {e^{ - \lambda \times 6 \times 24 \times 3600}}} \right)\) <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 «\(\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}\)»</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 «\(\frac{{291}}{{1.3 \times {{10}^{ - 5}}}}\)»<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>This question is in <strong>two</strong> parts. <strong>Part 1</strong> is about simple harmonic motion (SHM) and waves. <strong>Part 2</strong> is about atomic and nuclear energy levels.</p>
<p><strong>Part 1</strong> Simple harmonic motion (SHM) and waves</p>
</div>
<div class="specification">
<p><strong>Part 2</strong> Atomic and nuclear energy levels</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A particle P moves with simple harmonic motion.</p>
<p>(i) State, with reference to the motion of P, what is meant by simple harmonic motion.</p>
<p>(ii) State the phase difference between the displacement and the velocity of P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The diagram shows four spectral lines in the visible line emission spectrum of atomic hydrogen.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>(i) Outline how such a spectrum may be obtained in the laboratory.</p>
<p>(ii) Explain how such spectra give evidence for the existence of discrete atomic energy levels.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The energies of the principal energy levels in atomic hydrogen measured in eV are given by the expression</p>
<p>\({E_n} = - \frac{{13.6}}{{{n^2}}}\) where <em>n</em>=1, 2, 3 ..........</p>
<p>The visible lines in the spectrum correspond to electron transitions that end at <em>n</em>=2.</p>
<p>(i) Calculate the energy of the level corresponding to <em>n</em>=2.</p>
<p>(ii) Show that the spectral line of wavelength <em>λ</em>=485nm is the result of an electron transition from <em>n</em>=4.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The alpha particles and gamma rays produced in radioactive decay have discrete energy spectra. This suggests that nuclei also possess discrete energy levels. However, beta particles produced in radioactive decay have continuous energy spectra. Describe how the existence of the antineutrino accounts for the continuous nature of beta spectra.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) the acceleration (of a particle/P) is (directly) proportional to displacement;<br>and is directed towards equilibrium/in the opposite direction to displacement;<br><em>Do not accept “directed towards the centre”.</em></p>
<p>(ii) \(\frac{\pi }{2}\)/90°/quarter of a period;</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) light from a hydrogen discharge tube/hot hydrogen gas/ hydrogen tube with potential difference across it;<br>is passed onto a prism/diffraction grating;<br>and then is observed on a screen/through a telescope;<br><em>Accept good labelled diagram for explanation of any marking point.</em></p>
<p>(ii) each wavelength corresponds to the energy of the photon emitted;<br>when an electron makes a transition from a higher to lower energy level;<br>since only discrete wavelengths/finite number of wavelengths are present, then only discrete energy levels are present / <em>OWTTE</em>;</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) −3.40 eV;<br><em>Award <strong>[0]</strong> for omitted negative sign.</em></p>
<p>(ii) energy difference between levels\( = \frac{{hc}}{{\lambda e}} = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{4.85 \times {{10}^{ - 7}} \times 1.6 \times {{10}^{ - 19}}}}\);<br>=2.55eV;<br>\(\left[ {3.40 - 2.55} \right] = 0.85 = \frac{{13.6}}{{{n^2}}}\) to give <em>n</em><sup>2</sup>=16;<br><em>n</em>=4;<br><em>Award<strong> [3]</strong> for reversed argument.</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the total emitted energy is shared between the electron and the antineutrino;<br>the energy/velocity can be shared/distributed in an infinite number of ways / <em>OWTTE</em>;</p>
<div class="question_part_label">f.</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">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Part 2</strong> Atomic spectra</p>
<p>The diagram shows some of the principal energy levels of atomic hydrogen.</p>
<p><img 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" alt></p>
<p>The emission line spectrum of atomic hydrogen contains a blue line of wavelength 490nm.</p>
</div>
<div class="question">
<p>(i) Calculate, in eV, the energy of a photon of wavelength 490 nm.</p>
<p>(ii) On the diagram above, identify with an arrow, the electron transition that gives rise to the emission line of wavelength 490 nm.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>(i) \(\frac{{6.7 \times {{10}^{ - 34}} \times 3.0 \times {{10}^8}}}{{4.9 \times {{10}^{ - 7}}}}\);<br>2.5 <em><strong>or</strong></em> 2.6 eV;</p>
<p>(ii) transition between –0.85 and –3.4;<br>correct direction of arrow (down);</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><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="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 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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>Determine the radius of the magnesium-24 nucleus.</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>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>\( \propto \frac{1}{{\sqrt E }}\) <em><strong>OR</strong></em> <em>λ </em>\( \propto \frac{1}{E}\)</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><em>R</em> = 2.7 x 10<sup>–15</sup> x \({2^{\frac{1}{3}}}\)</p>
<p>3.4 – 3.5 x 10<sup>–15 </sup>«m»</p>
<p><em>Allow use of the Fermi radius from the data booklet</em></p>
<div class="question_part_label">d.i.</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><span style="text-decoration: underline;">single smooth curve</span> 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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (<em>β–</em>) decay to form a stable boron (B) nuclide.</p>
</div>
<div class="specification">
<p>The initial number of nuclei in a pure sample of beryllium-10 is N<sub>0</sub>. The graph shows how the number of remaining <strong>beryllium </strong>nuclei in the sample varies with time.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the missing information for this decay.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxAAAABtCAYAAAAxrYd/AAASaUlEQVR4Ae3dD2yU9R3H8c+VDlnSMiWSeIf/gk2LC41mJZjNGgtoi9tIXOu/6GhZG6eLOA2h7VR0ZpQZSocaZIimnZTEOLUXIhqlWOwSjJH0MjOM0qYSUOiRoa5CM5HRe5Zr79q73p1c7+557u65d5Om1989z+/3+75+T+7ue8/z/H4OwzAM8YMAAggggAACCCCAAAIIxCGQ79/G4XDEsSmbIIAAAggggAACCCCAQK4KBM87jCUQfoRgQa6CEDcCCCCAAAIIIIAAAghEFwg94ZAXfRNKEUAAAQQQQAABBBBAAIFIARKISBNKEEAAAQQQQAABBBBAIIYACUQMGIoRQAABBBBAAAEEEEAgUoAEItKEEgQQQAABBBBAAAEEEIghQAIRA4ZiBBBAAAEEEEAAAQQQiBQggYg0oQQBBBBAAAEEEEAAAQRiCJBAxIChGAEEEEAAAQQQQAABBCIFSCAiTShBAAEEEEAAAQQQQACBGAIkEDFgKEYAAQQQQAABBBBAAIFIARKISBNKEEAAAQQQQAABBBBAIIYACUQMGIoRQAABBBBAAAEEEEAgUoAEItKEEgQQQAABBBBAAAEEEIghQAIRA4ZiBBBAAAEEEEAAAQQQiBQggYg0oQQBBBBAAAEEEEAAAQRiCJBAxIChGAEEEEAAAQQQQAABBCIFSCAiTShBAAEEEEAAAQQQQACBGAIkEDFgKEYAAQQQQAABBBBAAIFIgfzIIkoQQAABBMwUcDgcZlYfUbdhGBFlVhVYHas/rnTGa5Ur7SCAAALpFCCBSKc+bSOAQM4KWPUhNx0f4KcOqlWx+tvNhHinxs//CCCAgN0EuITJbiNKPAgggAACCCCAAAIImChAAmEiLlUjgAACCCCAAAIIIGA3ARIIu40o8SCAAAIIIIAAAgggYKIACYSJuFSNAAIIIIAAAggggIDdBEgg7DaixIMAAggggAACCCCAgIkCJBAm4lI1AggggAACCCCAAAJ2EyCBsNuIEg8CCCCAAAIIIIAAAiYKkECYiEvVCCCAAAIIIIAAAgjYTYAEwm4jSjwIIIAAAggggAACCJgoQAJhIi5VI4AAAggggAACCCBgNwESCLuNKPEggAACCCCAAAIIIGCiAAmEibhUjQACCCCAAAIIIICA3QRIIOw2osSDAAIIIIAAAggggICJAiQQJuJSNQIIIIAAAggggAACdhMggbDbiBIPAggggAACCCCAAAImCpBAmIhL1QgggAACCCCAAAII2E2ABMJuI0o8CNhYwOfdq0eXVKnNMxIS5SkN7H1adS6HHA7/b6nq2tzyeM+GbMNDBFIpEP8xN35MBo9N8/+mMkrqQgABBGIJkEDEkqEcAQQySsDnfV/P/mGNnuoNTwx8A6/rwcoOqXG/hkYNjQ5t1ry3VmvFM/t1KqMioDN2EZjuMWcYhqz4tYsvcSCAQOYLkEBk/hjRQwRyXGD8297f3PCCRst/roowjTMa3P+Ouq+q0+8fvF7OPCnPeYNWrSyXd+e76jvlC9uafxBIXoBjLnlDakAAgWwXIIHI9hGk/wjYXuAbffzKZ7rxzS1a+8vrdHlYvCM61n9Yun6+XPnBJ2Zp/jWLdZV3UEdOhJ+tCG7BXwQSF+CYS9yOPRFAwC4CE2+5dgmIOBBAwG4Cl6m6/bnxoLxTY/tWwyeGpxYG/j+pr0+fi/EcxQgkKsAxl6gc+yGAgH0EOANhn7EkEgQQQAABBBBAAAEETBcggTCdmAYQQAABBBBAAAEEELCPAAmEfcaSSBDIQYGLdEXpZTHinqs5hVylGQOH4oQFOOYSpmNHBBCwjQAJhG2GkkAQyEWBfBXOmSvt7dOnEzMundPJo4P6zFmkKy+ZmYsoxGyqAMecqbxUjgACWSFAApEVw0QnEUAgusAsFZUvV6V3t3a8/on8y8v5vO9py5Y35Fx5kxbNzpN8h9RR5QosMjd1Ia8qNXfs08CI9dO9WrXAmN/NN9ChqrFF9qbG75BjSbM69g2M2UU3Tr7Uqlj97Zj/E8cxZ34naAEBBBBIqwAJRFr5aRwBBJIVyCu+TVu6VujzhlIVOhya4arTB4s3avfD5Zp93sq71dqwTBUP7dJxC3MIKxYVC23jexl6W9WwrEYPuY/KDILQflj1+HvjTcGTyR1zKegAVSCAAAJpFnAYhmH4v7Xxv7DzgwACCNhOwH8G4palalCL+t+uV3Ho1yYjh+Re/5BqWr9SU8872rj0YtuF7w/IfwbilpJ1Uvs+vV2/QJMEPo0M7NL6+1artX+Veg61aKn/rA0/KROw8v3VyrZSBkRFCCCQNQKhrzG8U2TNsNFRBBBIuUDBAlU/1qwmp0c79/xLp1LeQKZXmKeC4lv12OOr5PR2a0/f15neYfqHAAIIIJABAiQQGTAIdAEBBNIt4FRpiUsFod3weeVxt6nOFbxvoErNOw7Ia8Z1PqHtpu3xfJVcGiaQtp4k3vBZeT1utdWVBu55cWlJ8055vKxInrgpeyKAAAKRAiQQkSaUIIBArgj4L2HasFGt3nLdWX7l5KU9vqNy31upRTWN6pxY/bpbrauuU9m97iTulxiWp+1XWvLo3gxJRMYvYdqw/iV5K5ervGhWikb+C7nrFqnO/UWK6ounmrM67l6jskU1auz8OLCDV72ttVpUtkbu49NMIrxu1Tnul9vLaubx6LMNAgjklgAJRG6NN9EikLsC3Q0qmRE8mxD4W3i1alqlpq4/6Y7i4Ifnszq+a5NWd3yliqYu9Z8eHbtHzBgdUt9LTSrp+KOe2JXoDccXquy3D2rxS3W6+xG3xbM/edXdcLVmhM3GNEOFJTVq1Sp1bbkt/P6QLDtSfMff1BOrt8pb8Yi6+r8ZHzPjOw31daqpxK3VT7yZROKXZRh0FwEEEDBZgATCZGCqRwCBTBc4qAMffqKh4FSuvsPas90tb2WLtj9VreKCwMtknlNldY16vOkCdWzv0WCilzLNrtDjuxul1hpVPLBNBzLh8ppejz78eMjUqVzNPQrOaHDPK+rw3q727U+oujg4/9ZMOcvuGbvHQx2vaM/gGXO7Qe0IIIBAjgiQQOTIQBMmAjkvUNmu/lEj8M108O836u9u1OU7a1Sxvnf8JuqRIfUf9ErRzlg45mpZq0c6OKhjwYRj2rB5Kih7QC/3PKmSztW6zrVCze5DFnx4d6qy/VONGsHYA39P96t70yXaWfNrrd/35bSjyYwdRnSs/7Ck19RQ8sMpa37M0I+WPSWvDqv/mH+lEH4QQAABBJIVIIFIVpD9EUAgiwVmq/jm3+mxltvl3fmu+iZWsz5PSN5BHTkRuKb+nEdtRVMujQq7TCjacxfItexJ9Y41063Wmqt1bZtHabnavqBYN695RC2VQ4nPRDV2v0BonJerptOjzprLwz/M17k1cUvJeYhT//SQPjryZYy1Ls7J674/vK+uGnVqu2pcPwgpL7L4vo7UK1AjAgggkAoBEohUKFIHAghkv0AwKShwqaTUKUU9YxH89v5V1Qfvmcgv09rBYHm8f7/TUM+TqvCrOWu1qbtfH60tU36aFb0fHdGJRC7NclZrR9iZjc/VVVum2q7Pw8/47KiW05QYC3RpyXxJt6u9/9vwNif6NaQ9YWtghHYkX87q58P3G+pSre5T19D/QsoHtaP6stAdeYwAAgjkpAAJRE4OO0EjgMC4wCkN7N2mDetek4KzEOXNV9V91XJ2P60Nm/eE3OjsnyJ0p5qXuOSo6tBAIh+0xxr1acSzVXcve1L9tc/pQ8+LWntzcfgUstManhF52paEfEseOBNQ1CZPPKc0Rga0d/NTWtctVd75MxVl5bvCLBVV3aV652tat2Gb9g5Mrujh8x7QjuYqORx3qGOAeyCmdWixMQIIIBBDIN1feMXoFsUIIGAnAf/qlVb/GIYR3uTYPQ0N4WUT//1Cm3ZXB2Yhmql5lferpfYfamhcrs7GiY3GHzjr1b4viRmLRvr0/Nqt0iPd8rTcLGfSH9j/o6MHv5CzqUeHNi5V8PbhKb2WFJiFKRZBxWbtvqN4cirbyAoyuiRv3k1qbKnX2w1rVNm5ZkpfF6q2/S8hM21NeZp/EUAAAQSmJZD0W9e0WmNjBBDIWQH/B3qrfuNHdqqi6QXt6ntRa8ounNytYKHq/9atvq5Nqp245sa/bbt6ep9W/YLYH9MnK4n26IwGXn1Wb/10m15OSfIg6dy/dfj9/0YuhBet+ahllWpq362+lx9QWXDGqajbZXrhbC2o3yZPX5c21S6c7GxFk9p7urS1fmESZ3kmq+MRAggggIDkMAzD8H87GPFtHToIIIBAigSsfo2xur0UMSVUjW+gQ7eU/FXX9ryjjUsvTqgOdjJPwMpj0cq2zBOjZgQQyFSB0NcYzkBk6ijRLwQQQOC8Aj6NHBvUQQ3rwPrlgfsgXFrSvFOeTFhf4rz9z9YN/PfOPK06V3DmqVLVtbkxz9bhpN8IIDBtARKIaZOxAwIIIJApAmd14sigvFqgX7S9G7hE7JC2lfRqxd1b5Ul4rYpMiS8z++EbeF0PVnZIjfs1NGpodGiz5r21Wiue2T++lkhmdpteIYAAAikT4BKmlFFSEQIIxBIIPe0Za5tUllvdXir7noq6uKwpFYqx6jijgY5alfx5sfoOrVXZ2FQkgbJ1Reo51KKlsye/m7PyWLSyrVg6lCOAgH0FQl9jJl/l7BsvkSGAAAI5JZBXeKEu0bBODH+b9rj9bzhW/5obdGDV6+vnyzUxj+Eszb9msa4KriVibgeoHQEEEEi7AAlE2oeADiCAAAKJCnypfc2LItal8J0e1gn9RDcunJtoxSndz6rZt6yZDORbDZ8YjuFzUl+fjmfxjRi7U4wAAghkiQAJRJYMFN1EAAEEIgXmaPEd96ii2603/hn4UOs7rt6X/q6D9XepqmhW5C6UIIAAAgggkKQACUSSgOyOAAIIpE8gTwVlD+jlvjt1cu2Pxy8VmrFcO+asUe+zt2oer/DpGxpaRgABBGwsMHEFp41jJDQEEEDAxgIz5SxbqY3vrdRGG0eZOaFdpCtKL5MORuvRXM0p5G01mgxlCCBgLwG+n7LXeBINAggggICpAvkqnDNX2tunT0/5Ai2d08mjg/rMWaQrL5lpautUjgACCGSCAAlEJowCfUAAAQQQyBKBWSoqX65K727teP0TjUjyed/Tli1vyLnyJi0KmcI1SwKimwgggMC0BUggpk3GDggggAACuSyQV3ybtnSt0OcNpSp0ODTDVacPFm/U7ofLNTsKjFXT2EZpmiIEEEDAFAEWkjOFlUoRQCBUIHTxmdBysx5b3Z5ZcdihXqvHwur27DBGxIAAAgjEIxD6+soZiHjE2AYBBBBAAAEEEEAAAQTGBEggOBAQQAABBBBAAAEEEEAgbgESiLip2BABBBBAAAEEEEAAAQRIIDgGEEAAAQQQQAABBBBAIG4BEoi4qdgQAQQQQAABBBBAAAEESCA4BhBAAAEEEEAAAQQQQCBuARKIuKnYEAEEEEAAAQQQQAABBEggOAYQQAABBBBAAAEEEEAgbgESiLip2BABBBBAAAEEEEAAAQRIIDgGEEAAAQQQQAABBBBAIG4BEoi4qdgQAQQQQAABBBBAAAEESCA4BhBAAAEEEEAAAQQQQCBugfy4t2RDBBBAIAkBh8ORxN7sigACCCCAAAKZIkACkSkjQT8QsLGAYRg2jo7QEEAAAQQQyC0BLmHKrfEmWgQQQAABBBBAAAEEkhIggUiKj50RQAABBBBAAAEEEMgtARKI3BpvokUAAQQQQAABBBBAICkBEoik+NgZAQQQQAABBBBAAIHcEuAm6twab6JFAAEELBdgBi7LyWkQAQQQMFWABMJUXipHAAEEcluAGbhye/yJHgEE7CnAJUz2HFeiQgABBBBAAAEEEEDAFAESCFNYqRQBBBBAAAEEEEAAAXsKkEDYc1yJCgEEEEAAAQQQQAABUwRIIExhpVIEEEAAAQQQQAABBOwpQAJhz3ElKgQQQAABBBBAAAEETBEggTCFlUoRQAABBBBAAAEEELCnAAmEPceVqBBAAAEEEEAAAQQQMEWABMIUVipFAAEEEEAAAQQQQMCeAiQQ9hxXokIAAQQQQAABBBBAwBQBEghTWKkUAQQQQAABBBBAAAF7CpBA2HNciQoBBBBAAAEEEEAAAVMESCBMYaVSBBBAAAEEEEAAAQTsKUACYc9xJSoEEEAAAQQQQAABBEwRyA/W6nA4gg/5iwACCCCAAAIIIIAAAghEFRhLIAzDiPokhQgggAACCCCAAAIIIIBAqMD/AZms2klHLgpbAAAAAElFTkSuQmCC"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>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>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>\(_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}} \to _{{\mkern 1mu} {\mkern 1mu} 5}^{10}{\text{B}} + _{ - 1}^{\,\,\,0}{\text{e}} + {\overline {\text{V}} _{\text{e}}}\)</p>
<p>antineutrino <em><strong>AND</strong> </em>charge <em><strong>AND</strong> </em>mass number of electron \(_{ - 1}^{\,\,\,0}{\text{e}}\), \(\overline {\text{V}} \)</p>
<p>conservation of mass number <strong><em>AND </em></strong>charge \(_{\,\,5}^{10}{\text{B}}\), \(_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}}\)</p>
<p> </p>
<p><em>Do not accept V.</em></p>
<p><em>Accept </em>\({\bar V}\)<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><em>λ</em> <strong>«</strong><span class="Apple-converted-space">= \(\frac{{\ln 2}}{{1.4 \times {{10}^6}}}\)</span><strong>»</strong> = 4.95 × 10<sup>–7</sup> <strong>«</strong><span class="Apple-converted-space">y<sup>–1</sup></span><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 \(\frac{{8.0 \times {{10}^{-3}} \times 365 \times 24 \times 60 \times 60}}{{4.95 \times {{10}^{-7}} \times 7.6 \times {{10}^{11}}}}\) <strong>«</strong><span class="Apple-converted-space">= –0.400</span><strong>»</strong></p>
<p><em>t</em> = \(\frac{{ - 0.400}}{{ - 4.95 \times {{10}^{ - 7}}}} = 8.1 \times {10^5}\) <strong>«</strong><span class="Apple-converted-space">y</span><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>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.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><strong>Part 2</strong> Radioactivity</p>
<p>Radium-224 \(\left( {{}_{88}^{224}{\rm{RA}}} \right)\) is a radioactive nuclide that decays to form radon-220. Radon-220 is itself radioactive and undergoes a further decay. The table shows the series of radioactive nuclides that are formed as the decays proceed. The series ends with a stable isotope of lead.</p>
<p><img 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zqIEJl+d06n2jDBE5NLNX59kx2IcQIysV8Prx+vfmFWfp1+ebd+5cvXgNtvVnGmgiFheTKBAAII9BABT693zfF4Z43qT9hN2/t/Tate+plWVJRqYOjY3E8lE+bryU1LNMoJuvve0osvfxgV1N+8Vy846eUP19zHHtb0sDhBngpKxqvyqVottAKv1p/vgJ7d+m5yDfOCa8T43xkbRHRXFkOo22fnDdLEWV9TfxNNOrl5tZ5q+rjbi9QbCkDAvTfsZbaxRwiEnUTNY1oPzR2hmO3+84o0fvlslYUuoA/p1/8rok84R8X0Jbql0jxKPq798bP8K4v1eWddZ7k4rxkrW5w8+QgBBBBAAAEE4gmYgbLMDfcG+3o+v3iWNj6zLPwCPK9QpRXL9PRzs0JBd9/BrdrWnOqFmPdBhHhb2HWfpdMwIVtMPtQrv3jLXGoX6rZbrnA11ug6RXJCAAEEclXA2+td53hsaZiboOPu0ZjCPlFp8gonaGmgOxDr4zb96hf7Oz69ZI7sv3/7QGj8tT7j7tXfFUVPTybwOm7KcJOr9Wca5r12UL8PvE/9P2dsEJnoxPVTbqO7stQpM7imueFy4wSNGWDt+SOqX7s7yvcog9n30qQJuPfSHc9m55qAudD7XYuc+9l9vnStvhC6+x1jW/oN11ducELybTrc8oeOC1qDKV09Xgs2O33Cm5bzd/1Qu7c9oCsTpR9KLUNlC6XPGwQQQAABBBDotID/Pe15vtVebbDKH56poQXRTu7mImzonbo7VGf4QK+/7XRf19lcvQ4idDb/DCyfdsOELDEJdSdTplHFF2QAiiQRQACBnirg8fWu/1917Ld/tLES3QQ13YHcdKuutxvD+V7drVc6dCvj09kz/26n10eDBn3GDqhH2x8mvWuGaUi0j1Ka54wNYlYecIe+OfbSlFJhpS4QyLta02ZbfbmbWy37arSeVu4ZRyfgnjbxEdWNvsLuT3Gy6lqtZkRWK5idqqkcoyGhPhUH67ppy1W3ralz/SWZSv722ie0YHRxeJ+Ng8ZowZMbtL2pQ++MqW9R2nm5LUZoQYPpI9K2qFs5XdeFLApVFCj/T9QYc3CuNjVWjrC32UnLvWnR8nJ/HvHeCiw7+Q+Zr8YOA5O48nN97m9t1Iawsgf344aG1ohHr8xAWA3PqHra9a79VKyxlT/0aB+ZE+OEp3TY7qv93erSOCdRZ9sv0EX9YtzZdhZxv/Yfqfvrd2nbsq+6HmVzLxDrfReULVbWzEeglwkEjknRzgnm+DZk9HzV1O5UU8oD4biPqxk4nzn7yjrXPDlfYweZc4FzXE54TnBWDr5m1iE8L6YQyFWB8NZ4iYKsnawzxELxPIgQK6Mumu9Fw4QsMfF/cFRHTP03/68H6XPR7rt0ESnZIIBADgn4W9VYXxNxjZvMtXz0bfSu/haMt4THGGJdp0cvS+fmeny9+8FBve50/9Lnag37QoKboO6GdL5oT67n66KL/9LepPM6evSfTdv12H++1mM6GvvjTn3S3ro92e7K7H0XeS1gXRMMn67q2ugxIl/DfF1pLVO6TIecEp7frOnO9YQrhuN87Lx6971zUrReo8X8rPjPE+oYK3Kv18n3nv4Gzfc4dPOGVu6d3BMpLU7APSW2eCuZwKtpHXzbuNmqDrUatpY3fSXte0rL55iuO0Y/rL0xA81O2qfVVHuvrjOtj+ctfVRbIgeG8DVry4pHNG9cqflRP5dGgMXKL0N5mYPD3iqrq5LZWr5uX6j/0MAWBsr/XU0vHaX7trVEBK8dg+58tfbjt3RDabmWhJU9uB+XlI/RhJVvBG+eBLbz67q1/CHV7HO3CDunQ6Z/LGsfTYw7onimtvMPajls3fSw/go0pOhTwbeR/5tA+4w123Vgf50eDOvnLXJBL6eTLJuXWZIWArksEDjOjNGV1jEp2jnBbJuvebOql87WxGGTVH3Ai5uxXp3PHHiT3p6HNXaYOa+t2Bwa1CnwabLnhG5xcMrPKwK5JZBXMl+vOIOq/9P8BAOYfayzp53BUvvokov/IrWN9TyIEKUYVj/q0+Zre8K6dPi6/tbNun/aYzqQ6k3JVBsmdIVJ+KZGmTKBgcCTkvn69ODLYndJGGXN+LNSC5zETNMc470M7ilWeoGgTpI3qLOqQZJbzrZPqmGQe71o7z3ej9GyYF6OCdh1tiFlmv7IiohrXLMpoXrbtRpb9Qsd9yfYPC/rb4G0osUYXNfpVpn+lKBMGf849vVuWMB78OUqtFuvxy6S+6Z4tCfX8/XZslEqsdM5v2OTnu/QCt5O3X9YP177ooJn/L4quf16fTZ2xgk++VjNLzXYXdkkaqlvkrIGHb/3Jg214kOR1wJWTif3qWapFSNK8nuVoHTWOWBvVSaun6z42cwoMT8r/vOolpSX6cqkYn7xNsDj36CTlevmTfSnJZwFefVCgIC7F4qhNP6fzry1Vg8s+Hl4cDn0efCNr/lpzbjzETXGrPCfMq27J2ji0j1x0wmmZv2oF+rOux9P8QIiU3mZ/sW+W64ZP3W6KolACE2e0J4539SarHqc5WO1bJ2nKXPi7Ufjvu77ZrAJc2GwcGqC7TQjii/9Ttdv4+nf6M337Ivn/Kt07d/Yg6OE7M2bwgrtNIH2ygklHl58uTOI8T6ZssVYldkI9DoBq3I68+4ExxmXiq9JNXfMUl2LEzxzfZb0W6/OZ06Gfp16vkpTKp4OD7Q7H4de45wTusUhVDDeINCDBayba8u1Zp99k77/V3TXyE+ntL3eBxEii3FeLVt+oPp9m1X1nR8mXfcNBNvvXKzd+3Zpy8EzkYnGn06zYULmTeIXP/jpf+iDY+/HbfGYTCphy3gaOPE6sJAgvUBQx7pBPV6L9kQ+tepsZRY3SPIy4OjpfnTseM1tAeucYK6FKxLV2aytNNfEP31AU2Zujh1097L+llRaVpkWaG5Nc/c26ot5vevXR2fPhsrWZ8jl+kzCL8wnVTjICYv7Tfcx50LrO6vmFY3V/eMuC0769qhqapXqIp7Kt1p61y2cr9UH7bHdzGCt908alPqYHu6u6xK21Ddxp4XTNO8ldwNFp/SRr/Y+rD/cYTsjl4w5ndR3xbV20tdPf9ThjYs1K0GsLnHMz5V3h7ce/wbD0i9Q4WC7IWacQXjDVmEiZQEC7inTRVuxVbsefSYQTMgvnqyF9Q06YrcsOtJYr4WTi9u7ATm5VYuXNUTpXsZcSNR+WzM3v9+egVPRd1opHX9P++of1oyRA0LL+Jpr9O2o6YUWifImk3md18mT1oWb6RN88lyt2vG2WmJZZNugDf43teHRX5qbHVbZzYmq8T277Jb7t1XmjBJulXvmXab/c7Ov8os1aVG99rW0BpdtaVDdrJFmFGjnr1UvvPRe6icMJ5mkX80JbeUP7IHS8tV/3CSV9cuW54ezuWxJA7MgAl0kYA22t1JVocpp5HEpeMyxzjGLZ7qOOb4Denbru2kcc7w4n7mJTKuj5nfNcdUcj0beF3ZOaHlnu1a4z49Rzwnd5eDeBt4j0NMEgq1aayrNU3qhRgaXadKy2SqN2td7ou3PTBAhPNc+KqpYq40zS6TmtZqSRIMTJ9i+52QfXTVzuRaUXRKeZLyptBsmdIVJvA1wPrtAJfN/aeqoR/TK/KGpB1ec5ORl4MTrwIJ1fTNVt1YkESw0rXSfq5iqRQ2nQlsWfGO2LyONnzxokJRUECnZgKOX+zGCkMmcFfC3PKu5rgaEVlyj0noaOhSLaFV4vdPU8V5aorlRg6Ne1t/Mb7t+satO3LFO2V4u0+Bt88/1v7ttL8S73v2Tzp1pS+MGqE//dvojdWzAf4lKl28IxSCsJ1+Xm5bWg53uG83rYPOk7HK7F4b84ntUs+l7KZ7vg7Duruvyr/uiiuO01Pc31ev7oRjXAJXNXKOt7xwLxk4C361jOrBjjSvGZfZh9aPaZbfUzy9bqXet5RqrdJWzX/uYLjCP2vGXwytVGsrfy++dk5nzao6v+/ZHvaZJPubnpBX91dvfYGQeF6j4ljIFI4ltev3N36bxXYxMm+lIAQLukSJpTbeZILNf/W9Zqd07Vmq6q3uOvMJSTa+uD1wgBI8D5sRkuht5KrJld9uvVLv+QOhLn188S5t310S0QO6jgWV3q3L9Tm02Fxzt6S3Vig4VxjgblPG8BmjUmh3aVn2/xpf0CxUkaFGndZPtO7DmE99vj+qDRI+ihVLI8BvfKZ081UclizabsleoNDRiuOX+ba0IjRJuyn3ypP4tf7gW7v6ZVlSUtvd9nleo0rk/0NqZg+3CejMCeHJbbi6gGx7TYueElj9UU2dc37Ut2GMWNJvLFrPQfIBA9wn439H6x162zwnmsc8Ox6Vg0azj6tT5a/XMouGhc8KJ1w7q9ymX3IPzWYe8zc2CmT/WC+vnh50TVFCiSdUJzgnd5tBhI5iBQO4LnN6uikCfp5cHHusOdYHYf5QW7timFZ0JSIdpZCqIEJaJmeinofNrAvVIX4Kge3iwvUZPzx/RxfWhrjKJNMrsdLqBE3fpvA4sWOnNr94fupbq0Cjm+NvaWn2nrgoFZt7XlqrHXE8eZ3ODJG8Djl7uR/c+5X0uC5gBMJf9SE2BDsCtettPtf8fV2pGxNPQwXpnjV7YNsv+LYUHR0MCXtbf/O9q24+dOIkJtk/+YYc6Zahc9Xe6Gr6FStNFbzJxvfv/qe/FBe2NN2NtSSAGsVJrF42Ku/1WjGnjM4t1cyjOESvBePPNdga6KrOWSdRdmXtZs/TI2Voxf7xKwm7umwHcS8ar8qlaLbzGfjI/1RbYXn7vohJEv6YJxrkiYn476rW1U08de/wbjFL+vM8N0mD7HHj+9V/rN9kSh4tS1lyfRcDd6z3Yf6KWVE9oD7yGpW8uEOYu01znAKLIVs/mTty+Ldp50h7iIn+Ulm14QEPDDkTuBK0LjrVaNrLAnvm+dm78lemRPZm/zOeVf83dmje2KEYrmkt0w51fse+smfL+2xm1dbxNm8yGZGaZAVO0qHxIlLK7B5qwsjaDg0yfq6lF0QYnvUBfGHa1Qp+cOaOzGT+YmZPZgcd1z4xNdndEpqVazQ80PWr5MkMXO9VsLlvsUvMJAt0q0Pa+jn7onBOG667x8R77NC0/by7TEKfAR44pMI63M93Z17TOZ1EyM8fVh+bGCnYlOCd0p0OUTWEWAjkt8NFpnbIPK+7tyP/URfL/7oMoT1+6l/L6fZJBhA7ZWi351mvVLQNMV8IxWrqbvt7XfGeJgi3buyPY3qHQSc5I1STJ5NNezMvAideBBXd6ZkNNdwmrXopoFGNu2JRMXqZtu6tC/R3r5Iv66b4PgzLZ3CDJ04Cjl/sx7S8VCWSLwOn9evFVu3uxuPU2q8AmQDp0ph6abjcwixYc9bD+5m5NLauOWlUW4waqKVfZYlfDt67EzdT1bp4uvOiiKLEJ97aZvJtqVTF8RMKuia3z5uS4XWq504313t1V2Sc1+PL/Hqd8ETefT7XqeKzulfOGaPr2Zrvle5NqJ1waqwCx53v4vYuaSdzfRkTMr7NPHXv9G4y2ARdepFDnBx+2qDXWvoi2LvM6JUDAvVNciRY2wddxE3RDzAC5WT9vkMZNidUC0X3QsgK5MzQm9EuIlfelGjPrjlDgOvmW4pnOy9zl/OI1MW48BLclr+BiXRRrs7p1foIRtt0HKMUfHCS/8HINcrYl4zcV7BP8HWvtPpKtO6+dfHTaKavnr9lcNs83lgQR8E6g33jVOo9KHn1K4xOdEy7sp0tCrfbSKUa657PIvBMcV83i7tYWOm8eDz3high2m0PkdjCNQO4LBPoUt7orXFSlha6uqAIDL88xA9GNXpN03+jpayQTRIiRS16Rxq97uj3oXl6vFqdhgzWw6t0zZLrwNXWhXAq2W9uahkkMKm9nexg48Tqw4E7PhOLK5i3U+BgtOPOKbtNdNziNlpzH6rO7QZK3AUcP96O3XzBS6zYB8/1/ebd+Fah+Ja63BYuZoHsKz+pv7sE5k6ijyl2urgLN5PVuePdk0bbI31Kv6eZmYkOg8WbH7nas7n3bu9wxKQS61Lpb929rSbELyja1HvmDXZQ+6nfRBdGKZc8zg7r+7dD2mJUd8F/wZK3qapMcwDpO6h0+8ux71yFlM8OcW2Z/I/5A9BExvw+PvJ9kY4YM/AajbUL+Z3T5YLtZqO99HfvgP6ItxTwPBD7hQRokERKIH3wNLmZaSF8zzLRA3KND1gy7BeLAQIDEfdBKdJcwlGkoSBGITdh3qEoSBWXMT779AJmJvJJPs31LsuVdni66uG+cO7Tucv6lLi5IJbp1RHWjx2h5c7xBDU1fo4t2aWeF0y2NO9/I99FO8NlygZnNZYt0ZBqBXBMwfd82bNXelv8r+Y/p52s2JxiUNNntS/d8FplPEsdV52amK84emUrs6Uw5xM6RTxDIVYFAP6j7ndJXaPp86/ezTkur1gUu1AMtxssv1AtbKlSU8eFfEgcRnJJGfbWD7pp5jxmIbZXunvmX2rj8s9o81Qq2nw90OdD13chELWknZqZp0omcUlvUCZy8JWvou2BLyVc1ac7XdHneJRo66faIbgJi5ZJGYGHdEZO3HSQ3rR+dmrjvf72p151zSP4wfeWmeIP/Xqrx65s0Pqx4H7sGlzVBvU40fvqHfU8GPexuMqNfiiXfIKnjsIIpBhwDVmEbaU94tR+jpc283BRwN8gz3aGum6jB6zq3JecPH9M/y3SzmvRqydbf/lNtpt/y4F9ycYa8L1yrEX2e1Jaol9u5di0ecYMs0td/WBvmPWF3BWR3t1M9qsMTAMEud27QuGHf1W3l1hPxJ7RnwUrtumld4kY9kXnq/+jMKQf3Ql180Z93WMI9I694jL5xzUYtdwZsNQH/LSvMXXHrb+ls85/Vr/v/1Bcvv1YTI7owCizj6X/Jfu+iZfopDfofzs3aaJ9b88xTFv+jSJ82Mb/AefK1N9XsG+/qYz7Wel31G/wLXXyJFXC39t9HOnP2P81rvBsmscrL/EQCBNwTCXXq81SDr04m7oNWoruEzjrm1R2k8LXpzEemb5botTzXSpnOqxPld5UqO94WaEiRPXJzdhQoQSnMCWPPSj3wTWdwKKtle7YE27O5bAlY+RiBLBPwtzbqmb1HdGr/T1Szr+OluLfFTfd85m1p3Kl1rYM7Z94j0FMFrDFqZuvJjX+hr9+6LHDB7ju4UbWvjE2jP/dkrRIEEZJJJizoPl8jX7JWMgGHW5aY4HvHgEMySXbvMh6YZHgDvAmceB1Y8OmfW1oD4YPA5n+6SIXxnjqOapTNDZK8DjiakFBWBcCi7hBmdqmA+zuWYsZhjQnD00iv/vYHtRy2u7oxHbbGb01t5+u04o3bwC28jKlNdfZ6t73bMOf+YOfyzddf9btQ7q4q/M279KwTyM6/SXPmx+pux8rJ6nJnluaMfFHz9hlTuyug8al03RIqeBLXDVZXMfUbpDkPaHnU65gTali3Qg0mzeVzTDxjcpUeqpqU5A3cUEE6vEnve9chOTMjiW01Szm9OXTuii2zv8H2rblAF/WzW7i3z+RdBgTcv9MMJE+SCCCQWYHTaqr9tqZUOMF2e6DaLh8ULNpWZnPZopWXeQhkqYC/VXurxujK0nItWbqiC4LtOGSpAMVCIKMCeUVm/BqnL169r+d3/6Z94Mmkcm4PIiS1eIeFOgYROiwSa4YVdF8+W2VOU+c+47Tkh5Pjdm0YKylv53ejibcbEp6aHThZOHJA+PzQVDBwstx0UTR0YLHGVj6npg59xHoXWAhl635zsem6stNPaKTZIMnK32n85C5L6H2SgcLQ8u43aQQc3cm433uyH90J8h6BKAI9uh6byvVueLdhwacCoriFzfLp7Jl/t+dEPjVqniYPDV5qbjffcKtuTNj48tO68avD7KeDnC61wjLMzETBUE1f/7IO7HgsrEu7jpmd06HNCzXx1ge0vdVpRd9xqbhzevT3Lu6W82EWCdDC3dOd8e8602bdp3Rq+9ET97eZwTOdj/7qYhWEbnu4H+04r9NnPzZLJXpcxSzy0VmddvqszC/QxReGEnRyifLalXlFyb7Xzxqs6f/4nqan49B2QHXuO8T5xbrjR4/rkVGFSXaHk07mCdbN5rIlKDofI5BVAv4WbQ90lRCtfYTVP+NUTR3+V8EiX/y3mnjN27qndFmwy7K0NiTd81lamXdcudscOhaFOQj0XAF7sHfTBYV1edv5rgHagwhWbTi59eMFETohbR0jFj6mBqe54PkdWrzoZr0Q5ZH6TqTqwaLdaOJB6eMmYQdOJjY9r60v/Vwb1u0z3RNE+7MDJ6++plWbVsXsUz3amszrAgH2Yxcg50oWf64C03JagV9yZ7o2jbN9ntXfPqWiISYu0mwdZZKMk/jP6cwZJ0gSWcbuvRZ3xnkLdDF8xsSGTDEHxr1B6H76JvJp/PCnovL6XSRrL8b/S+XcFC/F3+tY6x9lHiuKt5D9mWlhXzJW061/883NAusc8vaHOhPtCd6TP1fVklLduH68Ge66E3+efe+i5ZnJa6QM/AajbYLcN3CjLsBMjwQIuHsEGUzmDzr6O/NYTkm8/o8i7kD+9SB9LnRwLVDhYNOVifVoj/5ounf/VzOAxaUJgqfu/g/Nakk/PtmVeXmKHCWxxCfdwABhUdbMzVnWiale82ausgdFMVvR/2tZchGTzWXLzb1NqXuzgPk9vbJea15ygu1W34az9c0ZY2I/Xtn6tkdg6Z7PPCpGIJnudPByO0gLgZ4v4G0QIUmv0IX1h6YbmZXtfbhvnqN7+nV/F3vdYpIkXfqLpRM4yXBgIakgVqRANjdI8jrg6N72dPajOx3e57bAf9PnLr/MNB08Yp5uOq/D+3+j02YssU4FOsMAvKy/uY8XHcdvCMvWmWh7X0c/dO7COjO9ePXgevdz1+hLA/J1yBqE78QBHfjAp5LCOI02/f+qY781Ae3A32d1eeEnXRvS/iSVtbX+02dNr9ymh2HXEh3fho8Vkn9JP/XtuFCCOe5jUoJFY37sHHvMAhUzVGmiX21Nu/TU2sdCT/T6Xt2tV06P6UQf815+76IVPJPXSF7/BqOVP3Je5Pcp8nOm0xFIpil0Oun3snXb9KuNL6gl1o1US8N/VDs27rcf0S3Q9V8d7joYOj8wa0EzUEldjXaFmq5b86L9fahXfvFW6JHf/LAAfrTlnXldmZeTp5evToXYStO5OREr/VP6p91vBlprxVoid+abE8iBx3VPaARy8zxF8Sxt3v14FrQYyuay5c4epqQItAucU9PuRrvFoBm8bebjenL++NjBdlNJPX3wLR1uTyCNd+mez9LIusOq3enQoTDMQCBHBHw6XjtZRQMLA/+GTNuu0wlL7sEFuB1ECGRlBxHiZhs3iBB3zeCHoWD7CVMfmqEfVE/QwH4jVPlMjWYUS4fWzdA9K98ww2t2419Xm3TbptqBEytosv5Xajl+zHQbsEYzXN3OBAMnzoWS+1rEDu6lVfZ8faao0PTubP992KLWDt3YOB/ar621Gmv/RooGTlZd6wXBxk+BjxNdXzhppdr4yVk/2Vcn4Ggtn2QXECkFHDu7H5MtP8tlv4DZ94GBHoMl9b26RTtaEnXnYb7/2+7VkKjnGi/rbxeo+JYyM6xm8O/8jk16Pm6c5Lxatm/RrzyPt3t0vWu6QRv2JSckfli797aYWnysPyuAvE27rOC89TdgqIZ+zh2cj9hv9sDNwYVj/e+OIZnBnAdflky/ChGJhR+TDrf8IeJz96Q1SO0Vdp3ky6pusnpyiPZnHX/Gq/LJRzTJOZjH7aYrWhpefu+ipW+ukX6xP36dKm7ML1qazryIfZn2b9BJN+LV9886dsT+bSfdQ0ZEGkwmJUDAPSmm5BfyHXxCc1bHqtif1oHVVVodGtBimL5y06ddieep38hJGtvfPoD69qhq6uM6ELOyaNJbOUtVgRbxVjKXaeyU610BfFfSHd52ZV4dMvdghnugB3NzYsc2vRrVyZygGh7T4s3ve5Bn9yfhb6nX9DvW6lDgfGsNCLZSu3fM0dBODwrl/bZkc9m831pSRCDbBKwBm5Zo2oI9oRuw6ZYwvfNZurmnur73DqmWhPUQ6F6BfH32b4eGghPhgc5YJfPgAtzTIEKsctrzw4Lts7TxmQfa60MFWRR070qTBGTefOxV4MT7wEL+33xRX3LiUPZAgLG3OeImdSCI1ddu4WutlenGT7FLFv0TrwOOXu3H6KVlbm4KBAfStds6+/Zr9ewfxolFmLaE5tp0Rqju2ZlYRKRP4vpbXvHNus20Cg/8+V7WmoXbdDxqlNoKiv9Qc6qdRo6ReaU+7d31bl+V3Fqq/oGimABx9cPaEOvmRluDVlRtbW+Ac/vNKg71kBDcljCbExu1tP5w/AB+w1qtCcWQCnXbLVck6FUhmpn7pqnf9DF/Lk6eAzT0us/ZiRxR/d9vjNtI1f/BMR1z9m0f03DA2e/RipHWvMTfu2jJ+/Z9XzNqYxknivlFS7F9Xpf8Bk8c02HnXlrSPWS0l5F3yQsQcE/eKsklTT+FVmuaylo1hgZ4MAf9pu2qnjZWk9c12cEQc5CtfFBjIge0KLheFdOGhnqB9zWv1eRbZ6h6W5OrdY45MDQ8E5Geael8zRRV3HhJkuU0i3VlXsmXKskl+6r4i1eFnHRyk2be/V1taWpvv2WNSL1h5QzdVr5JJ/MvUf9LnBp4kllk22L+w9ow7wk12Te386+Zp2fWZcOAYAYqm8uWbfuR8iCQtMAnVTjos/bS5sJ/3QO6b+X2iIHnzGBN22rN+WCURlY4gyfbq/jP6uxHTm3VnteplzTPZ53KK97C3e0Qr2x8hkD2CoRdgPtMcGJlg6suGVluU7fctrz9Ajx/qL4x8coULsC9DSJElrJ92rqgnacq0+WW9aRfWLDdWcgE3ef8w2KN6n++m1u6d5WJs+GZfvUucOJ5YKHfcH3lBqcP4TY1rFoec8A9f+s2LVr1sn1dZp4iCwSxsrtBUoffdFoBR+/2Y6a/caTfhQJ5gzRx1tfsQLC57WTFIoaN14Ind4bXP9uatP3J+Zpw6zLXtWlkLMLj+lve1br3kYl22Xw6+dJ83TpuvuoaWtsDvVa5rOv/CU4DNQ/tPL3eNTccb5ygMU4g2dzcWH7r17WgttF1E8Gq469Uxa33a8tJJwBwk74z/eqO5+YwGxPAXzpaN0xbrrqwGJKxcHys+EiAxjTgmzxX98btEjmWoTleXjNMQwIfm+uU1w7q97EWlblhOHGiSpz7JQeX6Taz72oiy2cGOm2sX677pqyyv1emfKNvDq0XSP7CfgqFdc6/qV/+6lRErh5/7yJSD05axpM1IdWYX9Q07Zme/gajZ+TubrnPl67VFyJu4ERfi7mpCNCHeypqMdfpq88Xf0pHm1vMqMrLNN38i/5ntUxerNXlQzoeLM2DkEUVP9C6o5PM+nar7JP7VDPH+hc9NWtu4GKjvlxFnfqxdGVescue2ifmAD92hsofe1k19uNVvuZNWjDO/OuQoHVzo0qjnl+o6lP2yarDMtk+w7TC2flo+9MRprg+c6K6pSjWdyzK9hRXad8/VmhglI/Sm5XNZUtvy1gbge4VyNfA8XeorPoteyDAE2pYNyfwL6lyOY9gRt7YTWplL85nSWWUxELd6ZBE8VgEgWwVsC/AdwUurE1wwurTXDN09513aHyJ8yi71Sjkef1s0wY9trnZ1SjkIU0tcp7n7swGOkGErcH6mR1EOFZpbhiWl9qDwllBhDr9aNX69rFo8mMEEaJmbT3hWaEpphGLYgXb7fXyCifrh5uk++9crD2mQcz0izfrZxXR6t9RM/JoZleYeFTUpJKxAyd1wUCbVR+9bdwxzf67O/T1CSXt3RJYgZMfP6efPrUhduDEDixssIM/weDeq5o0Z6q+fsft7V2oWUGi557TM2s22095xmpodKnGVH1TP33VDgKaAffm3fKBfp3o+9d/or4/ww5i2Q2Sdi4Nto4NNn56TzPm3a97Q9tnNX7arM0ba0P9DFt0nW78lJS3a6HI33Qg4HhAcx+4T1PLCoPXlZZVzQ+1JuYgtk56Hu5HJ0lee4CAOV6VfU/PLGrVbfZvwETdtWXF7MC/mBtoxhNbtuYbEbEIr+tvVtnm6AczDweO/9ZVva95s5aXm38dCmbiLWNv1+d3b1eD05K3wzKdmZGB692w33NgY7Rlabn5F6tcVkwjSoPNwOKRNuacv+8pLbf+xY0hma7Yqsraj9uxso41390X/Xtv6eDpctOtW/SAVF7RN7SysiH0vbL2XfUc61+sxM18c2xeElm+Cy9SIItAWOd9bSm/VlusJPJHadX+daavd6+/d5HlK9GMRYXatXR7GjG/yDTd017+Bt3pOu8/1m/eesfubrlAX/riX7c3YnUW4dUzAVq4e0ZpJfRJXfmtVVp7V3GcL21fXXXX49oYt2XyJSqt3qati0aF7i7HLqZJb/JybXI/Rht74SifdGVeUbJPZ1beUM15dolpuRSv5boZZHDRBtVVfD7KzY10Mu/qdd2PeXd13onyy+ayJSo7nyOQ5QL9xmjVc7N0VbzDnLMJ/Ufq/vpntWKk07rvqN48GNnqw1k40atX57NE+ST5ebc5JFk+FkMgKwWcC/ASu15qnlrZvFrzxv1tqG/3ooGXa+i42aoOBdvjNQqxNtLdDUWhrqxstIP0LoCwlnZmvhWsMUGEkaZ/7WCf8n+riXOebA+2m6HaYgcRXOkG3pp+eWtnJRVsd9YMBt2t+uJ50yLtPi1qSPW46KSYwmtGTVIoT5qrBAMnw0PXO8HAyXgNDfWHbvZ1UZmmP/JU+36OFjgxtfNgcK89LSe4N/Hqy9u/p1eP17wV7cF2RQ3uBTfKKtvqFe0tdBN//y7TpGWzVRrqntFukDT5snalQOMn9/ZdoZHlD4UH262bP51u/NSeRXLvIn/TTsCxTIMde8sqEGy3Ao7jVRbnvpl3+zG50rNUrghYv4EN2l17T1L1z/zie1SzaVX08cQ8r7/109D5tdoUN05inceWaKM5Dji3ltOXz8T1bvD3vDbutjgld2Ia8W4YJ2PjpGeMRlalEUOy08m7QqNuLwxOJOzGy/perU2w75zyWQ1Kre/V91zHZvuz/C/oy6Ndx2dnFd/7OvbBfwSnPP/eOZlYr5/QxTd/XxvXuM4z7o8D75OJ+XVYyTXDw9+gK9XAW/972vN8a3BufmQX15ELM52uAAH3dAUj188r1M3Lfqbd9Q+HDRJkjhiatODvVdf4a+1c9lW7hU/kyu7pfiqpeEqvvbNdqxY9qEnFfd0fmrt9I82dNTu96jvaW4CEL5XkVFfmlWSRklzMuoh68rVfqu57kUbWjYi5WrVjp2orhqZ+1zbJcmR8Md9v9evXunXIr9ibmM1li11qPkEgRwRMZXzoHO18yzoX3KuyyBuMgXNLlRbXN+jI/jo9WDZCZV8dZgdBkhjUJ56CZ+ezeJkk+1k3OiRbRJZDICsFOnMBbl3Qb9ILT6XbXZ3XQQQ3rLkInfRtlY+crGX/cH97n+3uRaK8d4Lut97yd53rfjFKWqnNyqRJaiVKby2PAieBQngdWOijgRNWaWMywUJzDr2jdoOWlkV2yZnNDZKS+U0nG3D0cj+m941i7WwTML+jUQ9p5+EGc529IDyuESiqOV/MXBCof777jw/p5sJYd3YyUX8Lxi5ebazX4gWTw28KWDGSNT/z4DwWsT8ydr2bbBxmT5IxjQTpBa4bvmdiJG/otfUVacaQLCN3VzHJXHe49l206xoz8kzi75V9fF5zX8R10Uc6c/Y/7R2Xie+d+zthnWce1wsRA4ObEW1N+auMb2OSMT93mpHvvfoNhqfrb96rFwI9RJjzxLhJKovxREL4WkylKvBn/2X+Ul3ZaqVi/bUct++QpJpQTq9ntfQZo+XN1rNK/TWp/kWtKHNaF+b0hlF4BBDIoADHzwziknSKApzPUoRjtR4s0KOO1VZXE1t268X1G9pbHZt9l188WbNvH6FrJ7m68Ii5T93HCanP5Hq9U10aauncYbVAnv+kXz9fqy3N59o/toIi027SsJsnqjRmoKZ98ax752vUgqvMo/9W9b/PZNUdWqnSZJ5Esjakh5lYYyY9s3e/Xo/4XgUDD/9TXxp2i+52ujtJtCMD3dC8pLde+0lY6/GU0rLyCqT3c/1yZ7Tv39c0KpnvfNr7y/2bSeJasbVWY0uX6ZBV/gTfrYD9L3drl6urnUCjLKf7m058Tz3dj1bZe/Bfjzov9OD9xKZ1lcC/aPu02zTPGoQ11K1L9G5luqpE5BNL4GM1rRynieuOmAUGa8aOHapMqf/+WOn3zPnpHPMJuKf9nehkJSrt/EgAAQR6gkA6B+6esP1sQzYKcD7Lxr1CmbpXgGN19/qTOwIIIJBtApwXsm2PUJ7uFvA3rVTZuCd1wvQrULbmBdVOuLS7i0T+0QT8B1R9452BMXbyR64xTzmM97DbpWgZ9ox56Rzz6VKmZ3wH2AoEEEAAAQQQQAABBBBAAAEEEEAAAQS6TCCv5Bv6TmAMqTY1PPasmvxdljUZJS1gDfxbo/pAdzKDVT7rVoLtSdulviAB99TtWBMBBBBAAAEEEEAAAQQQQAABBBBAAIFeKnCpxlR9UyVW12onXtTPXumGwcl7qXzSm+1/R+sfe9kMdG/6bjdjHd5LVzJJ06WzIAH3dPRYFwEEEEAAAQQQQAABBBBAAAEEEEAAgV4qkFf0Da2sHG7Cue9ry/fqaeWeVd8DV+v2/hO1pKrMdP7DX1cIEHDvCmXyQAABBBBAAAEEEEAAAQQQQAABBBBAoMcJ9FFR+UOae01f08p9o5bWHxY9y2TJTm5r0KpVVuv2yzRp2WyVFjCobVftGQLuXSVNPggggAACCCCAAAIIIIAAAggggAACCPQ0gbwhmrrqW6ZrmXNqqn5Uu04Tcu/+XfyxmmpWa8tJma5kFmlB2SXdX6ReVII/+y/zl+r2pjNaa6p5sh4CCCDQEwQ4fvaEvcg2IIBATxfgWN3T9zDbhwACCHROgPNC57xYGgEEEMhlgXSO+bRwz+U9T9kRQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEskaAgHvW7AoKggACCCCAAAIIIIAAAggggAACCCCAAAIIIJDLAgTcc3nvUXYEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACBrBEg4J41u4KCIIAAAggggAACCCCAAAIIIIAAAggggAACCOSyAAH3XN57lB0BBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgawQIuGfNrqAgCCCAAAIIIIAAAggggAACCCCAAAIIIIAAArksQMA9l/ceZUcAAQQQQAABBBBAAAEEEEAAAQQQQAABBBDIGgEC7lmzKygIAggggAACCCCAAAIIIIAAAggggAACCCCAQC4LEHDP5b1H2RFAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQSyRoCAe9bsCgqCAAIIIIAAAggggAACCCCAAAIIIIAAAgggkMsCBNxzee9RdgQQQAABBBBAAAEEEEAAAQQQQAABBBBAAIGsESDgnjW7goIggAACCCCAAAIIIIAAAggggAACCCCAAAII5LIAAfdc3nuUHQEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQCBrBAi4Z82uoCAIIIAAAggggAACCCCAAAIIIIAAAggggAACuSxAwD2X9x5lRwABBBBAAAEEEEAAAQQQQAABBBBAAAEEEMgaAQLuWbMrKAgCCCCAAAIIIIAAAggggAACCCCAAAIIIIBALgsQcM/lvUfZEUAAAQQQQAABBBBAAAEEEEAAAQQQQAABBLJGgIB71uwKCoIAAggggAACCCCAAAIIIIAAAggggAACCCCQywIE3HN571F2BBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAgawRIOCeNbuCgiCAAAIIIIAAAggggAACCCCAAAIIIIAAAgjksgAB91zee5QdAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAIGsECLhnza6gIAgggAACCCCAAAIIIIAAAggggAACCCCAAAK5LEDAPZf3HmVHAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQyBoBAu5ZsysoCAIIIIAAAggggAACCCCAAAIIIIAAAggggEAuC/zZf5m/VDagaGBhKquxDgIIIIAAAggggAACCCCAAAIIIIAAAggggAACWS/Qcry102WkhXunyVgBAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAIGOAp/oOCu5OVZ032nlnkqkP7lcWAoBBBDomQIcP3vmfmWrEECgZwlwrO5Z+5OtQQABBNIV4LyQriDrI4AAArkj4BzzUykxLdxTUWMdBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQiBAi4R4AwiQACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAKgIE3FNRYx0EEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBCIECLhHgDCJAAIIIIAAAggggAACCCCAAAIIIIAAAggggEAqAgTcU1FjHQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEIgQIuEeAMIkAAggggAACCCCAAAIIIIAAAggggAACCCCAQCoCBNxTUWMdBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQiBAi4R4AwiQACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAKgIE3FNRYx0EEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBCIECLhHgDCJAAIIIIAAAggggAACCCCAAAIIIIAAAggggEAqAgTcU1FjHQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEIgQIuEeAMIkAAggggAACCCCAAAIIIIAAAggggAACCCCAQCoCBNxTUWMdBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQiBAi4R4AwiQACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAKgIE3FNRYx0EEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBCIECLhHgDCJAAIIIIAAAggggAACCCCAAAIIIIAAAggggEAqAgTcU1FjHQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEIgQIuEeAMIkAAggggAACCCCAAAIIIIAAAggggAACCCCAQCoCBNxTUWMdBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQiBAi4R4AwiQACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAKgIE3FNRYx0EEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBCIECLhHgDCJAAIIIIAAAggggAACCCCAAAIIIIAAAggggEAqAgTcU1FjHQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEIgQIuEeAMIkAAggggAACCCCAAAIIIIAAAggggAACCCCAQCoCBNxTUWMdBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQiBAi4R4AwiQACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAKgIE3FNRYx0EEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBCIECLhHgDCJAAIIIIAAAggggAACCCCAAAIIIIAAAggggEAqAgTcU1FjHQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEIgQIuEeAMIkAAggggAACCCCAAAIIIIAAAggggAACCCCAQCoCBNxTUYu3zkdtavNHW+CI6kZfoaKBhebfFRpbeyTaQt00z122EVrQ0BZRjkSft6mxcoS9bdHWj0iOSQQQQACBJAUSHX+TTKYrFot5/uuKzMkDAQQSCrQ1aXvtclUMH2zX2aw6abHGVj6hum1Niqz9JUwvxQX8TSt1o1UfHjJfjb4UE8mK1XpQ/Zfjd1Z8oygEApkXyKF6ZboYrbUaG4i9ZOZ8429t1IYO51ST16AxWvDkBm1vOp38FgTOz09owehi1/nZpDV8uqprf6LG1vPJp2Ut6W9VY72H6XUid39LrSYOshzu1fbTUQNjnUgtwaJddu7y8nfjZVoJfAIff6ymlV8236vBuq5yT5fV9ZIpWW9YhoC7Z3v5tJo2V2nsdcvV9CfPEiUhBBBAAAEEslyA81+W7yCK1+sFzuv4noc1dth4zVv6lBpOuqPc53Ro86NaPme8ho9+WHs7e1HfWdu2N7TmoY060dn1WD5DAhy/MwRLsggg0FMFTDB7b9UYXVlariUdzqlmo33N2rLiEc0bN0LXTatVU/TWmLaO+/z8qLY0nwtXO7lPNUu/q+mlo1RReyCJYKlfbU21qrjuy5r+iBfphRcn4ZT/sDbMe0JNvr4qqXxQY/rlJVwltQU4dyXvdoFKZszVpP7Syc1LtaLhVPKrsmTaAgTc0yY0CZiLh+rRpZpYuUmH3NcwXqRNGggggAACCGSrAOe/bN0zlAsBW8BcfDc8oikVTyeso/qan9aMW6aqrqWTLemStfa3aHtlpWoiAwrJrs9y3gpw/PbWk9QQQKDnC1jnsZl3a8ZPm5U47OPTyX3LdGd5vVqiNvRO/vwsc5u6YelUTa89rKhJBeRNegce1z2Tl0XcWI+2W5JJL9p68eadV0v9w1p90Nw0GDBFi8qHKCPhds5d8XZC9M8KyjRv3k3K1/vaUvWYGuPeBIqeBHNTEyDgnppb+Fpnf6PXe/XFQ4FKq99Qy/FW8+8NrSgrCPdhCgEEEECgZwr0+vNfz9ytbFUPEji9S/NmbNJJe5PyiydrYX2DjgTqbKbe1tKgukWTdVW+vYBvv1bPezZGcCANF+sCedw4zXupJ7Vtz/H6L8fvNL7QrIoAAr1PwAooL1ZV6DyWr/4j79Vi9zn1+HvaV1+lScV9Qzy+g6tUvvpAx0C5/x099b2tofOz8os1aVG99rVYMRXr39vauuY+lfV3TtDn1FT9qHbF6qbFSu87NaGb6x3O98eP6cCONZoxcoBdNiu9h7XBo5vs/pZnNb96v7kRcZkmPVKukoxE203ROXeFvlvJv8lTv7EPau415nt5cqsWL2tI4mmJ5FNnydgCBNxj2/AJAggggAACCCCAAAI5KmD67ayrUYPdDC+/eJY2PrNM08sK21ud5RWqtGKZnn5uVijo7ju4VduaP/Zom+3H22/9O1q2eyRKMggggAAC3SDgf1fbfnzAbtneV1fN/LFeWL9QU93nVPXRwLIKrdixQ6tucQLbPp0w5+LwQLlfp3fWqP6EfYLu/zWteulnWlFRqoGhQHU/lUyYryc3LdEoJ+jue0svvvxh1I33N+/VC056+cM197GHw8/35sxfUDJelU/VaqEVeLX+fAf07NZ3O94MCH7aif//RbuW/ch0JSPlXzNFFTde0ol1WbRLBPIGaeKsr6m/+Qaf3LxaTzV5Vc/rktLnbCYE3HN211FwBBBAAAEEEEAAAQRiCPjf057nW+0PB6v84ZkaWhC6knetZC7Ch96pu29wnlD8QK+/7UFLdDMI3JZK0zf8uPbH2/OvLNbnncZ6rhLwFgEEEEAAgWwWCAtomy5THpo7Qs5Zs0O584o0fvlslTnnO98h/fp/uftn/1Cv/OItO3ifrwHj7tGYwj4dkrFm5BVO0NJAdyDWVJt+9Yv96jgcq0+/f/tAaHyUPuPu1d8VRU9PJvA6bspw072I9WduBrx2UL8PvE/9P3/Ts/qHfdbQ6wW6fsptKopW1Ug9edb0RMDU9W6coDEDrD1/RPVrd0f5HnmSEYm4BAi4uzB4iwACCCCAAAIIIIBATxAIDw6UaVTxBXE26wJd1C/GxXmctWJ+1FqrsVeP14LNTj+3pjXgXT/U7m0P6EouxGOy8QECCCCAQDYKmKe1ftcip215ny9dqy8kOpf1G66vhG5kt+lwyx/aN8z/rzr22z/a04W67ZYr2p88a1/Kfme6A7npVl1vB+99r+7WKx26lfHp7Jl/t5fvo0GDPmMH1DskZmaY9K4ZpiHRPkppnmndvva5YLB/wB365thLU0qFlbpAIO9qTZtt9eVubrXsq9F6WrlnHJ2AexrEvob5unJgoYpKl+mQk875zZo+yMyz5g+Zr8ZEo2mY1j/bn5yvsc461nqDxmjBkz9RY2vyg1b5Wxu1ofYJLRhdHMzbSsf+N2T0fNXU7kwwQrazAam8tqmxcoSd3wgtaLDubrr/jqhu9BVxPncva95bF2lO+TsYuvJyfRbY/pXTdZ2z3sDBZlTw5drQ0BrxiJQZCbzhGVVPuz7kUzSwWGMrf6jtTR3vFUeUjEkEEEAgCwSsLhp2qqZyjIaEjnnWceyJKMe8OMX1t6qxvibieJjcOSid81/3nq/iePARAj1MIK9kvl5x+mr/p/kJ+lP9WGdPO/XOPrrk4r/wTqP/SN1fv0vbln3V9ai8d8kHU+qO+qErz4HJ1n+Dx++6sDprMsdd7+rS6Ry/lcZ5o32P2waR1z/W+Wz4dFXXdu4aqD1d3iGAgOcCnvzm20vlXR0w2rE01vV/e/6pvzNB6glP6bB9Tn23ujROQNvJJc6N7A8O6nWn+5c+V2vYF+LdEDfpuYP3HVrLW/nl66KL/9LO+LyOHv1nu/W8PSvixdd6TEcj5qU62d663bTUv/1mFSe6EWGiM9Z1TF0nzwHpnLu8+965lYLbkfb1mDvJaO89/Q26b97Qyj0at9fzCLh7LZp0eibwu+dhjR02XvNWbA4NbhFY3desLSu+q+mlo3TftpaIgHFEBuYHuLdqjK4sLdeSpY9qS5TBW33Nm1W9dLYmDpuk6gM9LahsHLd9SzdY279uX/ugI1bfVPue0pLyMZqw8o3goBABq6/r1vKHVLPP/aj0OR0y/VjNG1eqiXFH/o6wZxIBBBDocoHTaqqdqdvGzVZ1qOWoVQjrOPaoOeaV6crRD2tv3Bu29vlnSJmmP7Ii4nhokgqdg67V2Kpf6Ljfo43s9ecrjxxJBgHPBay61HKtCTwObhLv/xXdNfLT6ediAu0z1mzXB27E0QAAIXpJREFUgf11ejCsj9v0k06cQhbWDwPHQKuLndlaHlZnNVsTOu4mUfdPvPEZWMKj84a/RdvvvUlDLYPI6x+r1Cf3qWapdQ3k8fknAyIkiUDPFvDoN+8geVkHjHksdV3/W/XXPzmZd9frH9Ry2GmIWKAhRZ8KFSQs4D34chXarddDC3R44w7eR7SWDyybr8+WjVKJnc75HZv0fIdW8Hai/sP68doXFbzF3lclt1+vz3bIL9kZH6v5pQa7K5tELfVNml19DvDyexdG4sX1WFiCUSY8/g06Obhu3kR/WsJZkFcvBAi4e6HY6TT8OvV8laZUPB0eaO+QzgntmfNNrYn1qId1wJp5t2b81Hlct0MC4TN8Taq5Y5bqPBqJOjzx7pj6WC1b52nKnJ+7Au2R5TBBqHXfN4NCmJacC6cmsDIjdS/9TmzvyKSZRgABBLpU4I86vHGxZi3dE+eYZ8VtntaMOx9RY1u0SLkVhDLHzYpE5x9rw8zx86cPaMrMzekH3Xv9+apLvyhkhkCSAk7rLNMYIVSXukyTls1WadS+3pNM1lqssEI7TaC9ckJJ7D5uO5Fc5xbNxvqh6Xf3u+UJ6qHWViao+3cOwqOlvTpvnDJ18Wma95K70UusIlrnnwWaW384fsOjWKszHwEE0hDw6jdvF8HLOmBSadnHj5rm7j1+nP6N3nzPfnIs/ypd+zf2QKWmVB+dPRsqW58hl+szCffWJ1U4yAmL+033MedC6zur5hWN1f3jLgtO+vaoamqV6iKe9rdaetctnK/VB+3+5M1grfdPGhSnOxsn9Riv7rFiErbU7+JzQFLfFdd2JR0r8+J6zJVv1Lce/wbD8ihQ4WD75k+cQXjDVmEiZQEC7inTmQd3ylbqXeuxosYqXeWk02ey6o6aedb8wytVGvVupbn72vyuCZjkq//I+7Rqx9vB5a113tmuFZOLXY8oxXrUwxrZeqWqQpVW0zfmZHNQbXyvPS2T3pHGei2eOdKMRmz/eTYStZNgN776///27gY6irPe4/jPG9fLqZYbiFiut7bEtIjeNseA9M1jW8KLaF+AEGIV6aGUNGK5Wi7vUFuvAuGllJ5KBRoI2ooo79jW0hfSN+mhIk0PrbcUEimIV1oEYrn2ojnR+8xmZjK7mX3J7mze9ptzYGdnZ56Z5zO78zzzn2ee5xWtv/8p4xid9ze1u/pbKnZG87YGhZjyNdOP6FFz0Ao1bn61dtfbx6i+Rmunenx0RE88/WarAqwDc8mmEUAAAVvAXEDs3utbdljn+rnesuPEFt29qKb56R6PX1P9o5oxp+UmZaiwTLOsFqhW+WP/iyw3THn19IJWQY+2lX+UV55DwCQCHS9wapvKw10ZXhJuaew+LdN3uOZu36rFxX06fh/T2YNOWT88pxMnrJaOVp11RkTdv9X526q3ZnAws7adv60GicGUG0211fquVRcP/12o4inLteW1OrfsqX+7Tvu3L1fF0AvtZUxDmKX3a2esVpr2UrwggECwAkH95pv3Ksg64DnVV9/tiX+0jqW01GHN+WPT4/rvYGnakJoJLi95UDXh7oXNfo4Zp+I8p6+Vv+vs6Ya4Xb7E31Cj/nTqPbVuwN9HQyrXu7ENq5eDSvPka3+3+8l89Te9AlTaT8iGCidqzcZ70rrB7h0rJvT5K1XoG/uyvwlplgFtK7uC/N5FH430r8eiU4x+H+xvMDr181Q4oljNJW2DXn7lrTS+i9Fp8z5agIB7tEi7vTcV7ik/1hPrZqukKK9lq7lFGrd0rVaV2XcnzSeNbx3WseiGik2vad2K5+0fh3kUaP4mbV1ariFRo1vn5A/RbbNX6pH5wY5E3bLDHTjVeFInTvbwyXsP9Sv+lha7o3kbwxMn9KfQVZq76+daXD6kpQ/RnHwNmfGgVk7pb2ckmJG6O1CFTSOAQLcW8C87rHP95KXV2jClyL5hawLl26u1JeKJJjOo0aIfqjZc+bfS+an2/mKJKqJaoDaXG2v0xNapujxccU4z6EF51a2/kWSuCwq8d0onw+eByH0PfayXmn53rNWNusilusC7Tls/vFDDl2839fU7I+r+zefvJOr+HUIfVLlhnqbwDDgYGjpNi2eXqCjiSYoc5RaVaNbDVZo70G4JSuu7DjnqbDSbBYL6zduGQdYBm36rrT/eb8c/TBC77KFWsRS3Dlv91ZYGh+1+OM35rmaF7nZuMIYG6baKL6T5tNc/6fzeuZ5GmTEyFY5tLNHK+cPj5j9UOFUbHrlbw6JiRzFSjTHbe14P6YL+F8fJo3dZ0wYy02VAkN8739yncz3mm6BnZsC/QU/KzmTORZeqv9P90Mu/1hvRsUZnQV7TFiDgnjZhiglcOF73zrg6xkmpj6796pfsu04m/T+dVkP0LcyGozr8jn21ZALJXyuJ9yhQDxUMK24ZifpQnY74XGilmJOOXc04zp80wOcxKO+AENYumkE8Js/QbQU9fPb3PF02+LNyPzl9Wmc46fg4MQsBBDpcIG7ZkadBMxZphhuo2K9Ht/y25YmdU3v15It2X5Jx07FyaQIfg6bo3sn2zch0gh6UVx3+tWEHEPAKhPuOtfpXnz9Pcz1PQYbH/Jlu+hi/ebn2+3ZJ5U2lk093wvphaOCtmjm6wKfOalkmUffvCPLAyo2oFp0nj+jtWN+xnAGavO2A3fK9VlVjP94ROWebCGSnQGC/eZsvwDqgtzW1+pZqwbziGLEUU4ctvtvToK49D6UJLO9/QBMrNtrdP5pu2tY8qMm+MYi27FeOevbqFaP8cNIx266tUvlVV6s0YfeTK1VmxhKc/8yRlusEJ5mkX/+qY3VH7RsgH1b/S/41zv61cxkQ4PfOlyPudVSC6zHfBD0zg/4NepJ2J3v2kvvAxTv1OhKrPHZXYCJVAQLuqcqltV7iEZy9d510zjzq74xi7Ww3r0RVTtc1hx9WifuLcRaIeu2Zpz5xHvGJWrqLvE3g6D2RKP4gHqH8S3Spk2u/GxzOZ7wigAACHSaQq+JpE1TkPJHqtx85l2rM+JYnmt45dNRurWoerXx+l14K32xNcO500w3okUPKK1eUCQQ6g0D4sWyrf/Xyck2evVZ73o7siq/xwEqNn1St+i7b+CDBOa5D6oem9d+VA1uesPT5IuTk9lYvn/kdNyvIcsMM6Pe5QW5jIus7ZgV75qyu0tqqHarlYr/jDjNbRsAVCPI3bycaWB3QOzinOcePGatrI56QcTNhT3jrsNGfZeq9HWy/ZaU9Tp/VCrpScwLppi2y33e/HDTVV2ty2SLVnLAq+62727G6jmzpcscsYgbr/ln5rbpza32KQfcGHTn0rr0rPZTX6zy/3bLntXMZENj3zi9L6VyP+aXnnZeB36A3eWc69G+6pL/d3LTxqOqO/dX5hNeABT4YcHokl5RAjnr1Pj/OHUCTiHMxkHJLdDPQQs0WPVv/f6bzxTo9vnxTggFak9rxTrZQEo7uHv+Leud2uzsObu6YQACBbBD4mC79ZG6CjJpWPZ8s0AV6xgy9Z+rSe17RgcYSM56ItxWK6TprVan6r0qQVNTH5w7W6Q8yXXJFzU//bTaUV+krkQICmROwuuKbptUbPqKvjFwU7naq8dUNqnphdBftz70z1g8Ttf7L3NFNPeVgy42cwlGaMHCDKp3B+kywZ/PiA827t3CaebX6df+6rrzkCpVGdXWWeh5YEwEEkhcI9jef3HaTrQP+TQ2m3/Lmv+TOpzmXXaGre6zWZnvc0sj9OaS1N49S5QHfD+1Fe+jy+Tu1o9zpejYyhch3fsH2NfrR7Fg9GkSunfhdVAvx6BWaDmr9zB/Y3Uba3e0sHd7qCYDmLneu1ZjB39ENk6xW+Gag7jlLtPP6VYkbcEZvU/+r0ycdv57q3etDrZbwzuhcZUCy3ztvDpzpdK7HnDRivbbXb/Aj6t3HCrhbx+89nT7zN/Ma74ZJrP1lfiIBAu6JhLrA59Zo0488e0gn9/5Ea3ZbIZZs+cvVgAJ7hOVsyTL5RACBLBZI7sah00oysjTwXqikSGh3R9YvjXuX2VtepWjOagi0o0BOgemmb/IWla46ZLZ6VI/tekPfLx6SuM/YdtzH5DbVGeuHiVr/JZez9l0q4HLD6iqmer00/S5V+l6vHFfNqsWqMZmsnG5ahpbN073zxkX1896+AmwNgewSCPg3H4WXXh3wXdUftLtFNB3Bxm9NbW/YacUbN6getZMpvTXB22eW6K5v/sjTsj1esL2lP/bU2laG9NG8nvJ2VdF0YKcedW5mhq7X9NmxutuxMmh1uTNV04c+qZm7jandbWRJWt13JXGN0kFlQHrfO78vRBJ5tZTtp9Yir8f80vPOy+xvsGVL56lXntuhcstspgIXIOAeOGk7Jth0RM9+5y5N/ekBRhZuR3Y2hQACCCDQRgHKqzaCsTgCHSFgj2ljAu5Wm6fMPdXSEXljm51CIHeQJq97XqW1j2nL049r/arddj/H0Xt3Vq9vmqvSF/do2cZlKklrYL/otHmPAALtKtCt64CnVFs1V1PdPtOtwbF/pIfGxhqvw5Jv6Y/dCrgnV9Y26szpP9uHLfopLtO63jso9bUjdV2i7obNs7DXfXmwQrufMXGkBr38yltqNAH3NNrU2PuW4KU9y4Bu/b1L4MzHnUaAgHunORRt3JGmem2bMlEzn/a7Z2b12XWbbrvqo82J9v6cSgf+RhOHLNLrbdwMiyOAAAIIdBaBP+t0g1U1j18dbmowAz87u/zR3soNN4H5kHJNaxiFQxtteUTWSSiNV8qrNPBYFQEEEOgogUyVG6Z1ZdFoTbb+zbYG+TPB99+8o9N+T+qeeFzzFgzRdetKlNdRDGwXgawRyMBvPrA64MdUMMB0q3jghDka53TqzPvmNUE3i01ndfp0rMFI+mvyL97U5HSObcN+rfU+sRMq1C0/fEDfG54fv+tgs01n/LhwbOa0qbeb3ewXb4wmExRv6S89+imuyO5mcvJ6yarxx/9LJegfL8Xfq+7IX6T8BMcknEQ7lAGBfe/88pzO9Zhfet55GfgNepN3p71PjLgzmciAAAH3DKBmPklTOX1hnZa7wXarz8Np+mbFqNiPXR75TeZ3K6ktJC4gG4/U6XBSabEQAgggkE0C7+rw78yjn0Xx+tiLauXyqUt1UbgC/8+66JKLTaj+kGnJck4H976hU6ZPyswHMLpyeZVN3y3y2v0EGvV21XgNXbgvnLXQ0OXakzBoGTkoW6hPns7vfjDdIEftVZduj3LDCbyYw1JeoVlm6L6G2p16eOUKt5vMxhd36YVTo1LoX7gbHGqygEC7CgT9mw+yDugNRCbZIrvhqA6/YzVUCfrPOk9Va+aUZfYApSb9vje27WmciwbqmgtDev242b/j+7X/WKOK8uM0qGn6o+reMgHt8N8ndEn+h+1p6yWyi5qmU2dMr9xKUMcPorz33gTx7E6bJjNRBgT5vfPLTDrXY37peecF/Rv0ph1rOvr7FGs55qci4O36KZX1WadDBM6qdtdz9iOYZpTuKQ9o9eyS2MF2U3k99eo+HeyQfbU26gzKYE3/RYfq/hhnJOyT+tWuV8KPMltL84cAAggg4Ag06KVf7tUp563fa9Nhbd+w1+5mLFdf+PJVdoXbVGjDg6k2r9T44mZtr3cGOvJLyJpnyo6td2hAv3wVmH8Dbt8Wf9u+yXS18so3E8xEoAsKhPSJzw0yw1A2/zUHLWO19HOy945e+OU++/wR0gX9L07UftBZkdeMC3REXTrIcsMaoPDT4bKkoN8XtbTWap3q92cFX0o0a/X3NM7pXraxQaff+7vfwsxDAIFABYL8zVs7FmQd8DwVjih2y7Rz2zfqsVPxyrRzqt+2WS8FHm83wdz9D2hi2SI32B4qnKpNux5oW9dXOQUafI3T7OWgdj1bHyc+YgWQt2qnFZy3/i4cpEEXeYPzUcftrcM6Fo8mnEgQ5b1zE8RKsEEH698Np+z/X3uWAUF+7/xyk871mF963nlRxzJT12uNf1DdIfs6MJSr3j0JC3uPQpDTyAap2SnTsgbxWKDb51j9c3XUn3dQhkYd375VLzb4lQKmMKlZobs3He2oHWW7CCCAQKcWaNz9XVVUHYxRKT+l/ffN033uoEmD9aXrL3Dzk1M4ShMG2u1VG/fqvmkPab/vubh5lab6alW4ZcfFGj3+Cwlay7ibSnGiM5RXKe46qyHQCQVyCofpBtOCLvzX+LyWL6kxl8Sx/szvb2ulllsDqFl/oUGaUPrvCR+Lb16Y/zMv0DF16eDKjQs16PMX2UyHVP39Dar3uxSwl2g6Vqc65/Me5qav8z3OPDRbQCCrBYL7zbeVMXEdsFWZNner3nbOExGbs4LiD2n6UqcBSsSHab2x6saTb1lpD45quvEdsUS7tk/XoNy4/cH4bPN8FY0cor7hT0yAeOl/aX2shjANNVo8b0tLY8ubhqkwanMRNsc3aGF1rGsFa4NWzGVlS3mvfN0w4tMplPdOa+zmNM+cPhvj+sT6vLOWAYm/d9beR/+lcz0WnVb0+3b5DR6v00Gn3dUFBaYnoKgvVPRO8T5lAQLuKdN5VuyZpz7OTcZzr+ipl056PszE5IeVf+kn7IRNAHvVXfrGkm2qjQicmAE8tlZp6e3DNbTcGTHbXqXpjM6851s62QsE/XK+Cq+8vKXX4RMbNeXW72hzbUs7TWv06PVLKnTDpI06Eeqjvi5o0PtCeggggEBXFjCV8oVlGjurSs8dcWpKpuJcu82c70erbFWtfXPVVORn/adGeQdNyrlUpVNvtCv3UuOBlSobXKI5q3dElh8Ntdq2erbGjlykWvtObWjgeJVf16c1XMLyr6uVV62zyBwEuqxAzmd1x/dK7d98o05smq6Jsx7SNk/9K3zhXbtDa2Z9RSOnP25f0Fvnj3t1W4HTxLjLCnSjHc9AXTrh+dvwBVZumNappaUqcu7/vLpIN4yZrTVbayNvAplB7p6rrtQ3xi+zyx8T0Lp5mLteNzqgZAWBzikQ2G/eyl7AdcDoMu3p2RppziNra460BHqtOqwVUxjrBMUDZG46qPUzf+CpG8/UI6vKEvS9Hmv7piXzdWM1yrmZaBrCVI78iuZUPee5iWDFc5aofOSd2nzCqZBfr29P/mzr4HiEjXWtcLOuvb1Sa6PPsY6PFXMJ75o5x5bN0B1xu6uMnYe8gYM1IPyxiUnteVW/j7WoAiwDEpZdAX/vfPOUxvWYb3qemYH+Bj3peia9XTj3uOYKXUa83aMT7CR9uAfh2bOXwjGN8HnwqDZPukKbrXRDw7Vs76oM9DkYUr+SW1S8dJ9qwts8rppV08P/ksqO82imNxCT1IqpLpSjvNEVmrTiea2xH4VqPLBRc8aYf62StC7y5mn4Y3O19KRdsLRahhkIIIBANgoUqWJ+vnYu3KbXNy3SZPPP/89qcXO37ps0IKpCbir3xffokflHdMNCu9VP4wFtXjwt/M8/LTPX9Eu5aPkEFfhVxhKWf12tvIqpwAcIdEEB6zc/XQ9OOajx4ZtxZ8254z7NtP7FzE2s84ezgvVY+ChVHmi+4dejrFqvLR3S0qjCWYzXgAUyUJdOeP62TvrBlRs5BRO0ZFaNW/40HtikpdOtf3Go+pZqwbxiujaKQ8RHCAQrENxv3gRDAo5ZRJdpVuORTaqcZP61QjBl2eib9Jld21TjtE9ptUxbZphuFnfc3/IUqVm10dw4HFEQqy7uk3bhPO3+Rbn6OR/ZQfKdTvDbqpMvnGT+OQtEv/o0pnEXibYxN9l3P6xK61+cc2yosEIPpnOO9fZF/+Y+vXpqkvrFiDEFVgYkLLuC/t65yPZEutdj0elFvw/yNxidtvX+fb2x7zW7C+dcXXPlp6jD+TEFNI8W7kFAhi7TF2++uHVKjUdVd+yvrecHMSdvlJb9bKoud1rWx0uz71DdWf2oFg91Ro0+rFdezXQr/Kgdyhmk6Y8u0PC+8XbYDP46f73Wln8mKkgUlRZvEUAAgawU+KB6D/uuNixvaaXemuF8Xf61B7QhZoubHiooX69dVROTKj9ChRO1ZuOy2P1SJlP+dbXyqjUqcxDowgJ5GjS7ShvnD3efbomdGasetlFPPJxqi73YKfNJAAJB16WTOX+HdzuocsNKZ2WS30UTqguXP/doCI+6B/DlIQkE2iIQ1G/ebDPwOmAyZZp143iBNiy+McCuEL19nrfFMt6yzUHylUmXz1acJLoxjTf9ZGyc5Y3R0Hna+MhdKXSH46RhXnM+reE35TfPaNynJ59/x/Nh9GRAZUAyZVfg3ztvXoK4HvOm5zcd4G8wOvmmN/XMY0ea54Yiux+NXpT36QvQwj19Q5NCHw1ZulVbrlyrHy5b5w6gITM+9OkzfzOfnxfIViITMSfoQdO1Y1+xtm3epSfXrfds1ywZKtS46TfqU/2H6dbifBPANndlzwxWaLfVl7s90MPYkgALoci983uXk1+m1XsG67kfP66ndlRp84Gz9mImQFRWoVu/eotKiqzBQw75rc48BBBAAAH1UL+xD+iJTw7RwytXaM3u47aJCZRNuVVfGlFin0fjUZk0ht+rHQdvNefjp7Vvz0886VjrWWl9XdcMHmGXH/HSSqb863rlVbwc8xkCXU8gT0XlD2vPOPOovU+dMVRYpmk3Xa0rxt2kIoKbnfrwBluXTub87XAEVW40fxdfHPacHnl2r16Ovn5pU/nj7BuvCCAQvEBQv/lM1AE955Gndmnn8k12n+pGwTQ0rJh5p+4YW6TcxueCY2l8S7/eE3sUlNQ35C2ff6VfP+aNkdj5uf16DR5WqiH5yXTzliC9cIxotK648uYkrheSyZXdVcxaqxvKZGJMnmOXchmQTNmVie+d1yOI6zFven7TQf0GI9NuOvCsngj3OmFuuowZp+IYTyRErsW7VAU+8A/zl+rKBf2a72bVv23fIUk1IdZDAAEEskyA82eWHXCyiwACXVKAc3WXPGzsNAIIIJAxAcqFjNGScJcU+B9tu/0GzbQGXc9Yl8pdEqYT7vT7ql0yRqWrrAau/VWxfbtmpdR/fyfMWgZ3KZ1zPl3KZPDAkDQCCCCAAAIIIIAAAggggAACCCCAAALdT+DjGjX1FvN8kvlL2K1M98t9l8qRpzuZ0NAK3U6wPeOHj4B7xonZAAIIIIAAAggggAACCCCAAAIIIIAAAt1LIKdogr4dHi+wQTUrHlVtU/fKX/fIjTXw7xpVh7uT6a9JU0e2a/fS3cOw7bkg4N52M9ZAAAEEEEAAAQQQQAABBBBAAAEEEEAgywVMK/d531RRyDAcf1I/f+Fklnt0wuw3vaZ1K5434zmavtvLZugOWre3y0Ei4N4uzGwEAQQQQAABBBBAAAEEEEAAAQQQQACB7iWQUzBBS2ZdZcK5R7X5nmpauXeqw+tp3d63VAvmFSu3U+1f990ZAu7d99iSMwQQQAABBBBAAAEEEEAAAQQQQAABBDIo0EMFk+7VjIHnm1buG7Sw+qDoWSaD3G1JuqFGy5ZZrdsv1rhF0zQkN6cta7NsGgIE3NPAY1UEEEAAAQQQQAABBBBAAAEEEEAAAQSyWiBngG5b9h+ma5mzql16v3aeIuTe8d+H91W75j5tPiHTlcx8zSnu0/G7lEV78MEsyitZRQABBBBAAAEEEEAAAQQQQAABBBBAAIGABXIKyrXlcHnAqZJc6gLnqWj2U6qfnXoKrJm6AC3cU7djTQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEXAEC7i4FEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIpC5AwD11O9ZEAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQMAVIODuUjCBAAIIIIAAAggggAACCCCAAAIIIIAAAggggEDqAgTcU7djTQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEXAEC7i4FEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIpC5AwD11O9ZEAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQMAVIODuUjCBAAIIIIAAAggggAACCCCAAAIIIIAAAggggEDqAgTcU7djTQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEXAEC7i4FEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIpC5AwD11O9ZEAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQMAVIODuUjCBAAIIIIAAAggggAACCCCAAAIIIIAAAggggEDqAgTcU7djTQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEXAEC7i4FEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIpC5AwD11O9ZEAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQMAVIODuUjCBAAIIIIAAAggggAACCCCAAAIIIIAAAggggEDqAgTcU7djTQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEXAEC7i4FEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIpC5AwD11O9ZEAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQMAVIODuUjCBAAIIIIAAAggggAACCCCAAAIIIIAAAggggEDqAgTcU7djTQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEXAEC7i4FEwgggAACCCCAAAIIIIAAAggggAACCCCAAAIIpC5AwD11O9ZEAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQMAV+MA/zJ/7rg0TBf3y27A0iyKAAAIIIIAAAggggAACCCCAAAIIIIAAAggg0HUE6t8+0uadpYV7m8lYAQEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACB1gIpt3BvnRRzEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBDIXgFauGfvsSfnCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgEKEHAPEJOkEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBLJXgIB79h57co4AAggggAACCCCAAAIIIIAAAggggAACCCAQoAAB9wAxSQoBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgewUIuGfvsSfnCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgEKEHAPEJOkEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBLJXgIB79h57co4AAggggAACCCCAAAIIIIAAAggggAACCCAQoAAB9wAxSQoBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgewUIuGfvsSfnCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAgEKEHAPEJOkEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBLJXgIB79h57co4AAggggAACCCCAAAIIIIAAAggggAACCCAQoAAB9wAxSQoBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgewX+H4lYoRhGC/F4AAAAAElFTkSuQmCC" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the final thallium nuclide, identify the</p>
<p>(i) nucleon number.</p>
<p>(ii) proton number.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Radon-220 is a radioactive gas. It is released by rocks such as granite. In some parts of the world, houses are built from materials containing granite. Explain why it is unlikely that radon-220 will build up in sufficient quantity to be harmful in these houses.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Calculate, in hour<sup>−1</sup>, the decay constant of lead-212.</p>
<p>(ii) In a pure sample of lead-212 at one instant, 8.0 × 10<sup>−3</sup> kg of the lead-212 is present. Calculate the mass of lead-212 that remains after a period of 35 hours.</p>
<p>(iii) A sample of pure radium begins to decay by the series shown in the table. At one instant, a mass of 8.0 × 10<sup>−3</sup> kg of lead-212 is present in the sample. Suggest why, after 35 hours, there will be a greater mass of lead-212 present in the sample than the value you calculated in (h)(ii).</p>
<div class="marks">[6]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
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<p><span style="font-size: 11.000000pt; font-family: 'ArialMT';">(i) 208;</span></p>
<p><span style="font-size: 11.000000pt; font-family: 'ArialMT';">(ii) 81; </span></p>
</div>
</div>
</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<div class="page" title="Page 13">
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<p><span style="font-size: 11.000000pt; font-family: 'ArialMT';">because the half-life is (only) 55 s;<br>radon is produced slowly but decays quickly (so cannot build up); </span></p>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \(\left( {\lambda = \frac{{{\rm{In2}}}}{{{{\rm{T}}_{\frac{1}{2}}}}} = \frac{{0.693}}{{10.6}} = } \right)6.5 \times {10^{ - 2}}{\rm{ hou}}{{\rm{r}}^{ - 1}}\)</p>
<p>(ii) use of <span style="font-size: 11.000000pt; font-family: 'SymbolMT';">λ </span><span style="font-size: 11.000000pt; font-family: 'ArialMT';">from (h)(i); <br>correct substitution into </span><span style="font-size: 11.000000pt; font-family: 'Arial'; font-style: italic;">N </span><span style="font-size: 12.000000pt; font-family: 'SymbolMT';">= </span><span style="font-size: 11.000000pt; font-family: 'Arial'; font-style: italic;">N</span><span style="font-size: 6.000000pt; font-family: 'ArialMT'; vertical-align: -3.000000pt;">0</span><span style="font-size: 11.000000pt; font-family: 'ArialMT';">e</span><span style="font-size: 7.000000pt; font-family: 'SymbolMT'; vertical-align: 5.000000pt;">−λ</span><span style="font-size: 7.000000pt; font-family: 'Arial'; font-style: italic; vertical-align: 5.000000pt;">t </span><span style="font-size: 11.000000pt; font-family: 'ArialMT';">;<br>8.0 to 8.3 </span><span style="font-size: 12.000000pt; font-family: 'SymbolMT';">× </span><span style="font-size: 11.000000pt; font-family: 'ArialMT';">10</span><span style="font-size: 7.000000pt; font-family: 'ArialMT'; vertical-align: 4.000000pt;">–4 </span><span style="font-size: 11.000000pt; font-family: 'ArialMT';">kg;</span></p>
<p>(iii) <span style="font-size: 11.000000pt; font-family: 'ArialMT';">the rate of decay/activity of polonium/radium;<br> is greater than the rate of decay/activity of lead; </span></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br>