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<h2>HL Paper 3</h2><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe how some white dwarf stars become type Ia supernovae.</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>Hence, explain why a type Ia supernova is used as a standard candle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain how the observation of type Ia supernovae led to the hypothesis that dark energy exists.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>white dwarf must have companion «in binary system»</p>
<p>white dwarf gains material «from companion»</p>
<p>when dwarf reaches and exceeds the Chandrasekhar limit/1.4 M<sub>SUN</sub> supernova can occur</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a standard candle represents a «stellar object» with a known luminosity</p>
<p>this supernova occurs at an certain/known/exact mass so luminosity/energy released is also known</p>
<p><em>OWTTE</em></p>
<p><em>MP1 for indication of known luminosity, MP2 for any relevant supportive argument.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>distant supernovae were dimmer/further away than expected</p>
<p>hence universe is accelerating</p>
<p>dark energy «is a hypothesis to» explain this</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>The graph shows the observed orbital velocities of stars in a galaxy against their distance from the centre of the galaxy. The core of the galaxy has a radius of 4.0 kpc.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the rotation velocity of stars 4.0 kpc from the centre of the galaxy. The average density of the galaxy is 5.0 × 10<sup>–21</sup> kg m<sup>–3</sup>.</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>Explain why the rotation curves are evidence for the existence of dark matter.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>v = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{4\pi G\rho }}{3}} r">
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mi>G</mi>
<mi>ρ</mi>
</mrow>
<mn>3</mn>
</mfrac>
</msqrt>
<mi>r</mi>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \sqrt {\frac{4}{3} \times \pi \times 6.67 \times {{10}^{ - 11}} \times 5.0 \times {{10}^{ - 21}}} \times \left( {4000 \times 3.1 \times {{10}^{16}}} \right)">
<mo>=</mo>
<msqrt>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mo>×</mo>
<mi>π</mi>
<mo>×</mo>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>5.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>21</mn>
</mrow>
</msup>
</mrow>
</msqrt>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>4000</mn>
<mo>×</mo>
<mn>3.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>16</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><em>v</em> is about 146000 «m s<sup>–1</sup>» <em><strong>or</strong></em> 146 «km s<sup>–1</sup>»<br><em>Accept answer in the range of 140000 to 160000 «m s<sup>–1</sup>».</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>rotation curves/velocity of stars were expected to decrease outside core of galaxy</p>
<p>flat curve suggests existence of matter/mass that cannot be seen – now called dark matter</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to star formation, what is meant by the Jeans criterion.</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>In the proton–proton cycle, four hydrogen nuclei fuse to produce one nucleus of helium releasing a total of 4.3 × 10<sup>–12</sup> J of energy. The Sun will spend 10<sup>10</sup> years on the main sequence. It may be assumed that during this time the Sun maintains a constant luminosity of 3.8 × 10<sup>26</sup> W.</p>
<p><br>Show that the total mass of hydrogen that is converted into helium while the Sun is on the main sequence is 2 × 10<sup>29</sup> kg.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Massive stars that have left the main sequence have a layered structure with different chemical elements in different layers. Discuss this structure by reference to the nuclear reactions taking place in such stars.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a star will form out of a cloud of gas</p>
<p>when the gravitational potential energy of the cloud exceeds the total random kinetic energy of the particles of the cloud<br><em><strong>OR</strong></em><br>the mass exceeds a critical mass for a particular <strong>radius and temperature</strong></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>number of reactions is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{10}^{10}} \times 365 \times 24 \times 3600 \times 3.8 \times {{10}^{26}}}}{{4.3 \times {{10}^{ - 12}}}} = 2.79 \times {10^{55}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>365</mn>
<mo>×</mo>
<mn>24</mn>
<mo>×</mo>
<mn>3600</mn>
<mo>×</mo>
<mn>3.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>26</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>2.79</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mn>55</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>H mass used is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.79 \times {10^{55}} \times 4 \times 1.67 \times {10^{ - 27}} = 1.86 \times {10^{29}}">
<mn>2.79</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mn>55</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>4</mn>
<mo>×</mo>
<mn>1.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>1.86</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mn>29</mn>
</mrow>
</msup>
</mrow>
</math></span> «kg»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>nuclear fusion reactions produce ever heavier elements depending on the mass of the star / temperature of the core</p>
<p>the elements / nuclear reactions arrange themselves in layers, heaviest at the core lightest in the envelope</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>In 2017, two neutron stars were observed to merge, forming a black hole. The material released included chemical elements produced by the r process of neutron capture. Describe <strong>two</strong> characteristics of the elements produced by the r process.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span class="fontstyle0">higher atomic number than iron </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">excess of neutrons </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">radioactive/undergoing beta decay </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle3">Allow heavier than iron for MP1</span></em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p>The rapid process proved to be known by many although fewer candidates were able to provide two characteristics.</p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Derive, using the concept of the cosmological origin of redshift, the relation</p>
<p><em>T</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto \frac{1}{R}">
<mo>∝</mo>
<mfrac>
<mn>1</mn>
<mi>R</mi>
</mfrac>
</math></span></p>
<p>between the temperature <em>T</em> of the cosmic microwave background (CMB) radiation and the cosmic scale factor <em>R</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The present temperature of the CMB is 2.8 K. This radiation was emitted when the universe was smaller by a factor of 1100. Estimate the temperature of the CMB at the time of its emission.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State how the anisotropies in the CMB distribution are interpreted.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the cosmological origin of redshift implies that the wavelength is proportional to the scale factor: <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto ">
<mo>∝</mo>
</math></span> <em>R</em></p>
<p>combining this with Wien’s law <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
<mi>λ</mi>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto ">
<mo>∝</mo>
</math></span> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{T}">
<mfrac>
<mn>1</mn>
<mi>T</mi>
</mfrac>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>use of <em>kT</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto \frac{{hc}}{\lambda }">
<mo>∝</mo>
<mfrac>
<mrow>
<mi>h</mi>
<mi>c</mi>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span></p>
<p>«gives the result»</p>
<p> </p>
<p><em>Evidence of correct algebra is needed as relationship T</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{k}{R}">
<mfrac>
<mi>k</mi>
<mi>R</mi>
</mfrac>
</math></span> <em>is given.</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>T</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto ">
<mo>∝</mo>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{R}">
<mfrac>
<mn>1</mn>
<mi>R</mi>
</mfrac>
</math></span></p>
<p>= 2.8 x 1100 x 3080 ≈ 3100 «K»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>CMB anisotropies are related to fluctuations in density which are the cause for the formation of structures/nebulae/stars/galaxies</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Sun is a second generation star. Outline, with reference to the Jeans criterion (M<sub>J</sub>), how the Sun is likely to have been formed.</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>Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.</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 critical density of the universe is</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{3{H^2}}}{{8\pi G}}">
<mfrac>
<mrow>
<mn>3</mn>
<mrow>
<msup>
<mi>H</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>8</mn>
<mi>π</mi>
<mi>G</mi>
</mrow>
</mfrac>
</math></span></p>
<p>where <em>H</em> is the Hubble parameter and <em>G</em> is the gravitational constant.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>interstellar gas/dust «from earlier supernova»</p>
<p>gravitational attraction between particles</p>
<p>if the mass is greater than the Jean’s mass/M<sub>j</sub> the interstellar gas coalesces</p>
<p>as gas collapses temperature increases leading to nuclear fusion</p>
<p><em>MP3 can be expressed in terms of potential and kinetic energy</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>fluctuations in CMB due to differences in temperature/mass/density</p>
<p>during the inflationary period/epoch/early universe</p>
<p>leading to the formation of galaxies/stars/structures</p>
<p>gravitational interaction between galaxies can lead to collision</p>
<p><em><strong>[Max 3 Marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>kinetic energy of galaxy <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mH</em><sup>2</sup><em>r</em><sup>2</sup> «uses Hubble’s law»</p>
<p>potential energy = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{GMm}}{r}">
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> = <em>G</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span><em>r</em><sup>3</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho \frac{m}{r}">
<mi>ρ</mi>
<mfrac>
<mi>m</mi>
<mi>r</mi>
</mfrac>
</math></span> «introduces density»</p>
<p>KE=PE to get expression for critical <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho ">
<mi>ρ</mi>
</math></span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>escape velocity of distant galaxy <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{2GM}}{r}} ">
<msqrt>
<mfrac>
<mrow>
<mn>2</mn>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>r</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>where <em>H</em><sub>0</sub><em>r</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{2GM}}{r}} ">
<msqrt>
<mfrac>
<mrow>
<mn>2</mn>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>r</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>substitutes <em>M</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</math></span><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span><em>r</em><sup>3</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho ">
<mi>ρ</mi>
</math></span> to get result</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>Recent evidence from the Planck observatory suggests that the matter density of the universe is <em>ρ</em><sub>m</sub> = 0.32 <em>ρ</em><sub>c</sub>, where <em>ρ</em><sub>c</sub> ≈ 10<sup>–26</sup> kg<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>m<sup>–3</sup> is the critical density.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph shows the variation with time <em>t</em> of the cosmic scale factor <em>R</em> in the flat model of the universe in which dark energy is ignored.</p>
<p><img src="images/Schermafbeelding_2017-09-26_om_10.24.01.png" alt="M17/4/PHYSI/HP3/ENG/TZ1/17.a"></p>
<p>On the axes above draw a graph to show the variation of <em>R</em> with time, when dark energy is present.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The density of the observable matter in the universe is only 0.05 <em>ρ</em><sub>c</sub>. Suggest how the remaining 0.27 <em>ρ</em><sub>c</sub> is accounted for.</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>The density of dark energy is <em>ρ</em><sub>Λ</sub>c<sup>2</sup> where <em>ρ</em><sub>Λ</sub> = <em>ρ</em><sub>c</sub> – <em>ρ</em><sub>m</sub>. Calculate the amount of dark energy in 1 m<sup>3</sup> of space.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>curve starting earlier, touching at now and going off to infinity</p>
<p><img 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"></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there is dark matter that does not radiate / cannot be observed</p>
<p> </p>
<p><em>Unexplained mention of "dark matter" is not sufficient for the mark.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ρ</em><sub>Λ</sub> = 0.68<em>ρ</em><sub>c</sub> = 0.68 × 10<sup>−26</sup> «kgm<sup>−3</sup>»</p>
<p>energy in 1 m<sup>3</sup> is therefore 0.68 × 10<sup>−26 </sup>× 9 × 10<sup>16</sup> ≈ 6 × 10<sup>−10</sup> «J»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A galaxy can be modelled as a sphere of radius <em>R</em><sub>0</sub>. The distance of a star from the centre of the galaxy is <em>r</em>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_16.21.46.png" alt="M18/4/PHYSI/HP3/ENG/TZ1/19"></p>
<p>For this model the graph is a simplified representation of the variation with <em>r </em>of the mass of <strong>visible matter </strong>enclosed inside <em>r</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of visible matter in the galaxy is <em>M</em>.</p>
<p>Show that for stars where <em>r </em>> <em>R</em><sub>0</sub> the velocity of orbit is <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{GM}}{r}} ">
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>r</mi>
</mfrac>
</msqrt>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw on the axes the observed variation with <em>r </em>of the orbital speed <em>v </em>of stars in a galaxy.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxIAAAE6CAYAAACCpGS5AAAcAElEQVR4Ae3df4jf9X0H8Nc3C2LKLS3qqBcthCwY/6glzmAHjcxadyaMdRJwm1syx6op7AdswiJ1+tecrEEqFNu6hGQuCmWyiWNrG5M26Kj7YVN7WwIzN5FsxJxVCS47lq7gfcfdEntnTOwn973k9br3IyDm7vv9fr7Pz+P5qdyz9/3e9fr9fj/8IUCAAAECBAgQIECAQAeBRR3u664ECBAgQIAAAQIECBCYFlg806HX68380N8JECBAgAABAgQIECAwS+DUC5pmDYmpe5y6Yda9fUCAAAECBAgQIECAQPMCM7/x4KVNzV8OAAgQIECAAAECBAh0FzAkupt5BAECBAgQIECAAIHmBQyJ5i8BAAQIECBAgAABAgS6CxgS3c08ggABAgQIECBAgEDzAoZE85cAAAIECBAgQIAAAQLdBQyJ7mYeQYAAAQIECBAgQKB5AUOi+UsAAAECBAgQIECAAIHuAoZEdzOPIECAAAECBAgQINC8gCHR/CUAgAABAgQIECBAgEB3AUOiu5lHECBAgAABAgQIEGhewJBo/hIAQIAAAQIECBAgQKC7gCHR3cwjCBAgQIAAAQIECDQvYEg0fwkAIECAAAECBAgQINBdwJDobuYRBAgQIECAAAECBJoXMCSavwQAECBAgAABAgQIEOguYEh0N/MIAgQIECBAgAABAs0LGBLNXwIACBAgQIAAAQIECHQXMCS6m3kEAQIECBAgQIAAgeYFDInmLwEABAgQIECAAAECBLoLGBLdzTyCAAECBAgQIECAQPMChkTzlwAAAgQIECBAgAABAt0FDInuZh5BgAABAgQIECBAoHkBQ6L5SwAAAQIECBAgQIAAge4ChkR3M48gQIAAAQIECBAg0LyAIdH8JQCAAAECBAgQIECAQHcBQ6K7mUcQIECAAAECBAgQaF7AkGj+EgBAgAABAgQIECBAoLuAIdHdzCMIECBAgAABAgQINC9gSDR/CQAgQIAAAQIECBAg0F3AkOhu5hEECBAgQIAAAQIEmhcwJJq/BAAQIECAAAECBAgQ6C5gSHQ384gOApNjO+OW3i/HzrEfzH7UxAvx0CfXxGee+o+YnH2LjwgQIECAAAECBAoILC6QUcTCAosuXx6rh1+JQ0cmIq66+OSZ/CDGnnwo/jB+PfaPfCSs2cIFi06AAAECBAg0K+BruGarP08nPrQsVl3zVowefvOd7zxMvvr1+Px9r8SW+zfFdUMuwfPUhKchQIAAAQIECAxUwHckBsrpYKcJLLoslq/+UBw4dDQm4upYGm/F9766M76x/t74zo2XnXZ3nyBAgAABAgQIEKgh4P8OrtFT4ZRDceWqFTE+ejhem4yYfHVffPkLEXf/9k1xhauvcK+iEyBAgAABAq0L+I5E61fAvJ//RXH58pUxfODlODLxehz54oPxjU1b4+HrPjTvz+wJCBAgQIAAAQIE5k/AkJg/W0eeFlgUQ1eujGvi5Xj7pb+Jhx7/2XjkO2tjKR0CBAgQIECAAIHSAoZE6fpqhJ/+yU3x5Xjwnv+NuHtHjFxxUY3gUhIgQIAAAQIECJxRwKvUz0jjhoEJTP/kpqPx7KFfjPs3r4mhdx14165dceTIkXd91ocECBAgQIAAAQKZBXr9fr9/KmCv14sZH576tH8TmDeB0dHRuPbaa+POO++M7du3z9vzODABAgQIECBAgMDcBWbuBd+RmLunI5yjwIkTJ2Lz5s3Tj37jjTdiz54953gkDyNAgAABAgQIEDjfAobE+Rb3fO8I7NixI2699dbpj7du3Rr33XdfHDt27J3b/YUAAQIECBAgQCCvgJc25e1mQScbGxuLjRs3xu7du+PSSy+dfknd1HslDh48GFOjwh8CBAgQIECAAIF8Al7alK+TphJNvaRpy5Yt8cADD8Qll1zyzrnfdttt8eyzz8bU+yb8IUCAAAECBAgQyC3gpU25+1mQ6aaGxM033xwjIyOzzm/JkiWxbdu2eP3112d93gcECBAgQIAAAQL5BLy0KV8nzSWa+S2y5k7eCRMgQIAAAQIECgnM/LrNdyQKFScqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAAQIEsggYElmakIMAAQIECBAgQIBAIQFDolBZohIgQIAAAQIECBDIImBIZGlCDgIECBAgQIAAAQKFBAyJQmWJSoAAAQIECBAgQCCLgCGRpQk5CBAgQIAAAQIECBQSMCQKlSUqAQIECBAgQIAAgSwChkSWJuQgQIAAAQIECBAgUEjAkChUlqgECBAgQIAAgS4Czz//fJe7uy+BTgKGRCcudyZAgAABAgQI1BF47LHH4q677oqxsbE6oSUtI2BIlKlKUAIECBAgQIBAN4Ht27fH+vXrY+PGjbFr1644ceJEtwO4N4GzCBgSZ8FxEwECBAgQIECgusCGDRti9+7dcfDgwbj99ttjdHS0+inJn0Sg1+/3+6ey9Hq9mPHhqU/7N4F5FZi67vwhQIAAAQIEzp/AoUOH4qqrrjp/T+iZFozAzL2weMGclRMpK2C8XvjqZv5H4cKnkYAAAQIEBi1w7NixePTRR+Ppp5+Obdu2GRGDBm70eF7a1GjxTpsAAQIECBBoQ2DPnj2xbt26WLp0aTz33HOxevXqNk7cWc67gO9IzDuxJyBAgAABAgQIXBiBLVu2TP/EpieeeMJ3IS5MBQv6Wb1HYkHX6+QI/HgCXtr04zm5FwECBKoJTH034oYbboglS5ZUiy5vUoGZXzN4aVPSksQiQIAAAQIECMxVYGRk5Cwj4s3Yd88n4pad/xQv7X047ljWi2WfeSpenZzrs3p8KwJe2tRK086TAAECBAgQIDBTYPLNODz6/Zh44Sux6/c+F186+gcxNPN2fyfwPgK+I/E+QG4mQIAAAQIECCxIgYmjcejA/8RFv/A7ce+Gq42IBVny/J6UITG/vo5OgAABAgQIEEgoMBnH938zHh9fG5s+/TEjImFDFSIZEhVakpEAAQIECBAgMFCBH8Zrh1+O8ZF1sXblxQM9soO1I2BItNO1MyVwRgG/FPCMNG4gQIDAAhWYiCOHXonh1cvjcl8NLtCO5/+0XDrzb+wZCBAgQIAAAQK5BKbfaP1WXLNqmZc15WqmVBpDolRdwhIgQIAAAQIEBiAw/Ubrn4lfWbs8fDE4AM9GD+HaabR4p02AAAECBAi0KnDyjdaxMpZfflGrCM57AAKGxAAQHYJAHYGpXz60JqZ+K+V7/bPsjodj79jxOqcjKQECBAicg8CiWHrTg3H06INx01JfCp4DoIecFHD1uBQItCRw/F/jmcePxsiOf4u3+/2YepP1j/75r9j3cwfjjhv/NPYd92tNW7osnCsBAgQIEDgXAUPiXNQ8hkBRgcnXDsfo+LJYvfyy93hN7NK4au0n4prxPfHM/mNFz1BsAgQIECBA4HwJGBLnS9rzELjgApMxceTlOBArYtWVQxc8jQAECBAgQIBAbQFDonZ/0hPoIHDylw8Nn+nNdT+M8YMvxoHhkbhlzSUdjuuuBAgQIECAQIsChkSLrTvnNgUmD8e3//LbMbzp5lhz2pvrjsfY3i/Fvb/7XPz8A78W1592e5tkzpoAAQIECBA4s4AhcWYbtxBYWALTPzN8PMa3fio+eNpPbbo6PvvNodjwt3viz3/ro3450cJq3tkQIECAAIF5ETAk5oXVQQnkE/j/N1pfF1u+9caPflLT20fiW58bieHf+KP4/O/fEb903fB7vAk737lIRIAAAQIECFx4AUPiwncgAYHzIHCGN1ovuiJuuveP4+7//JO49b6/i1f91Nfz0IWnIECAAAECC0PAkFgYPToLAu8jcCz2P7MnxkfWxdqVF8++79Ca2Hz/b0bs3Blf/d5bs2/zEQECBAgQIEDgDAKGxBlgfJrAghKYfDMOjx6N4dXL4/LT/le/KJZef2vcfeOL8YUnX4yp32s9Ob437v3kspO//fqWuOepl2JiQYE4GQIECBAgQGCuAqd9STHXA3o8AQIJBabfaB1xzapl7/1G6qGPxac3rY3xrY/GX41NxPf/8a/jsRWPxJG3347/3r8uXvizf4ijXvaUsFiRCBAgQIDAhRPo9fv9/qmn7/V602/CPPWxfxMg0KLARHz3oV+NL674SvzFho9EHN8X91z9ZHz8u4/EhuHFLYI4ZwIECBAgQOCkwMy94DsSLgsCBM4u8IEPxk994Ox3cSsBAgQIECDQnoAh0V7nzpgAAQIECBAgQIDAnAUMiTkTOgCBhSZwcSxbcWXs/ed/j+MxGRP/8vfxtZ++Pj76YS9rWmhNOx8CBAgQIDAXAUNiLnoeS2BBCiyOD398JNY/PvUbsH8ifnLNzljx2U/FSv+1WJBtOykCBAgQIHCuAt5sfa5yHkeAAAECBAgQIECgMQFvtm6scKdLgAABAgQIECBAYNACXqwwaFHHI0CAAAECBAgQINCAgCHRQMlOkQABAgQIECBAgMCgBQyJQYs6HgECBAgQIECAAIEGBAyJBkp2igQIECBAgAABAgQGLWBIDFrU8QgQIECAAAECBAg0IGBINFCyUyRAgAABAgQIECAwaAFDYtCijkeAAAECBAgQIECgAQFDooGSnSIBAgQIECBAgACBQQsYEoMWdTwCBAgQIECAAAECDQgYEg2U7BQJECBAgAABAgQIDFrAkBi0qOMRIECAAAECBAgQaEDAkGigZKdIgAABAgQIECBAYNAChsSgRR2PAAECBAgQIECAQAMChkQDJTtFAgQIECBAgAABAoMWMCQGLep4BAgQIECAAAECBBoQMCQaKNkpEiBAgAABAgQIEBi0gCExaFHHI0CAAAECBAgQINCAgCHRQMlOkQABAgQIECBAgMCgBQyJQYs6HgECBAgQIECAAIEGBAyJBkp2igQIECBAgAABAgQGLWBIDFrU8QgQIECAAAECBAg0IGBINFCyUyRAgAABAgQIECAwaIHF7z5gr9d796d8TIAAAQIECBAgQIAAgVkCs4ZEv9+fdaMPCBAgQIAAAQIECBAg8F4C/wcK6hhsbX/f/QAAAABJRU5ErkJggg=="></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when <em>r </em>> <em>R</em><sub>0</sub>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r} = \frac{{GMm}}{{{r^2}}}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> and correct rearranging</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>linear / rising until R<sub>0</sub> </p>
<p>then <strong>«</strong>almost<strong>» </strong>constant</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for <em>v </em>to stay constant for <em>r </em>greater than <em>R</em><sub>0</sub>, <em>M </em>has to be proportional to <em>r</em></p>
<p> </p>
<p>but this contradicts the information from the <em>M-r </em>graph</p>
<p><strong><em>OR</em></strong></p>
<p>if <em>M </em>is constant for <em>r </em>greater than <em>R</em><sub>0</sub>, then we would expect <em>v</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \propto {r^{\frac{{ - 1}}{2}}}">
<mo>∝</mo>
<mrow>
<msup>
<mi>r</mi>
<mrow>
<mfrac>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span></p>
<p> </p>
<p>but this contradicts the information from the <em>v-r </em>graph</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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="question" style="padding-left: 20px; padding-right: 20px;">
<p>The light from a distant galaxy shows that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>11</mn></math>.</p>
<p>Calculate the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>size</mi><mo> </mo><mi>of</mi><mo> </mo><mi>the</mi><mo> </mo><mi>universe</mi><mo> </mo><mi>when</mi><mo> </mo><mi>the</mi><mo> </mo><mi>light</mi><mo> </mo><mi>was</mi><mo> </mo><mi>emitted</mi></mrow><mrow><mi>size</mi><mo> </mo><mi>of</mi><mo> </mo><mi>the</mi><mo> </mo><mi>universe</mi><mo> </mo><mi>at</mi><mo> </mo><mi>present</mi></mrow></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how Hubble’s law is related to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hubble originally linked galactic redshift to a Doppler effect arising from galactic recession. Hubble’s law is now regarded as being due to cosmological redshift, not the Doppler effect. Explain the observed galactic redshift in cosmological terms.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>R</mi><mn>0</mn></msub><mi>R</mi></mfrac><mo>=</mo></math></span><span class="fontstyle2">»</span></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>11</mn></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>90</mn></math> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math></strong></em> ✓</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«Hubble’s » measure of v/recessional speed uses redshift which is </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math><br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle0">redshift (</span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></span><span class="fontstyle0">) of galaxies is proportional to distance «from earth»<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle0">combines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>H</mi><mi>d</mi></math> </span><span class="fontstyle3"><em><strong>AND</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mfrac><mi>v</mi><mi>c</mi></mfrac></math> </span><span class="fontstyle0">into one expression, e.g. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mfrac><mrow><mi>H</mi><mi>d</mi></mrow><mi>c</mi></mfrac></math> </span><span class="fontstyle4">✓<br><br></span></p>
<p><em><span class="fontstyle2">OWTTE</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">reference to «redshift due to» expansion of the universe, «not recessional speed» </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">expansion of universe stretches spacetime / increases distance between objects </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">«so» wavelength stretches / increases leading to observed redshift </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates got the ratio upside down and ended up with <em>R</em>/<em>R</em><sub>0</sub> as 1.11.</p>
<p><br>This was not accepted as it would have required an identification of the variables. Perhaps candidates need to look more carefully at which <em>R</em> is which here. <em>R</em> is the current value of the scale factor in the data book, so <em>R</em><sub>0</sub>/<em>R</em> = 0.9 was required.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>To show the link between <em>z</em> and Hubble's law many rearranged formulae to obtain <em>zc = Hd</em> or similar. Others stated that Hubble used redshift <em>z</em> to determine that <em>v</em> was proportional to distance. Either approach was allowed.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The galactic redshift was successfully explained by many in terms of the stretching of spacetime.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The data for the star Eta Aquilae A are given in the table.</p>
<p style="text-align: center;"><img 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"></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mo>⊙</mo></msub></math> is the luminosity of the Sun and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mo>⊙</mo></msub></math> is the mass of the Sun.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show by calculation that Eta Aquilae A is not on the main sequence.</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>Estimate, in <math xmlns="http://www.w3.org/1998/Math/MathML" class="wrs_chemistry"><mi>pc</mi></math>, the distance to Eta Aquilae A using the parallax angle in the table.</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>Estimate, in <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>pc</mtext></math>, the distance to Eta Aquilae A using the luminosity in the table, given that <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mo>⊙</mo></msub><mo>=</mo><mn>3</mn><mo>.</mo><mn>83</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mo> </mo><mi mathvariant="normal">W</mi></math>.</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>Suggest why your answers to (b)(i) and (b)(ii) are different.</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>Eta Aquilae A is a Cepheid variable. Explain why the brightness of Eta Aquilae A varies.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Eta Aquilae A was on the main sequence before it became a variable star. Compare, without calculation, the time Eta Aquilae A spent on the main sequence to the total time the Sun is likely to spend on the main sequence.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mi>L</mi><msub><mi>L</mi><mo>⊙</mo></msub></mfrac><mo>=</mo><mfrac><msup><mi>M</mi><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow></msup><msup><msub><mi>M</mi><mo>⊙</mo></msub><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow></msup></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><msup><mn>70</mn><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow></msup><mo>=</mo><mo>»</mo><mo> </mo><mn>442</mn></math></span><span class="fontstyle0"> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0">the luminosity of Eta (2630<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mo>⊙</mo></msub></math>) is very different </span><span class="fontstyle2">«</span><span class="fontstyle0">so it is not main sequence</span><span class="fontstyle2">» </span><span class="fontstyle3">✓</span></p>
<p><em><span class="fontstyle0">Allow calculation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi><mfrac><mn>1</mn><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfrac></msup></math> to give <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>5</mn></math> </span></em><em><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mo>⊙</mo></msub></math> </span><span class="fontstyle0">so not main sequence</span></em></p>
<p><em><span class="fontstyle0">OWTTE</span></em><span class="fontstyle4"><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>«</mo><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mo>.</mo><mn>36</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>424</mn><mo> </mo><mo>«</mo><mi>pc</mi><mo>»</mo></math> ✓</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msqrt><mfrac><mi>L</mi><mrow><mn>4</mn><mi mathvariant="normal">π</mi><mi>b</mi></mrow></mfrac></msqrt></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><mfrac><mrow><mn>2630</mn><mo>×</mo><mn>3</mn><mo>.</mo><mn>83</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup></mrow><mrow><mn>4</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>7</mn><mo>.</mo><mn>20</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></mrow></mfrac></msqrt></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>055</mn><mo>×</mo><msup><mn>10</mn><mn>19</mn></msup></mrow><mrow><mn>3</mn><mo>.</mo><mn>26</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>46</mn><mo>×</mo><msup><mn>10</mn><mn>15</mn></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>342</mn><mo> </mo><mo>«</mo><mi>pc</mi><mo>»</mo></math> ✓</p>
<p> </p>
<p><em><span class="fontstyle0">Award </span><strong><span class="fontstyle2">[3] </span></strong><span class="fontstyle0">marks for a bald correct answer between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">340</mn></math> and </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">344</mn><mo mathvariant="italic"> </mo><mo>«</mo><mi>pc</mi><mo>»</mo></math></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">parallax angle in milliarc seconds/very small/at the limits of measurement </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">uncertainties/error in measuring </span><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> </span><span class="fontstyle0">οr </span><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math> </span><span class="fontstyle0">or </span><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">values same order of magnitude, so not significantly different </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle3">Accept answers where MP1 and MP2 both refer to parallax angle</span></em></p>
<p><em><span class="fontstyle3">OWTTE</span></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">reference to change in size </span><span class="fontstyle2">✓<br></span><span class="fontstyle0">reference to change in temperature </span><span class="fontstyle2">✓<br></span><span class="fontstyle0">reference to periodicity of the process </span><span class="fontstyle2">✓<br></span><span class="fontstyle0">reference to transparency / opaqueness </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">shorter time </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">star more massive and mass related to luminosity<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle0">star more massive and mass related to time in main sequence<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle0">position on HR diagram to the left and above shows that will reach red giant region sooner </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates were successful in using the mass luminosity relationship.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The conversion to parsecs proved to be a very well known skill.</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very well answered by most candidates.</p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates related the difference in the two methods for finding d to the large uncertainty in finding parallax angle at this distance (>400pc). Fewer also spotted that the luminosity of the star is also error prone unless its distance is already known.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates were clearly familiar with Cepheids and the process leading to its variability in brightness.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates showed clear ideas and were able to explain successfully why Eta Aquilae A lifetime as a main sequence star is much shorter than the one expected for the Sun.</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The cosmic microwave background (CMB) radiation is observed to have anisotropies.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the nature of the anisotropies observed in the CMB radiation.</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>Identify <strong>two</strong> possible causes of the anisotropies in (a).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the temperature/</span><span class="fontstyle2">«</span><span class="fontstyle0">peak</span><span class="fontstyle2">» </span><span class="fontstyle0">wavelength/intensity «of the CMBR» varies </span><span class="fontstyle2">«</span><span class="fontstyle0">slightly</span><span class="fontstyle2">» </span><span class="fontstyle0">/ is not constant in different directions </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">quantum fluctuations </span><span class="fontstyle2">«</span><span class="fontstyle0">that have expanded</span><span class="fontstyle2">» </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0">density perturbations </span><span class="fontstyle2">«</span><span class="fontstyle0">that resulted in galaxies and clusters of galaxies</span><span class="fontstyle2">» </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0">dipole distortion </span><span class="fontstyle2">«</span><span class="fontstyle0">due to the motion of the Earth</span><span class="fontstyle2">» </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was not the best answered question in the Option. Candidates oscillated between correct identification of characteristics of the CMB radiation and more generic explanations about the Big Bang.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Those who correctly identified specific characteristics of the CMB radiation were able to quote causes for this during the early Big Bang.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain the evidence that indicates the location of dark matter in galaxies.</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>Outline why a hypothesis of dark energy has been developed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>rotational<strong>» </strong>velocity of stars are expected to decrease as distance from centre of galaxy increases</p>
<p>the observed velocity of outer stars is constant/greater than predicted</p>
<p>implying large mass on the edge <strong>«</strong>which is dark matter<strong>»</strong></p>
<p> </p>
<p><em>OWTTE</em></p>
<p><em>1st and 2nd marking points can </em><em>be awarded from an annotated </em><em>sketch with similar shape as the </em><em>one below</em></p>
<p><em><img src="images/Schermafbeelding_2018-08-14_om_10.48.40.png" alt="M18/4/PHYSI/HP3/ENG/TZ2/19.a/M"></em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>data from type 1a supernovae shows universe expanding at an accelerated rate</p>
<p> </p>
<p>gravity was expected to slow down the expansion of the universe</p>
<p><strong><em>OR</em></strong></p>
<p>this did not fit the hypotheses at that time</p>
<p> </p>
<p>dark energy counteracts/opposes gravity</p>
<p><strong><em>OR</em></strong></p>
<p>dark energy causes the acceleration</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A distinctive feature of the constellation Orion is the Trapezium, an open cluster of stars within Orion.</p>
</div>
<div class="specification">
<p>Mintaka is one of the stars in Orion.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Distinguish between a constellation and an open cluster.</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 parallax angle of Mintaka measured from Earth is 3.64 × 10<sup>–3</sup> arc-second. Calculate, in parsec, the approximate distance of Mintaka from Earth.</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>State why there is a maximum distance that astronomers can measure using stellar parallax.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Great Nebula is located in Orion. Describe, using the Jeans criterion, the necessary condition for a nebula to form a star.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>In cluster, stars are gravitationally bound <em><strong>OR</strong> </em>constellation not ✔</p>
<p>In cluster, stars are the same/similar age <em><strong>OR</strong> </em>in constellation not ✔</p>
<p>Stars in cluster are close in space/the same distance <em><strong>OR </strong></em>in constellation not ✔</p>
<p>Cluster stars appear closer in night sky than constellation ✔</p>
<p>Clusters originate from same gas cloud <em><strong>OR</strong> </em>constellation does not ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>d</em> = 275 «pc» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>because of the difficulty of measuring very small angles ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mass of gas cloud > Jeans mass ✔</p>
<p>«magnitude of» gravitational potential energy > <em>E</em><sub>k</sub> of particles ✔</p>
<p>cloud collapses/coalesces «to form a protostar» ✔</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The surface temperature of the star Epsilon Indi is 4600 K.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the peak wavelength of the radiation emitted by Epsilon Indi.</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>Using the axis, draw the variation with wavelength of the intensity of the radiation emitted by Epsilon Indi.</p>
<p><img 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giwsGjHeaJKBBBAAAEEEEAAAQQaLcAzFo0+PRSHgE+g7l5HX2+iEEAAAQQQQAABv0Dd5w6+sfAbEokAAggggAACCCCAAAI1AiwsamA4jAACCCCAAAIIIIAAAn4BFhZ+KyIRaLSAfkgybXfbTxOxYvL2qD7pYc2m1pbPOe3nD5fq2j0mZUx6L19V41TlLePTu6dPVa06b56jzDvdcXTOMoc+lo+T76c+1nVQ1Sc/Zu3PtLaqvNo2b48cJ+UuXzMdR9fatNr0/FJtea3l3HlHAIGWClT93Ebdj15UxXIMAQSOvYDnb9b6oSqrPc0yIsbzg1gR40TkSHO26o0ax8pjtXtq9ZxDzzgRMZarp1ZPTEStHtuocaw8Vrun1l66WfV6roNULy8EEGiWQN3nDh7ebumCkLIR0AJ1D1HpGLYRQAABBBBAAIEIgbrPHdwKFaFLDgQQQAABBBBAAAEE+lyAhUWfXwBMv38E8nub85lb7Sk+IsZzT3XEOBE50pyteqPGsfJY7Z5aPefQM05EjOXqqdUTE1GrxzZqHCuP1e6ptZduVr2e6yDVywsBBNohwMKiHeeJKhFAAAEEEEAAAQQQaLQAz1g0+vRQHAI+gbp7HX29iUIAAQQQQAABBPwCdZ87+MbCb0gkAggggAACCCCAAAII1AiwsKiB4TACs03AutfZak8eETGee6ojxonIkeZs1Rs1jpXHavfU6jmHnnEiYixXT62emIhaPbZR41h5rHZPrb10s+r1XAepXl4IINAOARYW7ThPVImAKaD/Bzxt5/t5gjwmted99H7ZXx/Lc+g2HZ8f1/t5Dt1Pb+d9yrbyvSpP3kfv6356W8fobR1TbpfvOi5t6/0yRr/nMVXx1rE8h85fbucxVk7dT29X9Svb07s1Tt5e9tV58xjdpuP1cb1dVYfup7d1P73tjUl96vp5c6S4PE+eM2/XufW27qe3vTHHepyyTt4RQKD9Ajxj0f5zyAwQkLp7HaFBAAEEEEAAAQSiBeo+d/CNRbQ0+RBAAAEEEEAAAQQQ6EMBFhZ9eNKZMgIIIIAAAggggAAC0QIsLKJFyYdAQwWq7r3WpVrtKTYixvOwZsQ4ETnSnK16o8ax8ljtnlo959AzTkSM5eqp1RMTUavHNmocK4/V7qm1l25WvZ7rINXLCwEE2iHAwqId54kqEUAAAQQQQAABBBBotAAPbzf69FAcAj6BuoeofL2JQgABBBBAAAEE/AJ1nzv4xsJvSCQCCCCAAAIIIIAAAgjUCLCwqIHhMAJtE9D3KqftbvtpblZM3k6fsStCu3pMypix3odz6Dx11rOlT938uhnQZ+rfaHktzTY3fZ2zjQACLRcoKl6dTqfiKIcQQKCpAp6/2U2bNnUt32pPnSNiBgcHu9YRNU5ErakWq96ocaw8VrunVo+tZ5yIGMvVU6snJqJWj23UOFYeq91Tay/drHo910GqlxcCCDRLoO5zB89YtHxhSPkIJIG6ex3RQQABBBBAAAEEogXqPndwK1S0NPkQQAABBBBAAAEEEOhDARYWfXjSmXJ/Clj/nrzVntQiYvT94XVnImKciBypPqveqHGsPFa7p1bPOfSMExFjuXpq9cRE1OqxjRrHymO1e2rtpZtVr+c6SPXyQgCBdgiwsGjHeaJKBBBAAAEEEEAAAQQaLcAzFo0+PRSHgE+g7l5HX2+iEEAAAQQQQAABv0Dd5w6+sfAbEokAAggggAACCCCAAAI1AiwsamA4jAACCCCAAAIIIIAAAn4BFhZ+KyIRaLSAfkgybXfbTxOxYvL2qD7pYc2m1pbPOe3nD5fq2j0mZUx6L19V41TlLePTu6dPVa06b56jzDvdcXTOMoc+lo+T76c+1nVQ1Sc/Zu3PtLaqvNo2b48cJ+UuXzMdR9fatNr0/FJtea3l3HlHAIGWClT93Ebdj15UxXIMAQSOvYDnb9b6oSqrPc0yIsbzg1gR40TkSHO26o0ax8pjtXtq9ZxDzzgRMZarp1ZPTEStHtuocaw8Vrun1l66WfV6roNULy8EEGiWQN3nDh7ebumCkLIR0AJ1D1HpGLYRQAABBBBAAIEIgbrPHdwKFaFLDgQQQAABBBBAAAEE+lyAhUWfXwBMv38E8nub85lb7Sk+IsZzT3XEOBE50pyteqPGsfJY7Z5aPefQM05EjOXqqdUTE1GrxzZqHCuP1e6ptZduVr2e6yDVywsBBNohwMKiHeeJKhFAAAEEEEAAAQQQaLQAz1g0+vRQHAI+gbp7HX29iUIAAQQQQAABBPwCdZ87+MbCb0gkAggggAACCCCAAAII1AiwsKiB4TACs03AutfZak8eETGee6ojxonIkeZs1Rs1jpXHavfU6jmHnnEiYixXT62emIhaPbZR41h5rHZPrb10s+r1XAepXl4IINAOARYW7ThPVImAKaD/Bzxt5/t5gjwmted99H7ZXx/Lc+g2HZ8f1/t5Dt1Pb+d9yrbyvSpP3kfv6356W8fobR1TbpfvOi5t6/0yRr/nMVXx1rE8h85fbucxVk7dT29X9Svb07s1Tt5e9tV58xjdpuP1cb1dVYfup7d1P73tjUl96vp5c6S4PE+eM2/XufW27qe3vTHHepyyTt4RQKD9Ajxj0f5zyAwQkLp7HaFBAAEEEEAAAQSiBeo+d/CNRbQ0+RBAAAEEEEAAAQQQ6EMBFhZ9eNKZMgIIIIAAAggggAAC0QIsLKJFyYdAQwWq7r3WpVrtKTYixvOwZsQ4ETnSnK16o8ax8ljtnlo959AzTkSM5eqp1RMTUavHNmocK4/V7qm1l25WvZ7rINXLCwEE2iHAwqId54kqEUAAAQQQQAABBBBotAAPbzf69FAcAj6BuoeofL2JQgABBBBAAAEE/AJ1nzv4xsJvSCQCCCCAAAIIIIAAAgjUCLCwqIHhMAJtE9D3MqftbvtpblZM3h7VJ91T3dTa8jmn/fwecF27x6SMSe/lq2qcqrxlfHr39KmqVefNc5R5pzuOzlnm0MfycfL91Me6Dqr65Mes/ZnWVpVX2+btkeOk3OVrpuPoWptWm55fqi2vtZw77wgg0FKBouLV6XQqjnIIAQSaKuD5m920aVPX8q321DkiZnBwsGsdUeNE1JpqseqNGsfKY7V7avXYesaJiLFcPbV6YiJq9dhGjWPlsdo9tfbSzarXcx2kenkhgECzBOo+d/CMRUsXhJSNgBaou9dRx7CNAAIIIIAAAghECNR97uBWqAhdciCAAAIIIIAAAggg0OcCLCz6/AJg+v0jkN/bnM/cak/xETGee6ojxonIkeZs1Rs1jpXHavfU6jmHnnEiYixXT62emIhaPbZR41h5rHZPrb10s+r1XAepXl4IINAOARYW7ThPVIkAAggggAACCCCAQKMFeMai0aeH4hDwCdTd6+jrTRQCCCCAAAIIIOAXqPvcwTcWfkMiEUAAAQQQQAABBBBAoEaAhUUNDIcRQAABBBBAAAEEEEDAL8DCwm9FJAKNFtAPSabtbvtpIlZM3h7VJz2s2dTa8jmn/fzhUl27x6SMSe/lq2qcqrxlfHr39KmqVefNc5R5pzuOzlnm0MfycfL91Me6Dqr65Mes/ZnWVpVX2+btkeOk3OVrpuPoWptWm55fqi2vtZw77wgg0FKBqp/bqPvRi6pYjiGAwLEX8PzNWj9UZbWnWUbEeH4QK2KciBxpzla9UeNYeax2T62ec+gZJyLGcvXU6omJqNVjGzWOlcdq99TaSzerXs91kOrlhQACzRKo+9zBw9stXRBSNgJaoO4hKh3DNgIIIIAAAgggECFQ97mDW6EidMmBAAIIIIAAAggggECfC7Cw6PMLgOn3j0B+b3M+c6s9xUfEeO6pjhgnIkeas1Vv1DhWHqvdU6vnHHrGiYixXD21emIiavXYRo1j5bHaPbX20s2q13MdpHp5IYBAOwRYWLTjPFElAggggAACCCCAAAKNFuAZi0afHopDwCdQd6+jrzdRCCCAAAIIIICAX6DucwffWPgNiUQAAQQQQAABBBBAAIEaARYWNTAcRmC2CVj3OlvtySMixnNPdcQ4ETnSnK16o8ax8ljtnlo959AzTkSM5eqp1RMTUavHNmocK4/V7qm1l25WvZ7rINXLCwEE2iHAwqId54kqETAF9P9Ap+18f+/evZNy5DGpPe+j91NnKybFW+OkPDpv2tb7UeNYtXrHSXH6Nd1aU1/LJOWsitHjeuaj49N2bhs1TlWt2iUfJ6+jrDPvk+9HjGO55bXWuZU1V7WnY1Hj6DlXuXnG0bVW1ZvPeabj6FpnOk5eK/sIINBuAZ6xaPf5o3oERgXq7nWEBwEEEEAAAQQQiBao+9zBNxbR0uRDAAEEEEAAAQQQQKAPBVhY9OFJZ8oIIIAAAggggAACCEQLsLCIFiUfAg0VsB6itNrTtCJi0v3c1itinIgcqU6r3qhxrDxWu6fWFGPlsdo9OTwxlqsnhycmaj5WvVHjWHms9mRi1dpLN6teT62pXl4IINAOARYW7ThPVIkAAggggAACCCCAQKMFeHi70aeH4hDwCdQ9ROXrTRQCCCCAAAIIIOAXqPvcwTcWfkMiEUAAAQQQQAABBBBAoEaAhUUNDIcRaJuAvpc5bXfbT3OzYvL2qD7pnuqm1pbPOe3n94Dr2j0mZUx6L19V41TlLePTu6dPVa06b56jzDvdcXTOMoc+lo+T76c+1nVQ1Sc/Zu3PtLaqvNo2b48cJ+UuXzMdR9fatNr0/FJtea3l3HlHAIGWChQVr06nU3GUQwgg0FQBz9/spk2bupZvtafOETGDg4Nd64gaJ6LWVItVb9Q4Vh6r3VOrx9YzTkSM5eqp1RMTUavHNmocK4/V7qm1l25WvZ7rINXLCwEEmiVQ97mDZyxauiCkbAS0QN29jjqGbQQQQAABBBBAIEKg7nMHt0JF6JIDAQQQQAABBBBAAIE+F2Bh0ecXANPvH4H83uZ85lZ7io+I8dxTHTFORI40Z6veqHGsPFa7p1bPOfSMExFjuXpq9cRE1OqxjRrHymO1e2rtpZtVr+c6SPXyQgCBdgiwsGjHeaJKBBBAAAEEEEAAAQQaLcAzFo0+PRSHgE+g7l5HX2+iEEAAAQQQQAABv0Dd5w6+sfAbEokAAggggAACCCCAAAI1AiwsamA4jAACCCCAAAIIIIAAAn4BFhZ+KyIRaLSAfkgybXfbTxOxYvL2qD7pYc2m1pbPOe3nD5fq2j0mZUx6L19V41TlLePTu6dPVa06b56jzDvdcXTOMoc+lo+T76c+1nVQ1Sc/Zu3PtLaqvNo2b48cJ+UuXzMdR9fatNr0/FJtea3l3HlHAIGWClT93Ebdj15UxXIMAQSOvYDnb9b6oSqrPc0yIsbzg1gR40TkSHO26o0ax8pjtXtq9ZxDzzgRMZarp1ZPTEStHtuocaw8Vrun1l66WfV6roNULy8EEGiWQN3nDh7ebumCkLIR0AJ1D1HpGLYRQAABBBBAAIEIgbrPHdwKFaFLDgQQQAABBBBAAAEE+lyAhUWfXwBMv38E8nub85lb7Sk+IsZzT3XEOBE50pyteqPGsfJY7Z5aPefQM05EjOXqqdUTE1GrxzZqHCuP1e6ptZduVr2e6yDVywsBBNohwMKiHeeJKhFAAAEEEEAAAQQQaLQAz1g0+vRQHAI+gbp7HX29iUIAAQQQQAABBPwCdZ87+MbCb0gkAggggAACCCCAAAII1AiwsKiB4TACs03AutfZak8eETGee6ojxonIkeZs1Rs1jpXHavfU6jmHnnEiYixXT62emIhaPbZR41h5rHZPrb10s+r1XAepXl4IINAOARYW7ThPVImAKaD/Bzxt5/t5gjwmted99H7ZXx/Lc+g2HZ8f1/t5Dt1Pb+d9yrbyvSpP3kfv6356W8fobR1TbpfvOi5t6/0yRr/nMVXx1rE8h85fbucxVk7dT29X9Svb07s1Tt5e9tV58xjdpuP1cb1dVYfup7d1P73tjUl96vp5c6S4PE+eM2/XufW27qe3vTHHevyHm7wAACAASURBVJyyTt4RQKD9Ajxj0f5zyAwQkLp7HaFBAAEEEEAAAQSiBeo+d/CNRbQ0+RBAAAEEEEAAAQQQ6EMBFhZ9eNKZMgIIIIAAAggggAAC0QIsLKJFyYdAQwWq7r3WpVrtKTYixvOwZsQ4ETnSnK16o8ax8ljtnlo959AzTkSM5eqp1RMTUavHNmocK4/V7qm1l25WvZ7rINXLCwEE2iHAwqId54kqEUAAAQQQQAABBBBotAAPbzf69FAcAj6BuoeofL2JQgABBBBAAAEE/AJ1nzv4xsJvSCQCCCCAAAIIIIAAAgjUCLCwqIHhMAJtE9D3MqftbvtpblZM3h7VJ91T3dTa8jmn/fwecF27x6SMSe/lq2qcqrxlfHr39KmqVefNc5R5pzuOzlnm0MfycfL91Me6Dqr65Mes/ZnWVpVX2+btkeOk3OVrpuPoWptWm55fqi2vtZw77wgg0FKBouLV6XQqjnIIAQSaKuD5m920aVPX8q321DkiZnBwsGsdUeNE1JpqseqNGsfKY7V7avXYesaJiLFcPbV6YiJq9dhGjWPlsdo9tfbSzarXcx2kenkhgECzBOo+d/CMRUsXhJSNgBaou9dRx7CNAAIIIIAAAghECNR97uBWqAhdciCAAAIIIIAAAggg0OcCLCz6/AJg+v0jkN/bnM/cak/xETGee6ojxonIkeZs1Rs1jpXHavfU6jmHnnEiYixXT62emIhaPbZR41h5rHZPrb10s+r1XAepXl4IINAOARYW7ThPVIkAAggggAACCCCAQKMFeMai0aeH4hDwCdTd6+jrTRQCCCCAAAIIIOAXqPvcwTcWfkMiEUAAAQQQQAABBBBAoEaAhUUNDIcRQAABBBBAAAEEEEDAL8DCwm9FJAKNFtAPQabtbvtpIlZM3k6fsdOvXT0mZcxY78M5dJ4669nSp25+3QzoM/VvtLyWZpubvs7ZRgCBlgtU/dxG3Y9eVMVyDAEEjr2A52/W+qEqqz3NMiLG84NYEeNE5EhztuqNGsfKY7V7avWcQ884ETGWq6dWT0xErR7bqHGsPFa7p9Zeuln1eq6DVC8vBBBolkDd5w4e3m75wpDyEUgCdQ9RoYMAAggggAACCEQL1H3u4FaoaGnyIYAAAggggAACCCDQhwIsLPrwpDPl/hSwfqjKak9qETH6/vC6MxExTkSOVJ9Vb9Q4Vh6r3VOr5xx6xomIsVw9tXpiImr12EaNY+Wx2j219tLNqtdzHaR6eSGAQDsEWFi04zxRJQIIIIAAAggggAACjRbgGYtGnx6KQ8AnUHevo683UQgggAACCCCAgF+g7nMH31j4DYlEAAEEEEAAAQQQQACBGgEWFjUwHEZgtglY9zpb7ckjIsZzT3XEOBE50pyteqPGsfJY7Z5aPefQM05EjOXqqdUTE1GrxzZqHCuP1e6ptZduVr2e6yDVywsBBNohwMKiHeeJKhEwBfT/gKftfD9PkMek9ryP3i/762N5Dt2m4/Pjej/Pofvp7bxP2Va+V+XJ++h93U9v6xi9rWPK7fJdx6VtvV/G6Pc8pireOpbn0PnL7TzGyqn76e2qfmV7erfGydvLvjpvHqPbdLw+rrer6tD99Lbup7e9MalPXT9vjhSX58lz5u06t97W/fS2N+ZYj1PWyTsCCLRfgGcs2n8OmQEC/I4F1wACCCCAAAII9EyAZyx6Rs1ACCCAAAIIIIAAAgj0nwC3QvXfOWfGCCCAAAIIIIAAAgiEC7CwCCclIQLNFKi691pXarWn2IgYz8OaEeNE5EhztuqNGsfKY7V7avWcQ884ETGWq6dWT0xErR7bqHGsPFa7p9Zeuln1eq6DVC8vBBBohwALi3acJ6pEAAEEEEAAAQQQQKDRAjy83ejTQ3EI+ATqHqLy9SYKAQQQQAABBBDwC9R97uAbC78hkQgggAACCCCAAAIIIFAjwMKiBobDCLRNQN/LnLa77ae5WTF5e1SfdE91U2vL55z283vAde0ekzImvZevqnGq8pbx6d3Tp6pWnTfPUead7jg6Z5lDH8vHyfdTH+s6qOqTH7P2Z1pbVV5tm7dHjpNyl6+ZjqNrbVpten6ptrzWcu68I4BASwWKilen06k4yiEEEGiqgOdvdtOmTV3Lt9pT54iYwcHBrnVEjRNRa6rFqjdqHCuP1e6p1WPrGScixnL11OqJiajVYxs1jpXHavfU2ks3q17PdZDq5YUAAs0SqPvcwTMWLV0QUjYCWqDuXkcdwzYCCCCAAAIIIBAhUPe5g1uhInTJgQACCCCAAAIIIIBAnwuwsOjzC4Dp949Afm9zPnOrPcVHxHjuqY4YJyJHmrNVb9Q4Vh6r3VOr5xx6xomIsVw9tXpiImr12EaNY+Wx2j219tLNqtdzHaR6eSGAQDsEWFi04zxRJQIIIIAAAggggAACjRbgGYtGnx6KQ8AnUHevo683UQgggAACCCCAgF+g7nMH31j4DYlEAAEEEEAAAQQQQACBGgEWFjUwHEYAAQQQQAABBBBAAAG/AAsLvxWRCDRaQD8kmba77aeJWDF5e1Sf9LBmU2vL55z284dLde0ekzImvZevqnGq8pbx6d3Tp6pWnTfPUead7jg6Z5lDH8vHyfdTH+s6qOqTH7P2Z1pbVV5tm7dHjpNyl6+ZjqNrbVpten6ptrzWcu68I4BASwWqfm6j7kcvqmI5hgACx17A8zdr/VCV1Z5mGRHj+UGsiHEicqQ5W/VGjWPlsdo9tXrOoWeciBjL1VOrJyaiVo9t1DhWHqvdU2sv3ax6PddBqpcXAgg0S6DucwcPb7d0QUjZCGiBuoeodAzbCCCAAAIIIIBAhEDd5w5uhYrQJQcCCCCAAAIIIIAAAn0uwMKizy8Apt8/Avm9zfnMrfYUHxHjuac6YpyIHGnOVr1R41h5rHZPrZ5z6BknIsZy9dTqiYmo1WMbNY6Vx2r31NpLN6tez3WQ6uWFAALtEGBh0Y7zRJUIIIAAAggggAACCDRagGcsGn16KA4Bn0DdvY6+3kQhgAACCCCAAAJ+gbrPHXxj4TckEgEEEEAAAQQQQAABBGoEWFjUwHAYgdkmYN3rbLUnj4gYzz3VEeNE5EhztuqNGsfKY7V7avWcQ884ETGWq6dWT0xErR7bqHGsPFa7p9Zeuln1eq6DVC8vBBBohwALi3acJ6pEwBTQ/wOetvP9PEEek9rzPnq/7K+P5Tl0m47Pj+v9PIfup7fzPmVb+V6VJ++j93U/va1j9LaOKbfLdx2XtvV+GaPf85iqeOtYnkPnL7fzGCun7qe3q/qV7endGidvL/vqvHmMbtPx+rjerqpD99Pbup/e9sakPnX9vDlSXJ4nz5m369x6W/fT296YYz1OWSfvCCDQfgGesWj/OWQGCEjdvY7QIIAAAggggAAC0QJ1nzv4xiJamnwIIIAAAggggAACCPShAAuLPjzpTBkBBBBAAAEEEEAAgWgBFhbRouRDoKECVfde61Kt9hQbEeN5WDNinIgcac5WvVHjWHmsdk+tnnPoGScixnL11OqJiajVYxs1jpXHavfU2ks3q17PdZDq5YUAAu0QYGHRjvNElQgggAACCCCAAAIINFqAh7cbfXooDgGfQN1DVL7eRCGAAAIIIIAAAn6Bus8dfGPhNyQSAQQQQAABBBBAAAEEagRYWNTAcBiBtgnoe5XTdrf9NDcrJm+nz9gVoV09JmXMWO/DOXSeOuvZ0qduft0M6DP1b7S8lmabm77O2UYAgZYLFBWvTqdTcZRDCCDQVAHP3+ymTZu6lm+1p84RMYODg13riBonotZUi1Vv1DhWHqvdU6vH1jNORIzl6qnVExNRq8c2ahwrj9XuqbWXbla9nusg1csLAQSaJVD3uYNnLFq+MKR8BJJA3b2O6CCAAAIIIIAAAtECdZ87uBUqWpp8CCCAAAIIIIAAAgj0oQALiz486Uy5PwWsf0/eak9qETH6/vC6MxExTkSOVJ9Vb9Q4Vh6r3VOr5xx6xomIsVw9tXpiImr12EaNY+Wx2j219tLNqtdzHaR6eSGAQDsEWFi04zxRJQIIIIAAAggggAACjRbgGYtGnx6KQ8AnUHevo683UQgggAACCCCAgF+g7nMH31j4DYlEAAEEEEAAAQQQQACBGgEWFjUwHEYAAQQQQAABBBBAAAG/AAsLvxWRCDRaQD8kmba77aeJWDF5e1Sf9LBmU2vL55z284dLde0ekzImvZevqnGq8pbx6d3Tp6pWnTfPUead7jg6Z5lDH8vHyfdTH+s6qOqTH7P2Z1pbVV5tm7dHjpNyl6+ZjqNrbVpten6ptrzWcu68I4BASwWqfm6j7kcvqmI5hgACx17A8zdr/VCV1Z5mGRHj+UGsiHEicqQ5W/VGjWPlsdo9tXrOoWeciBjL1VOrJyaiVo9t1DhWHqvdU2sv3ax6PddBqpcXAgg0S6DucwcPb7d0QUjZCGiBuoeodAzbCCCAAAIIIIBAhEDd5w5uhYrQJQcCCCCAAAIIIIAAAn0uwMKizy8Apt8/Avm9zfnMrfYUHxHjuac6YpyIHGnOVr1R41h5rHZPrZ5z6BknIsZy9dTqiYmo1WMbNY6Vx2r31NpLN6tez3WQ6uWFAALtEGBh0Y7zRJUIIIAAAggggAACCDRagGcsGn16KA4Bn0DdvY6+3kQhgAACCCCAAAJ+gbrPHXxj4TckEgEEEEAAAQQQQAABBGoEWFjUwHAYgdkmYN3rbLUnj4gYzz3VEeNE5EhztuqNGsfKY7V7avWcQ884ETGWq6dWT0xErR7bqHGsPFa7p9Zeuln1eq6DVC8vBBBohwALi3acJ6pEwBTQ/wOetvP9PEEek9rzPnq/7K+P5Tl0m47Pj+v9PIfup7fzPmVb+V6VJ++j93U/va1j9LaOKbfLdx2XtvV+GaPf85iqeOtYnkPnL7fzGCun7qe3q/qV7endGidvL/vqvHmMbtPx+rjerqpD99Pbup/e9sakPnX9vDlSXJ4nz5m369x6W/fT296YYz1OWSfvCCDQfgGesWj/OWQGCEjdvY7QIIAAAggggAAC0QJ1nzv4xiJamnwIIIAAAggggAACCPShAAuLPjzpTBkBBBBAAAEEEEAAgWgBFhbRouRDoKECVfde61Kt9hQbEeN5WDNinIgcac5WvVHjWHmsdk+tnnPoGScixnL11OqJiajVYxs1jpXHavfU2ks3q17PdZDq5YUAAu0QYGHRjvNElQgggAACCCCAAAIINFqAh7cbfXooDgGfQN1DVL7eRCGAAAIIIIAAAn6Bus8dfGPhNyQSAQQQQAABBBBAAAEEagRYWNTAcBiBtgnoe5nTdrf9NDcrJm+P6pPuqW5qbfmc035+D7iu3WNSxqT38lU1TlXeMj69e/pU1arz5jnKvNMdR+csc+hj+Tj5fupjXQdVffJj1v5Ma6vKq23z9shxUu7yNdNxdK1Nq03PL9WW11rOnXcEEGipQFHx6nQ6FUc5hAACTRXw/M1u2rSpa/lWe+ocETM4ONi1jqhxImpNtVj1Ro1j5bHaPbV6bD3jRMRYrp5aPTERtXpso8ax8ljtnlp76WbV67kOUr28EECgWQJ1nzt4xqKlC0LKRkAL1N3rqGPYRgABBBBAAAEEIgTqPndwK1SELjkQQAABBBBAAAEEEOhzARYWfX4BMP3+Ecjvbc5nbrWn+IgYzz3VEeNE5EhztuqNGsfKY7V7avWcQ884ETGWq6dWT0xErR7bqHGsPFa7p9Zeuln1eq6DVC8vBBBohwALi3acJ6pEAAEEEEAAAQQQQKDRAjxj0ejTQ3EI+ATq7nX09SYKAQQQQAABBBDwC9R97uAbC78hkQgggAACCCCAAAIIIFAjwMKiBobDCCCAAAIIIIAAAggg4BdgYeG3IhKBRgvohyTTdrf9NBErJm+P6pMe1mxqbfmc037+cKmu3WNSxqT38lU1TlXeMj69e/pU1arz5jnKvNMdR+csc+hj+Tj5fupjXQdVffJj1v5Ma6vKq23z9shxUu7yNdNxdK1Nq03PL9WW11rOnXcEEGipQNXPbdT96EVVLMcQQODYC3j+Zq0fqrLa0ywjYjw/iBUxTkSONGer3qhxrDxWu6dWzzn0jBMRY7l6avXERNTqsY0ax8pjtXtq7aWbVa/nOkj18kIAgWYJ1H3u4OHtli4IKRsBLVD3EJWOYRsBBBBAAAEEEIgQqPvcwa1QEbrkQAABBBBAAAEEEECgzwVYWPT5BcD0+0cgv7c5n7nVnuIjYjz3VEeME5EjzdmqN2ocK4/V7qnVcw4940TEWK6eWj0xEbV6bKPGsfJY7Z5ae+lm1eu5DlK9vBBAoB0CLCzacZ6oEgEEEEAAAQQQQACBRgvwjEWjTw/FIeATqLvX0debKAQQQAABBBBAwC9Q97mDbyz8hkQigAACCCCAAAIIIIBAjQALixoYDiMw2wSse52t9uQREeO5pzpinIgcac5WvVHjWHmsdk+tnnPoGScixnL11OqJiajVYxs1jpXHavfU2ks3q17PdZDq5YUAAu0QYGHRjvNElQiYAvp/oNN2vr93795JOfKY1J730fupsxWT4q1xUh6dN23r/ahxrFq946Q4/ZpuramvZZJyVsXocT3z0fFpO7eNGqeqVu2Sj5PXUdaZ98n3I8ax3PJa69zKmqva07GocfScq9w84+haq+rN5zzTcXStMx0nr5V9BBBotwDPWLT7/FE9AqMCdfc6woMAAggggAACCEQL1H3u4BuLaGnyIYAAAggggAACCCDQhwIsLPrwpDNlBBBAAAEEEEAAAQSiBVhYRIuSD4GGClgPUVrtaVoRMel+busVMU5EjlSnVW/UOFYeq91Ta4qx8ljtnhyeGMvVk8MTEzUfq96ocaw8VnsysWrtpZtVr6fWVC8vBBBohwALi3acJ6pEAAEEEEAAAQQQQKDRAjy83ejTQ3EI+ATqHqLy9SYKAQQQQAABBBDwC9R97uAbC78hkQgggAACCCCAAAIIIFAjwMKiBobDCLRNQN/LnLa77ae5WTF5e1SfdE91U2vL55z283vAde0ekzImvZevqnGq8pbx6d3Tp6pWnTfPUead7jg6Z5lDH8vHyfdTH+s6qOqTH7P2Z1pbVV5tm7dHjpNyl6+ZjqNrbVpten6ptrzWcu68I4BASwWKilen06k4yiEEEGiqgOdvdtOmTV3Lt9pT54iYwcHBrnVEjRNRa6rFqjdqHCuP1e6p1WPrGScixnL11OqJiajVYxs1jpXHavfU2ks3q17PdZDq5YUAAs0SqPvcwTMWLV0QUjYCWqDuXkcdwzYCCCCAAAIIIBAhUPe5g1uhInTJgQACCCCAAAIIIIBAnwuwsOjzC4Dp949Afm9zPnOrPcVHxHjuqY4YJyJHmrNVb9Q4Vh6r3VOr5xx6xomIsVw9tXpiImr12EaNY+Wx2j219tLNqtdzHaR6eSGAQDsEWFi04zxRJQIIIIAAAggggAACjRbgGYtGnx6KQ8AnUHevo683UQgggAACCCCAgF+g7nMH31j4DYlEAAEEEEAAAQQQQACBGgEWFjUwHEYAAQQQQAABBBBAAAG/AAsLvxWRCDRaQD8kmba77aeJWDF5e1Sf9LBmU2vL55z284dLde0ekzImvZevqnGq8pbx6d3Tp6pWnTfPUead7jg6Z5lDH8vHyfdTH+s6qOqTH7P2Z1pbVV5tm7dHjpNyl6+ZjqNrbVpten6ptrzWcu68I4BASwWqfm6j7kcvqmI5hgACx17A8zdr/VCV1Z5mGRHj+UGsiHEicqQ5W/VGjWPlsdo9tXrOoWeciBjL1VOrJyaiVo9t1DhWHqvdU2sv3ax6PddBqpcXAgg0S6DucwcPb7d0QUjZCGiBuoeodAzbCCCAAAIIIIBAhEDd5w5uhYrQJQcCCCCAAAIIIIAAAn0uwMKizy8Apt8/Avm9zfnMrfYUHxHjuac6YpyIHGnOVr1R41h5rHZPrZ5z6BknIsZy9dTqiYmo1WMbNY6Vx2r31NpLN6tez3WQ6uWFAALtEGBh0Y7zRJUIIIAAAggggAACCDRagGcsGn16KA4Bn0DdvY6+3kQhgAACCCCAAAJ+gbrPHXxj4TckEgEEEEAAAQQQQAABBGoEWFjUwHAYgdkmYN3rbLUnj4gYzz3VEeNE5EhztuqNGsfKY7V7avWcQ884ETGWq6dWT0xErR7bqHGsPFa7p9Zeuln1eq6DVC8vBBBohwALi3acJ6pEwBTQ/wOetvP9PEEek9rzPnq/7K+P5Tl0m47Pj+v9PIfup7fzPmVb+V6VJ++j93U/va1j9LaOKbfLdx2XtvV+GaPf85iqeOtYnkPnL7fzGCun7qe3q/qV7endGidvL/vqvHmMbtPx+rjerqpD99Pbup/e9sakPnX9vDlSXJ4nz5m369x6W/fT296YYz1OWSfvCCDQfgGesWj/OWQGCEjdvY7QIIAAAggggAAC0QJ1nzv4xiJamnwIIIAAAggggAACCPShAAuLPjzpTBkBBBBAAAEEEEAAgWgBFhbRouRDoKECVfde61Kt9hQbEeN5WDNinIgcac5WvVHjWHmsdk+tnnPoGScixnL11OqJiajVYxs1jpXHavfU2ks3q17PdZDq5YUAAu0QYGHRjvNElQgggAACCCCAAAIINFqAh7cbfXooDgGfQN1DVL7eRCGAAAIIIIAAAn6Bus8dfGPhNyQSAQQQQAABBBBAAAEEagRYWNTAcBiBtgnoe5nTdrf9NDcrJm+P6pPuqW5qbfmc035+D7iu3WNSxqT38lU1TlXeMj69e/pU1arz5jnKvNMdR+csc+hj+Tj5fupjXQdVffJj1v5Ma6vKq23z9shxUu7yNdNxdK1Nq03PL9WW11rOnXcEEGipQFHx6nQ6FUc5hAACTRXw/M1u2rSpa/lWe+ocETM4ONi1jqhxImpNtVj1Ro1j5bHaPbV6bD3jRMRYrp5aPTERtXpso8ax8ljtnlp76WbV67kOUr28EECgWQJ1nzt4xqKlC0LKRkAL1N3rqGPYRgABBBBAAAEEIgTqPndwK1SELjkQQAABBBBAAAEEEOhzARYWfX4BMP3+Ecjvbc5nbrWn+IgYzz3VEeNE5EhztuqNGsfKY7V7avWcQ884ETGWq6dWT0xErR7bqHGsPFa7p9Zeuln1eq6DVC8vBBBohwALi3acJ6pEAAEEEEAAAQQQQKDRAjxj0ejTQ3EI+ATq7nX09SYKAQQQQAABBBDwC9R97uAbC78hkQgggAACCCCAAAIIIFAjwMKiBobDCCCAAAIIIIAAAggg4BdgYeG3IhKBRgvohyDTdrf9NBErJm+nz9jp164ekzJmrPfhHDpPnfVs6VM3v24G9Jn6N1peS7PNTV/nbCOAQMsFqn5uo+5HL6piOYYAAsdewPM3a/1QldWeZhkR4/lBrIhxInKkOVv1Ro1j5bHaPbV6zqFnnIgYy9VTqycmolaPbdQ4Vh6r3VNrL92sej3XQaqXFwIINEug7nMHD2+3fGFI+QgkgbqHqNBBAAEEEEAAAQSiBeo+d3ArVLQ0+RBAAAEEEEAAAQQQ6EMBFhZ9eNKZcn8KWD9UZbUntYgYfX943ZmIGCciR6rPqjdqHCuP1e6p1XMOPeNExFiunlo9MRG1emyjxrHyWO2eWnvpZtXruQ5SvbwQQKAdAiws2nGeqBIBBBBAAAEEEEAAgUYL8IxFo08PxSHgE6i719HXmygEEEAAAQQQQMAvUPe5g28s/IZEIoAAAggggAACCCCAQI0AC4saGA4jMNsErHudrfbkERHjuac6YpyIHGnOVr1R41h5rHZPrZ5z6BknIsZy9dTqiYmo1WMbNY6Vx2r31NpLN6tez3WQ6uWFAALtEGBh0Y7zRJUImAL6f8DTdr6fJ8hjUnveR++X/fWxPIdu0/H5cb2f59D99Hbep2wr36vy5H30vu6nt3WM3tYx5Xb5ruPStt4vY/R7HlMVbx3Lc+j85XYeY+XU/fR2Vb+yPb1b4+TtZV+dN4/RbTpeH9fbVXXofnpb99Pb3pjUp66fN0eKy/PkOfN2nVtv63562xtzrMcp6+QdAQTaL8AzFu0/h8wAAX7HgmsAAQQQQAABBHomwDMWPaNmIAQQQAABBBBAAAEE+k+AW6H675wzYwQQQAABBBBAAAEEwgVYWISTkhCBZgpU3XutK7XaU2xEjOdhzYhxInKkOVv1Ro1j5bHaPbV6zqFnnIgYy9VTqycmolaPbdQ4Vh6r3VNrL92sej3XQaqXFwIItEOAhUU7zhNVIoAAAggggAACCCDQaAEe3m706aE4BHwCdQ9R+XoThQACCCCAAAII+AXqPnfwjYXfkEgEEEAAAQQQQAABBBCoEWBhUQPDYQTaJqDvZU7b3fbT3KyYvD2qT7qnuqm15XNO+/k94Lp2j0kZk97LV9U4VXnL+PTu6VNVq86b5yjzTnccnbPMoY/l4+T7qY91HVT1yY9Z+zOtrSqvts3bI8dJucvXTMfRtTatNj2/VFteazl33hFAoKUCRcWr0+lUHOUQAgg0VcDzN7tp06au5VvtqXNEzODgYNc6osaJqDXVYtUbNY6Vx2r31Oqx9YwTEWO5emr1xETU6rGNGsfKY7V7au2lm1Wv5zpI9fJCAIFmCdR97uAZi5YuCCkbAS1Qd6+jjmEbAQQQQAABBBCIEKj73MGtUBG65EAAAQQQQAABBBBAoM8FWFj0+QXA9PtHIL+3OZ+51Z7iI2I891RHjBORI83ZqjdqHCuP1e6p1XMOPeNExFiunlo9MRG1emyjxrHyWO2eWnvpZtXruQ5SvbwQQKAdAiws2nGeqBIBBBBAAAEEEEAAgUYL8IxFo08PxSHgE6i719HXmygEEEAAAQQQQMAvUPe5g28s/IZEIoAAAggggAACCCCAQI0AC4saGA4jgAACCCCAAAIIIICAX4CFhd+KSAQaLaAfkkzb3fbTRKyYySJdSgAAHeJJREFUvD2qT3pYs6m15XNO+/nDpbp2j0kZk97LV9U4VXnL+PTu6VNVq86b5yjzTnccnbPMoY/l4+T7qY91HVT1yY9Z+zOtrSqvts3bI8dJucvXTMfRtTatNj2/VFteazl33hFAoJ0CPGPRzvNG1QhMEqi713FSEDsIIIAAAggggECAQN3nDr6xCMAlBQIIIIAAAggggAAC/S7AwqLfrwDmjwACCCCAAAIIIIBAgAALiwBEUiDQBoH83ua8Zqs9xUfEeO6pjhgnIkeas1Vv1DhWHqvdU6vnHHrGiYixXD21emIiavXYRo1j5bHaPbX20s2q13MdpHp5IYBAOwRYWLTjPFElAggggAACCCCAAAKNFuDh7UafHopDwCdQ9xCVrzdRCCCAAAIIIICAX6DucwffWPgNiUQAAQQQQAABBBBAAIEaARYWNTAcRmC2CVj3OlvtySMixnNPdcQ4ETnSnK16o8ax8ljtnlo959AzTkSM5eqp1RMTUavHNmocK4/V7qm1l25WvZ7rINXLCwEE2iHAwqId54kqETAF9P+Ap+18P0+Qx6T2vI/eL/vrY3kO3abj8+N6P8+h++ntvE/ZVr5X5cn76H3dT2/rGL2tY8rt8l3HpW29X8bo9zymKt46lufQ+cvtPMbKqfvp7ap+ZXt6t8bJ28u+Om8eo9t0vD6ut6vq0P30tu6nt70xqU9dP2+OFJfnyXPm7Tq33tb99LY35liPU9bJOwIItF+AZyzafw6ZAQJSd68jNAgggAACCCCAQLRA3ecOvrGIliYfAggggAACCCCAAAJ9KMDCog9POlNGAAEEEEAAAQQQQCBagIVFtCj5EGioQNW917pUqz3FRsR4HtaMGCciR5qzVW/UOFYeq91Tq+ccesaJiLFcPbV6YiJq9dhGjWPlsdo9tfbSzaq36jr48pe/LGvXrpWhoaFUKi8EEGiRAM9YtOhkUSoCdQJ19zrWxXMcAQQQaKrA888/L9/73vdkcHBQzjjjDLn44otl6dKlTS2XuhDoS4G6zx18Y9GXlwOTRgABBBBAoJkCv/3bvy3nn3++bNu2TU455RR53/vexzcYzTxVVIXAFAEWFlNIOIAAAggggAACx1qABcaxPgOMj8D0BbgVavpm9ECgcQLpK0leCCCAQL8IfPCDHxy9Vapf5ss8EWiaQN2tUC9uWqHUgwACMxMYHh6eWcce96r7P0Y9LsM9XJvqpVb3aZ12ILbTJnN1mI7r/fffL9dff/1o3gsvvNCVnyAEEOitAAuL3nozGgIIIIAAAghMQ0AvKK644go57bTTptGbUAQQ6KUAC4teajMWAggggAACCLgEWFC4mAhCoFECLCwadTooBgEEEEAAgf4WSL9fsW7dulEEvqHo72uB2bdPgIVF+84ZFSOAAAIIIDBrBZ555hlhQTFrTy8Tm+UCLCxm+QlmeggggAACCLRJgGco2nS2qBWByQL8jsVkD/YQQAABBBBAAAEEEEBgBgL8jsUM0OiCAAIIIIAAAggggEC/CtT9U9F8Y9GvVwTzRgABBBBAAAEEEEAgUICFRSAmqRBAAAEEEEAAAQQQ6FcBFhb9euaZNwIIIIAAAggggAACgQIsLAIxSYUAAggggAACCCCAQL8KsLDo1zPPvFsjMLJni/yHRSfLum2/mFTzyN6H5JZ1qyQ9QDX6/85aJxu+s0P2jqiwkb2y45Z1clYZM7BK1m34ruzYe1AFHdnmyNAGWTWRf7yWtL9qgwyVtbjqOCh7d3xD1p21aHxOi+SsdV+T7+zYK2WaI6t0rPdktzTGNzIPXx2T8wzIQJX/jAv+hWxbd/LhczvFV10PjbHN3VbJulsemnw9Sh5TfY6Prm06KSNyYGibbJj4+3mNrL7ubhk6MPlKc9Xh8p/JhbBPdlz3Nlm0bpvsz7rH1eU7H9nwNbsjcmDHjXLWoo/Jtv2THcc6dGl3GUbWWjMFDiOAwJELFBWvTqdTcZRDCCDQc4FD/63Y/P6Tik5nRbF26zOHhx89vqJYufbrxfYnf1MUxW+KJx/8cnHRQh33m+KJzZcWC1euLTZuf7I4VBTFoSd/WNxw0UnFwrVbi+HD2Y5g61AxvPXqYuG564udaYDKl6+OQ09sLt6/8Nxi7cYHiyfHii0evOGiYuHCq4utw7XJK0esOzg6xtL3F+sfG5/9c48Vm9eeW3RU/a46XP51VRzB8eceLK5dubRYee2DxXOjaZpie6h4bvsNxcqFlxabn0jXY7rY0rW7QtVaFE2xnahj82MTjk9u/VSxcuUNxfbnxq+1sv5j8jc2XDy2cW1x7ukLp/6tBtY14XDEf3OHiuce+1ax9twVRafy77Vbe1Ou4bHLlv8fAQR8AnVrBanqXhdcFcsxBBA4WgLDxWPr318sXbmyOD1bWBzaub44t/POYv3O59Xgzxc717/z8AeRQ48V689dWpy7/rHRRUUZONq38n/8y4jpvD9TbF274vCYVV1ddYzVrj/gj6Ya7Xv65EVV1RiuYzW1Dm8t1k4syHx1uPxdNU0n6Nli+7VvLTqTPvx6zrFvTtOpZGpsle34onPiWvPVcfRtx2qtvtYO/7246nBd21O1uh059OSDxca1lxbXPvjDYv25UxcWcXX5zke3WkfbDj1ZbN94dXHRtX9dbF//zqkLC7O9KdewOVMCEEBACdStFbgV6si/9CEDAkdBIN02sEH+9FPHy2eueof8y0kjjMiBPT+TR+ctkcUvP061HCcvX7xE5NZ7ZUe6FeHAkzL06ICctPh3RP+hz3n5YjlJ7pG7dvxK9Z3h5sgvZffDw7Js6e/J3LoUrjoOyJ6h3TLvpMXy8knF/o4sPukFufWuR6bcDlI3XO3x/Y/IXbeKXHjOq6Wjgzpnyucff0g+f+ZLRcRTh9Nfj3HE2+l62ChXXvOUXPLx98ryueNITbHtNr99u2T3U+nWu4bYjl6zT9dcawPywG33y64R5zl2+XfDydpGdsrGNZ+WoXPWyUdel67H/BVZl+d85OPn+y/I0Mb/Ta4cOlM+95HXy7/Km8VqT5eF5/9ORdQ6pTgOIIDAURDQ/xN+FNKTEgEEZiRwYLt89cpvyStv/Kict/D4LMVBeWr3LtmXHZ3YHf8gN/LUbnm4NuhpeXj3L4/82YXRDwW/LS975i9lzaLx5ysWrZbrthx+1sNVx/iHvYk5ZBv7Ht4tT1Xdtp3Fddsdq2OxLO3skW0byudOsnvrXXX4/LvVMu22kZ/LPV/dKLveeZVcdsbhD5xNsRV5iay44N2y5NbNct+e8ed30n3z9z4iSz5xhbxz6fEiTbXNT8ajP5M9B144Nn9jcxbIqg3fks+cuWDSfww4XKLv2uvddXGc/N6qP5c7PvMmmV/5acJqF+ldrYcV2UIAgaMnUPl/Co7ecGRGAAFbYJ/s+Oqg3LnqS3LD+YsqPmCM/de77nnG/8tm96Ajbh37UDBfFpx8sWx4fFiGh4dl+KdXyase/JS8988fkgPpIdn07Yo10ugCpXYVZPV2tJd17JZvXvkf5d7Fl8k9qdbhH8hVL7lN3nr5HbInLVxcdXj8HSVNI2Rk133yF98+Ti589+myYOL/apdzMhK55mTkMJvnyNzlH5SbP/nfZfWy3x176PyEZXLe350nN3/k5LFvs1x19MB2TvoW7GVTZzRp4eOpw+k/daQuR+bK/Pm13/1NfOvTJcHYg+k9+5ubI3Pn/+v6byvFancauq6d7iq0IoBAbwQm/ieqN8MxCgIIdBc4KHu2fEL++M7T5QsffF2X/8HunqVXrXOWrpE7h++c/F9Y5/6+nHXOq2XXNdfLt4de6FUpznGeluPe81m5ZuK/CHfkxH/3bjn/7s/JTd+f/K9uORP2IOwF2fXDu+SB171bLljxkh6MN5Mh0r9g9E45+wf/Vh7a8+zYAnP45/LQBT+St665RXZm/9rSTEaI6/NSOeOyq+TNt35BBrftGfvWbmSvPPTFG+W2gxULjriByYQAAgjMegEWFrP+FDPBNgmM7Pmu/O8fflwu+8Lqw/fRT5nAXFmwdPGUo5MPzJG5C14lyyYf7NFeOfZuGdrzT7465v6eLF02rwf1vWzKMycyOvbw2K1hrjo8/oFTGXlcfnjbT+TU96yS15bPVoymL52NsVxzMnJYzfv/Xm676Sm58KK3yIkTNY4v2rZ9Wf7PH/9Kxpytc9wb2zkL3i433HO5nHDLW+SE9E/5nv2f5P87/Uq58T2LRZa9ShbM7TT0b8zj06Drwrpu0jcanv871Ytr2KyVAAQQ8AiwsPAoEYNATwRekF13/Rf59r7vyzUry99yGJATVlwuD8hOufm8V43/NsTYQ9q1H9HGH+oefUi7NqjiA/ZRmqOrjrrbU8ZrmvJQ97RrnSOd5W+SC2s9xhO66vD5T7vEmg4ju+6X2x6Y+hB+Cm+G7Yjs33Gv3Fp1J9voB8Knxx6+b5TtHJm79M3y0Y0/Gft25b7Py0XL/5U8OfEPCPjOscu/5rzO7HBgXa7zMbMqp9PLZdiQWqczL2IR6FcBFhb9euaZdwMFjpela/5y/DaS8ecVhofl2R/fIKfKiXLJ7T+T4TvXyNI54/+Vb+Jf2ymnMv5g5+h/cZ0z/l+Ix/9LfBmS7sAefah7sSxd0O1ebtWhdvMFGdrwLhmY8oNY4/dNzztbzln+EmcdY/8ldspD2qP3vRv/6lRtfVnD3FfK6998cOq/MDV6//aJctZJL0v//XT0v1R3r8Ppnw0/s93x26BKyzzJ6Ad36xx75pQnns5+l0XbqO3Lxv8lLk8dvbAdu26n/PDc6LV2/Hitzjpc/tOxtGIj6/KcD6uegHaXYUNqDZguKRCY9QLqn6Sd2Kz7t2knAthAAIGeCYz9u/X6h+/KHx87qVh40cbisdEf9OryA3kLD/8gXPgP5I3+YNuK4qL1j4z/0FhRFM89Uqy/aGXx/s3/bfz3M8Z/AMuoY+zHuk46nOvQk8E/kDf+I26dtxbXbn927PyNj7H0/ZuLJ8rfRRv9oT6jjtEfKbP8Iy6Rmt9cmEjdFNv0mysfLM5du77YurP86cWx32FZqH53w3WOe2A79jd1bnH11ifGrtHR31pYW5yrroOxH/izzrHPf+J0TWdj9Dcypv6ORWRdrvPhrnn8dzEmfrck71jX7jOMrTWvjX0EEJiuQN1agR/Im64k8Qj0WKByYVEcKp7bubVYn341utMZ+38LLyqu3bx97Feryxqf21lsXb+2WFnGdE4qLrp28/ivdZdBR/Z+6MntxeZrLyoWlmOsXFus37rz8EIjpXfVMVzs3Lq+WLty4cScFl50bbF5/FfDj6zKsndyu6u49qL0a+bJLXncVewsf215NMxTh9O/HHbG79bCokm2uVuTbX9TPLn96+paU7/4PnGunOfYdW1PJPVv1C0sQv/283PWKWb+N1e3cCin3KXdZRhZa1kT7wggMFOBuoXFi1LC/GuZgYGB0dsx8uPsI4AAAggggAACCCCAQH8L1K0VeMaiv68LZo8AAggggAACCCCAQIgAC4sQRpIggAACCCCAAAIIINDfAiws+vv8M3sEEEAAAQQQQAABBEIEWFiEMJIEAQQQQAABBBBAAIH+FmBh0d/nn9kjgAACCCCAAAIIIBAiwMIihJEkCCCAAAIIIIAAAgj0twALi/4+/8weAQQQQAABBBBAAIEQARYWIYwkQQABBBBAAAEEEECgvwVYWPT3+Wf2CCCAAAII1AqMDG2QVQPvkg1DL9TGHN2G/TJ07xflY7fslJHRgV6QoQ3vkoFFH5Nt+8eOzHz8g7J323+UswYGZNHqW2TngRnkG9kpG1a99xj6zHz29ETgaAiwsDgaquREAAEEEEAAgSMX2L9DNlx8vfzdoSNPNSXDyG65+95Xylf2PC53v/EncuM9Px9fvEyJrD9w4EkZ+hcr5Q1Ljq+PoQWBPhJgYdFHJ5upIoAAAggggMC4wNO75JnXnSEnzp0nJ/67t8nA//N38vS0cEZk/46/lkfPO02W8GlqWnIEz14B/hRm77llZggggAACDRcYu9XoZFm37ReHK92/TdYtGpBF67bJ/omjv5Bt606eODayd4dsuW61LBoYkIHR/7dK1m3YJkOjt/OM3y60aoMMTbq7Z0T2b/uYLFK3EY3sfUhuWbdqPMciOWvdBtk2dHjUieHVRvc+42MMvEu+tu37KvdrZPV1d4/XVyZLtzndKKsXjc1h0err5K82rJOzBsY9ksOrz5Ob9+2TBy4/WU5QdYvskR13/vlE34FFq+W6e4fkQJna8z7/LfLR818xFtlZIq+XR+Sxad1e9SvZcdd/l/PesEgqP0yNnsdFsupr98pDt6R5lfO8Ue6dMB47rwOrBmXL3YctBs5aJ7fs2CP7h+6W61a/Zuz8LFotNz60d/rfqngsiEEgSKDybyEoN2kQQAABBBBAoIvAnCWnyQWnPi233vXI+CIi/Vfwe+XWfSL7Ht4tT5ULg/2PyF23ilx4zqulc+Ah+fP3XiJ3vPg/yN8+OyzDw8Py7GNXyG9984NyyVe3ywE5Xpa84Rw59YG75Ie79LMR6YPwPSIXvkmWd+bIyJ4t8r+e8gHZ9vKPy2OjeR6Rryz9kaw++2OyZc/Byqr9fb4nV3z6bums+cvx+q6TBXdeNl5fSn1Q9mz5mJx98U/ljXf/XIaHn5WfXvW78n9/6mbZXo7cOVM+/8jtcsm8eXLqDQ/Js49/Rs7sjH9s2bdN7vz7V8nVP31Whoefkcc2vlLufMdH5as79pW9p/d+YK/87L/+SHb84z/5+6Vz8ugK4zaoffLAFdfL5s6fyB3DwzL87KOyccFd8o5LNsgO/UzHA1+RL21dNDafZx+V2095WD60cpm8+rO75I2fe0iGh38uD33yX8gNF3xW7qg5N/7CiUTg6AmwsDh6tmRGAAEEEECgu8CcRfKGC05Ri4iD8tTuXSJvPV/e+mi5MBhfbMjZcs7yebL/x3fITbvOlovW/JHMH/9f8Tnz3yAXvec1sv2+f5AnR0TGFiw/kW9+5/89/F/x9eJEfiHfv+lz8u1lH5KrP3TaeJ6OnLjmc7Lxwgflwzfdr74tKacwnT4nyiUfv1zOX9oZ7Txn/mvkTSsGJuqT/ffLTR/+G3nzjR+X1SemmDky98R/L1/ceKnMK4fr9j7vvfLxq98uS+cmgONk/hnvkveculPue/jpGfwX/YOy556vy03bH5X7Ht7j7D92TrYsWywvNz5JzbvkSrn6/BNlbprPnPmy/E1/KPO2/0geflIt3vR8yhg5Vz559Ro5ef5xItKR33/DH8myfQ/KgxPfdnQDog2BYyNg/Dkcm6IYFQEEEEAAgf4QyL5dGHlcfnjbXrlw9Z/IymV7ZWhPurlHf9PwYumc+Rl5/PFrZMVTfyNbtmyRLVv+SjasO19WXP69w2RzFss5H3iz7LrpDvnx6O09B2XPfZvl1iXvlgtWvERkdJGxU+adlH8wnisLli6WfbfeKzvy24Jm0meiorG88ujPZM+Bfx7/VuZE+aM/eJm6jWiOzF3wKlk20We6Gy/Io0NPHl5Iebsf+Inc+qXvyL6TlsjB2++XXeW3RF37pwXgr+T89A1S17i8sZzj7vFzm7ezj0C7BVhYtPv8UT0CCCCAQMsFym8Xbvvh4zKS/pWh/3q6nHPyCnnDBfPHbpEa+aXsfvj4sdug0lwP/INsWP2HsmDF++RLD/5SRH5LTjjn87L1hnNl7IN7+mR8nCw464/lQrlH7trxK5GR3XLXX9wty96zSl47+l/5x9D23XyevGLiOY30DMDLJi9QKmxn0qciTUMOld9WvEwu+dRN8vFlQ/LTp//Zri0tAG//13LO8pfYsZ6IZa+SBeq8eLoQg0ATBV7cxKKoCQEEEEAAgb4RGL0d6jXyqaGfy54d2+TWV75K1sw9Xl6+eInIbbtl7z/ultsePV2uHP0Q+4IMffsauXzb6bLx0evl/AXpNpn0+oVsu2u3iCwZ3093z7xazrlQZPVdj8i6BbvltgdeIxf8J/2gcXp24W757poT1bcGh7unrZGnJu+LWH1GKm6hynM0aL/8tuLUT8qaM14psntY7npsn5w//6VdixzZdb/cvux/lm+Uz3x0jaYRgf4R4BuL/jnXzBQBBBBAoJECx40tIm69WT6x/h5ZdkH650vnSGf5m+TCR78pn/vcN+XR8QeuRQ7InqHdIsteK38weu/9+IRGfi37fqnu2R89/BJZfs7ZIrdulq9t+a48cOo5hx80Hl10vEwe/dGjsnfSrT/7ZMd1b5OBKf+iVLlQmWafSu/xuc3LbwcakQN7fiaPVvY5GgfVtxVXvk2Wzkm3pZ0iw7t/Ofacxd4tcsl1O2Tq9xcvyK4f/liWTfs2qKMxB3Ii0CwBFhbNOh9UgwACCCDQdwLjH7TlXtnyf4mctPh3xr5BmPt7snTZLtmy5bnDt0HJ2GJh3gO3yS3fH3/QeGSvPPTFT8qHv52+sdCvOdJZ8Xa5bMl35JrPbpdTRxcsZftL5YzLrpI33/0p+dgX7x9fXOyXoS3XypXXiHzi038sS6d8QphJn3K87L1zmlx24+vl1k/fIFtGH0YekQNDd8hnP/0NmfTvOo0ajP/43D8dEP0PKWUZp7878W3FB2XNGWPfUMxZcoqsuP2rcseeA7Lnb7fLS5Yvkqm3dqTFncjSBaOPY09/XHogMIsFpvyfjVk8V6aGAAIIIIBAMwVGv0E4UWRe+pefxu/bH/8Xo0QWqw+xc6RzxqWy+Ysnyd+et0xOSM9HLL5KfvA/XCS3bbxk6r+oNPd/kre95xSReW+TD5yzeNItT3MWvF1uuOcGeeNTn5b/8YT0fMUr5Ow7TpBLt/4f8pHl1f8200z6VIMfJwvO/4zcc9Xvyh1nv0IGBk6QP/js47Ly0j+VU3WHOYtl1ZXvkYPpdyzmXyzfnvTP5+rAbHtkp2xYtaj6m5fR0PzbivH+abzLT5AvLVsgp96xVN6XHnTPX65/ZjbvxD4C/SHwoqIoinyq6cd20r+LzQsBBBBAAAEEEOiVQPrBwLec/TO58pFrDv9mxUwHTz9Q997dsub2NRXfvsw0Kf0QQCAJ1K0V+MaC6wMBBBBAAAEEeisw+qvUr5HVG/5h4p+HHdl7v3zxs1+Vg5e9XVYc8UPRI3LgHx+Whx2/M9HbiTMaArNbgIXF7D6/zA4BBBBAAIHmCXROkz/b/En5Nz94rywY/+duTzjlP8s/v/1m+cZHTh77MbkjqvpX8uNtIlf+2WnT/J2JIxqUzgj0vQC3QvX9JQAAAggggAACCCCAAAJ+AW6F8lsRiQACCCCAAAIIIIAAAtMU4FaoaYIRjgACCCCAAAIIIIAAAlMFWFhMNeEIAggggAACCCCAAAIITFOAhcU0wQhHAAEEEEAAAQQQQACBqQIsLKaacAQBBBBAAAEEEEAAAQSmKcDCYppghCOAAAIIIIAAAggggMBUARYWU004ggACCCCAAAIIIIAAAtMUYGExTTDCEUAAAQQQQAABBBBAYKoAC4upJhxBAAEEEEAAAQQQQACBaQqwsJgmGOEIIIAAAggggAACCCAwVYCFxVQTjiCAAAIIIIAAAggggMA0BVhYTBOMcAQQQAABBBBAAAEEEJgqwMJiqglHEEAAAQQQQAABBBBAYJoCLCymCUY4AggggAACCCCAAAIITBVgYTHVhCMIIIAAAggggAACCCAwTQEWFtMEIxwBBBBAAAEEEEAAAQSmCrCwmGrCEQQQQAABBBBAAAEEEJimAAuLaYIRjgACCCCAAAIIIIAAAlMFWFhMNeEIAggggAACCCCAAAIITFOAhcU0wQhHAAEEEEAAAQQQQACBqQIsLKaacAQBBBBAAAEEEEAAAQSmKcDCYppghCOAAAIIIIAAAggggMBUARYWU004ggACCCCAAAIIIIAAAtMUYGExTTDCEUAAAQQQQAABBBBAYKoAC4upJhxBAAEEEEAAAQQQQACBaQq8qCiKQvcZGBjQu2wjgAACCCCAAAIIIIAAAlMEhoeHJx2bsrCY1MoOAggggAACCCCAAAIIIOAQ4FYoBxIhCCCAAAIIIIAAAggg0F2AhUV3H1oRQAABBBBAAAEEEEDAIcDCwoFECAIIIIAAAggggAACCHQXYGHR3YdWBBBAAAEEEEAAAQQQcAiwsHAgEYIAAggggAACCCCAAALdBVhYdPehFQEEEEAAAQQQQAABBBwC/z+vgtR9xakLcgAAAABJRU5ErkJggg=="></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following data are available for the Sun.</p>
<p style="padding-left:150px;">Surface temperature = 5800 K</p>
<p style="padding-left:150px;">Luminosity = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_ \odot }">
<mrow>
<msub>
<mi>L</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span></p>
<p style="padding-left:150px;">Mass = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{M_ \odot }">
<mrow>
<msub>
<mi>M</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span></p>
<p style="padding-left:150px;">Radius = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{R_ \odot }">
<mrow>
<msub>
<mi>R</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span></p>
<p>Epsilon Indi has a radius of 0.73 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{R_ \odot }">
<mrow>
<msub>
<mi>R</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span>. Show that the luminosity of Epsilon Indi is 0.2 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_ \odot }">
<mrow>
<msub>
<mi>L</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{M_ \odot }">
<mrow>
<msub>
<mi>M</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span>.</p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.</p>
<p> </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>Describe the stages in the evolution of Epsilon Indi from the point when it leaves the main sequence until its final stable state.</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><em>λ</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.9 \times {{10}^{ - 3}}}}{{4600}}">
<mfrac>
<mrow>
<mn>2.9</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4600</mn>
</mrow>
</mfrac>
</math></span> =» 630 «nm» ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>black body curve shape ✔</p>
<p>peaked at a value from range 600 to 660 nm ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{L}{{{L_ \odot }}} = {\left( {\frac{{0.73{R_ \odot }}}{{{R_ \odot }}}} \right)^2} \times {\left( {\frac{{4600}}{{5800}}} \right)^4}">
<mfrac>
<mi>L</mi>
<mrow>
<mrow>
<msub>
<mi>L</mi>
<mo>⊙</mo>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>0.73</mn>
<mrow>
<msub>
<mi>R</mi>
<mo>⊙</mo>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>R</mi>
<mo>⊙</mo>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>4600</mn>
</mrow>
<mrow>
<mn>5800</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>4</mn>
</msup>
</mrow>
</math></span> ✔</p>
<p><em>L</em> = 0.211 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{L_ \odot }">
<mrow>
<msub>
<mi>L</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span> ✔</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>M</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{0.21^{\frac{1}{{3.5}}}}\,{M_ \odot }">
<mrow>
<msup>
<mn>0.21</mn>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<mn>3.5</mn>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msub>
<mi>M</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span> =» 0.640 <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{M_ \odot }">
<mrow>
<msub>
<mi>M</mi>
<mo>⊙</mo>
</msub>
</mrow>
</math></span> ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{T_E}}}{{{T_ \odot }}} = ">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mi>E</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mo>⊙</mo>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\frac{{{M_E}}}{{{L_E}}}}}{{\frac{{{M_ \odot }}}{{{L_ \odot }}}}} = \frac{{0.64}}{{0.21}} = ">
<mfrac>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>M</mi>
<mi>E</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>L</mi>
<mi>E</mi>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>M</mi>
<mo>⊙</mo>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>L</mi>
<mo>⊙</mo>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.64</mn>
</mrow>
<mrow>
<mn>0.21</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 3.0 ✔</p>
<p>T ≈ 27 billion years ✔</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>red giant ✔</p>
<p>planetary nebula ✔</p>
<p>white dwarf ✔</p>
<p> </p>
<p><em>do <strong>NOT</strong> accept supernova, red supergiant, neutron star or black hole as stages</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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<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 graph shows the variation with distance from the Earth of the recessional velocities of distant galaxies.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how Hubble measured the recessional velocities of galaxies.</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>Use the graph to determine the age of the universe in s.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>measured redshift «z» of star ✔</p>
<p>use of Doppler formula <em><strong>OR</strong> </em>z∼v/c <em><strong>OR</strong> v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{c\Delta \lambda }}{\lambda }">
<mfrac>
<mrow>
<mi>c</mi>
<mi mathvariant="normal">Δ</mi>
<mi>λ</mi>
</mrow>
<mi>λ</mi>
</mfrac>
</math></span> to find <em>v</em> ✔</p>
<p> </p>
<p><em>OWTTE</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of gradient or any point on the line to obtain any expression for either <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{H}} = \frac{{\text{v}}}{{\text{d}}}">
<mrow>
<mtext>H</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mtext>v</mtext>
</mrow>
<mrow>
<mtext>d</mtext>
</mrow>
</mfrac>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{t}} = \frac{{\text{d}}}{{\text{v}}}">
<mrow>
<mtext>t</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mtext>d</mtext>
</mrow>
<mrow>
<mtext>v</mtext>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>correct conversion of <em>d</em> to m and v to m/s ✔</p>
<p>= 4.6 × 10<sup>17</sup> «s» ✔</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by dark energy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>two</strong> candidates for dark matter.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>energy filling all space ✔</p>
<p>resulting in a repulsive force/force opposing gravity ✔</p>
<p>accounts for the accelerating universe ✔</p>
<p>makes up about 70% of «the energy» of universe ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>black hole ✔</p>
<p>brown dwarf ✔</p>
<p>massive compact halo object /MACHO✔</p>
<p>neutrinos ✔</p>
<p>weakly interacting massive particle /WIMP ✔</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph shows the variation with time of the cosmic scale factor <em>R</em> of the universe for the flat model of the universe <strong>without</strong> dark energy.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Light from distant galaxies is redshifted. Explain the cosmological origin of this redshift.</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>Draw, on the axes, a graph to show the variation with time of the cosmic scale factor <em>R</em> for the flat model of the universe <strong>with</strong> dark energy.</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>Compare and contrast, the variation with time of the temperature of the cosmic background (CMB) radiation, for the two models from the present time onward.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«according to general relativity» space expands stretching distances between far away objects ✔</p>
<p>wavelengths of photons «received a long time after they were emitted» are thus longer leading to the observed redshift ✔</p>
<p><em>Do not accept references to the Doppler effect</em>.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"> ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«since <em>T </em>∝ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{R}">
<mfrac>
<mn>1</mn>
<mi>R</mi>
</mfrac>
</math></span> » the temperature drops for both models ✔</p>
<p>but in the accelerating model <em>R</em> increases faster and so the temperature drops faster ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Cosmological origin of redshift. The cosmological redshift and variation with time of the cosmic scale factor proved to be a well-mastered concept by many students.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Cosmological origin of redshift. The cosmological redshift and variation with time of the cosmic scale factor proved to be a well-mastered concept by many students.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In (ii) however, many candidates did not directly answer the question, making little to no reference of temperature.</p>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe what is meant by dark matter.</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 distribution of mass in a spherical system is such that the density <em>ρ</em> varies with distance <em>r</em> from the centre as</p>
<p><em>ρ </em>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{k}{{{r^2}}}">
<mfrac>
<mi>k</mi>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>where <em>k</em> is a constant.</p>
<p>Show that the rotation curve of this system is described by</p>
<p><em>v</em> = constant.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Curve A shows the actual rotation curve of a nearby galaxy. Curve B shows the predicted rotation curve based on the visible stars in the galaxy.</p>
<p><img 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"></p>
<p>Explain how curve A provides evidence for dark matter.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>dark matter is invisible/cannot be seen directly<br><em><strong>OR</strong></em><br>does not interact with EM force/radiate light/reflect light<br><br>interacts with gravitational force<br><em><strong>OR</strong></em><br>accounts for galactic rotation curves<br><em><strong>OR</strong></em><br>accounts for some of the “missing” mass/energy of galaxies/the universe</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«from data booklet formula» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{4\pi G\rho }}{3}} r">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mi>G</mi>
<mi>ρ</mi>
</mrow>
<mn>3</mn>
</mfrac>
</msqrt>
<mi>r</mi>
</math></span> substitute to get <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{4\pi Gk}}{3}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mi>G</mi>
<mi>k</mi>
</mrow>
<mn>3</mn>
</mfrac>
</msqrt>
</math></span></p>
<p> </p>
<p><em>Substitution of ρ must be seen.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>curve A shows that the outer regions of the galaxy are rotating faster than predicted</p>
<p>this suggests that there is more mass in the outer regions that is not visible<br><em><strong>OR</strong></em><br>more mass in the form of dark matter</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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><span style="background-color: #ffffff;">Evidence from the Planck space observatory suggests that the density of matter in the universe is about 32 % of the critical density of the universe.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Outline how the light spectra of distant galaxies are used to confirm hypotheses about the expansion of the universe.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">State what is meant by the critical density.</span></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><span style="background-color: #ffffff;">Calculate the density of matter in the universe, using the Hubble constant 70 km s<sup>–1 </sup>Mpc<sup>–1</sup>.</span></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><span style="background-color: #ffffff;">It is estimated that less than 20 % of the matter in the universe is observable. Discuss how scientists use galactic rotation curves to explain this.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">spectra of galaxies are redshifted «compared to spectra on Earth» ✔</span></p>
<p><span style="background-color: #ffffff;">redshift/longer wavelength implies galaxies recede/ move away from us<br><em><strong>OR</strong></em><br>redshift is interpreted as cosmological expansion of space ✔</span></p>
<p><span style="background-color: #ffffff;">«hence universe expands»</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Universe expansion is given, so no mark for repeating this. <br>Do not accept answers based on CMB radiation.</span></em></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mfrac><mrow><mn>392</mn><mo>-</mo><mn>122</mn></mrow><mn>122</mn></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>21</mn></math> <span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>R</mi><msub><mi>R</mi><mn>0</mn></msub></mfrac><mo>=</mo><mo>«</mo><mn>2</mn><mo>.</mo><mn>21</mn><mo>+</mo><mn>1</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>3</mn><mo>.</mo><mn>21</mn></math> <span style="background-color: #ffffff;">✔</span></p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>R</mi><msub><mi>R</mi><mn>0</mn></msub></mfrac><mo>=</mo><mfrac><mstyle displaystyle="true"><mn>392</mn></mstyle><mn>122</mn></mfrac></math> </em><span style="background-color: #ffffff;">✔</span></p>
<p>= 3.21 <span style="background-color: #ffffff;">✔</span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">density of flat/Euclidean universe<br><em><strong>OR</strong></em><br>density for which universe has zero curvature<br><em><strong>OR</strong></em><br>density resulting in universe expansion rate tending to zero ✔</span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>70</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mfenced><mrow><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mn>3</mn><mo>.</mo><mn>26</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>46</mn><mo>×</mo><msup><mn>10</mn><mn>15</mn></msup></mrow></mfenced></mfrac><mo>=</mo><mo>»</mo><mn>2</mn><mo>.</mo><mn>27</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>18</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo>×</mo><mfrac><mrow><mn>3</mn><mo>×</mo><msup><mfenced><mrow><mn>2</mn><mo>.</mo><mn>27</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>18</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mn>8</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>27</mn></mrow></msup><mo> </mo><mo>«</mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>»</mo></math><span style="background-color: #ffffff;">✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: MP1 for conversion of H to base units. <br>Allow ECF from MP1, but NOT if H is left as 70.</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">rotation speed of galaxies is larger than expected away from the centre ✔<br></span></p>
<p><span style="background-color: #ffffff;">there must be more mass «at the edges» than is visually observable «indicating the presence of dark matter» ✔</span></p>
<div class="question_part_label">b(iii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(iii).</div>
</div>
<br><hr><br><div class="specification">
<p>Type Ia supernovae typically have a peak luminosity of around 5 × 10<sup>5</sup> L<sub>s</sub>, where L<sub>s</sub> is the luminosity of the Sun (3.8 × 10<sup>26</sup> W). A type Ia supernova is observed with an apparent peak brightness of 1.6 × 10<sup>–6</sup> W m<sup>–2</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the formation of a type Ia supernova.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the distance to the supernova is approximately 3.1 × 10<sup>18</sup> m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one </strong>assumption made in your calculation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a white dwarf accretes mass <strong>«</strong>from a binary partner<strong>»</strong></p>
<p>when the mass becomes more than the Chandrasekhar limit (1.4M<sub>s</sub>) <strong>«</strong>then asupernova explosion takes place<strong>»</strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>d = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{\text{L}}}{{4\pi {\text{b}}}}} = \sqrt {\frac{{5 \times {{10}^5} \times 3.8 \times {{10}^{26}}}}{{4\pi \times 1.6 \times {{10}^{ - 6}}}}} ">
<msqrt>
<mfrac>
<mrow>
<mtext>L</mtext>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mrow>
<mtext>b</mtext>
</mrow>
</mrow>
</mfrac>
</msqrt>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>3.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>26</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mo>×</mo>
<mn>1.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p>d = 3.07 × 10<sup>18</sup> <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><em>At least 3 sig fig required for MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>type Ia supernova can be used as standard candles</p>
<p>there is no dust absorbing light between Earth and supernova</p>
<p>their supernova is a typical type Ia</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The homogeneous model of the universe predicts that it may be considered as a spherical cloud of matter of radius r and uniform density <em>ρ</em>. Consider a particle of mass <em>m</em> at the edge of the universe moving with velocity <em>v</em> and obeying Hubble’s law.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify that the total energy of this particle is <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{1}{2}m{v^2} - \frac{4}{3}\pi G{\text{r}}{r^2}m">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mi>G</mi>
<mrow>
<mtext>r</mtext>
</mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>m</mi>
</math></span>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At critical density there is zero total energy. Show that the critical density of the universe is: <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{{\text{r}}_c} = \frac{{3H_0^2}}{{8\pi G}}">
<mrow>
<msub>
<mrow>
<mtext>r</mtext>
</mrow>
<mi>c</mi>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>3</mn>
<msubsup>
<mi>H</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>8</mn>
<mi>π</mi>
<mi>G</mi>
</mrow>
</mfrac>
</math></span>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The accepted value for the Hubble constant is 2.3 × 10<sup>−18</sup> s<sup>−1</sup>. Estimate the critical density of the universe.</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>total energy=kinetic energy+potential energy</p>
<p><em><strong>OR</strong></em></p>
<p>total energy= <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}m{v^2} - \frac{{GMm}}{r}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mi>r</mi>
</mfrac>
</math></span></span> ✔</p>
<p>substitution of <em>M </em>= <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}\pi {r^3}\rho ">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mi>ρ</mi>
</math></span></span> ✔</p>
<p>«Hence answer given»</p>
<p><em>Answer given so for MP2 look for clear evidence that M<sub>Universe</sub></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{4}{3}\pi {r^3}\rho } \right)">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mi>ρ</mi>
</mrow>
<mo>)</mo>
</mrow>
</math></span><em> is stated and substituted.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>substitutes <em>H<sub>0</sub>r</em> for <em>v</em> ✔</p>
<p>«total energy = 0»</p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}mH_0^2{r^2} = \frac{4}{3}\pi G\rho {r^2}m">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<msubsup>
<mi>H</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mi>G</mi>
<mi>ρ</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>m</mi>
</math></span> </span>✔</p>
<p>«hence <em>ρ<sub>c </sub></em>= <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3H_0^2}}{{8\pi G}}">
<mfrac>
<mrow>
<mn>3</mn>
<msubsup>
<mi>H</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>8</mn>
<mi>π</mi>
<mi>G</mi>
</mrow>
</mfrac>
</math></span></span> »</p>
<p><em>Answer given, check working carefully.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>9.5 × 10<sup>−27</sup> « kgm<sup>–3</sup>» ✔</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The vast majority of the candidates could state that the total energy is equal to the sum of the kinetic and potential energies but quite a few did not use the correct formula for the gravitational potential energy. The formula for the mass of the sun was usually correctly substituted.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a relatively easy demonstration given the equation in 22a. However many candidates did not show the process followed in a coherent manner that could be understood by examiners.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The question was well answered by many candidates.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the mechanism of formation of type I a supernovae.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the mechanism of formation of type II supernovae.</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>Suggest why type I a supernovae were used in the study that led to the conclusion that the expansion of the universe is accelerating.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>a white dwarf star in a binary system accretes mass from the companion star ✔</p>
<p>when the white dwarf star mass reaches the Chandrasekhar limit the star explodes «due to fusion reactions»✔</p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>it can be formed in the collision of two white dwarf stars ✔</p>
<p>where shock waves from the collision rip both stars apart ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a red supergiant star explodes when its core collapses ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«it was necessary» to measure the distance «of very distant objects more accurately» ✔</p>
<p>type I a are standard candles/objects of known luminosity ✔</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Supernova. The mechanism of the formation of supernovae Ia was well described by many candidates.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In (ii), for the description of the mechanism of type II supernovae, many responses lacked detail and did not make mention of core collapse.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part b) was well answered by most of the prepared candidates with a good understanding that these stars behave as “standard candles”.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Proxima Centauri is a main sequence star with a mass of 0.12 solar masses.</span></p>
<p><span style="background-color: #ffffff;">Estimate <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>lifetime</mi><mo> </mo><mi>on</mi><mo> </mo><mi>main</mi><mo> </mo><mi>sequence</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Proxima</mi><mo> </mo><mi>Centauri</mi></mrow><mrow><mi>lifetime</mi><mo> </mo><mi>on</mi><mo> </mo><mi>main</mi><mo> </mo><mi>sequence</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Sun</mi></mrow></mfrac></math>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Describe why iron is the heaviest element that can be produced by nuclear fusion processes inside stars.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Discuss <strong>one</strong> process by which elements heavier than iron are formed in stars.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">realization that lifetime <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>∝</mo><mfrac><mi>mass</mi><mi>luminosity</mi></mfrac></math> ✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>T</mi><msub><mi>T</mi><mo>⊙</mo></msub></mfrac><mo>=</mo><msup><mfenced><mfrac><mi>M</mi><msub><mi>M</mi><mo>⊙</mo></msub></mfrac></mfenced><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow></msup><mo>=</mo><mn>0</mn><mo>.</mo><msup><mn>12</mn><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow></msup><mo>=</mo><mn>200</mn></math> <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">the binding energy per nucleon is a maximum for iron ✔<br></span></p>
<p><span style="background-color: #ffffff;">formation of heavier elements than iron by fusion is not energetically possible ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: For MP2 some reference to energy is needed</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 1 — s-process</strong></em><br>s-process involves «slow» neutron capture ✔<br>in s-process beta decay occurs before another neutron is captured ✔<br>s-process occurs in giant stars «AGB stars» ✔<br>s-process terminates at bismuth/lead/polonium ✔</span></p>
<p><span style="background-color: #ffffff;"><br><em><strong>ALTERNATIVE 2 — r-process</strong></em><br>r-process involves «rapid» neutron capture ✔<br>in r-process further neutrons are captured before the beta decay occurs ✔<br>r-process occurs in type II supernovae ✔<br>r-process can lead to elements heavier than bismuth/lead/polonium ✔<br></span></p>
<p><em><span style="background-color: #ffffff;">N</span></em><em><span style="background-color: #ffffff;">OTE: If the type of the process (r or s/rapid or slow) is not mentioned, award <strong>[2 max]</strong>.</span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[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="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the temperature of the universe is inversely proportional to the cosmic scale factor.</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 present temperature of the cosmic microwave background (CMB) radiation is 3 K. Estimate the size of the universe relative to the present size of the universe when the temperature of the CMB was 300 K.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«wavelength of light/CBR» <em>λ</em> ∝ <em>R</em> ✔</p>
<p>reference to Wien’s law showing that <em>λ</em> ∝ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{T}">
<mfrac>
<mn>1</mn>
<mi>T</mi>
</mfrac>
</math></span> ✔</p>
<p>combine to get result ✔</p>
<p> </p>
<p><em>OWTTE</em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{R_{{\text{past}}}}}}{{{R_{{\text{now}}}}}} = \frac{3}{{300}} = 0.01">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mrow>
<mtext>past</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mrow>
<mtext>now</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mrow>
<mn>300</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.01</mn>
</math></span> ✔</p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to the Jeans criterion, why a cold dense gas cloud is more likely to form new stars than a hot diffuse gas cloud.</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>Explain how neutron capture can produce elements with an atomic number greater than iron.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>For a star to form<strong>»</strong>: magnitude of PE of gas cloud > KE of gas cloud</p>
<p><strong><em>OR</em></strong></p>
<p>Mass of cloud > Jean's mass</p>
<p><strong><em>OR</em></strong></p>
<p>Jean’s criterion is the critical mass</p>
<p> </p>
<p>hence a hot diffuse cloud could have KE which is too large/PE too small</p>
<p><strong><em>OR</em></strong></p>
<p>hence a cold dense cloud will have low KE/high PE</p>
<p><strong><em>OR</em></strong></p>
<p>a cold dense cloud is more likely to exceed Jeans mass</p>
<p><strong><em>OR</em></strong></p>
<p>a hot diffuse cloud is less likely to exceed the Jeans mass</p>
<p> </p>
<p>Accept <em>E</em><em><sub>p</sub> +</em> <em>E</em><em><sub>k</sub> <</em> <em>0</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Neutron capture creates heavier isotopes / heavier nuclei / more unstable nucleus</p>
<p>β<sup>–</sup> decay of heavy elements/iron increases atomic number <strong>«</strong>by 1<strong>»</strong></p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain the formation of a type I a supernova which enables the star to be used as a standard candle.</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><span style="background-color:#ffffff;">Describe the r process which occurs during type II supernovae nucleosynthesis.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>white dwarf attracts mass from another star ✔</p>
<p>explodes/becomes supernova when mass equals/exceeds the Chandrasekhar limit / 1.4M<sub>SUN</sub> ✔</p>
<p>hence luminosity of all type I a supernova is the same ✔</p>
<p><em>OWTTE</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">«successive» rapid neutron capture ✔<br></span></p>
<p><span style="background-color:#ffffff;">faster than «β» decay can occur ✔<br></span></p>
<p><span style="background-color:#ffffff;">results in formation of heavier/neutron rich isotopes ✔</span></p>
<p><em>OWTTE</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The formation of Type 1a supernovae was well known by most candidates but few were able to explain how this process resulted in a standard candle.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates could describe the r process correctly but quite a large number of candidates seemed completely at a loss and could not relate the r process to neutron capture.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>