File "HL-paper3.html"
Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Physics/Option D HTML/HL-paper3html
File size: 223.37 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html>
<html>
<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../../../../../../index.html">Home</a>
</li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
<div class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<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>
<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 src="data:image/png;base64,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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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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 src="data:image/png;base64,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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>
<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>
<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>
<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>
<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 src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>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>
<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>
<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>
<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>
<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 src="data:image/png;base64,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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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<br><hr><br>