Unit 5 High-Yield Topics | Flowxiom<\/title>\n<meta name=\"description\" content=\"Unit 5 High-Yield Topics \u2014 Edexcel A-level Physics WPH. Question types: Identify SHM; describe phase relationships; calculate velocity\/acceleration; energy g...\">\n<link rel=\"canonical\" href=\"https:\/\/flowxiom.com\/edexcel-physics-unit-5-high-yield-topics\/\">\n<script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"FAQPage\",\n \"mainEntity\": [\n {\n \"@type\": \"Question\",\n \"name\": \"Q1. SHM: amplitude \\\\(A = 0.1\\\\ \\\\text{m}\\\\), \\\\(\\\\omega = 10\\\\ \\\\text{rad\/s}\\\\). Find maximum speed and maximum acceleration.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(v_{max} = \\\\omega A = 10 \\\\times 0.1 = \\\\mathbf{1.0\\\\ \\\\text{m\/s}}\\\\) \\n \\\\(a_{max} = \\\\omega^2 A = 100 \\\\times 0.1 = \\\\mathbf{10\\\\ \\\\text{m\/s}^2}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q2. Mass defect \\\\(\\\\Delta m = 0.00318\\\\ \\\\text{u}\\\\). Find the energy released in MeV.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(E = 0.00318 \\\\times 931.5 = \\\\mathbf{2.96\\\\ \\\\text{MeV}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q3. Initial activity \\\\(A_0 = 800\\\\ \\\\text{Bq}\\\\), half-life \\\\(T_{1\/2} = 2\\\\ \\\\text{h}\\\\). Find the activity after \\\\(6\\\\ \\\\text{h}\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(6\/2 = 3\\\\) half-lives: \\n \\\\(A = 800 \\\\times (1\/2)^3 = \\\\mathbf{100\\\\ \\\\text{Bq}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q4. A star has surface temperature \\\\(T = 6000\\\\ \\\\text{K}\\\\) and radius \\\\(R = 8.0\\\\times10^8\\\\ \\\\text{m}\\\\). Find: (a) peak wavelength; (b) total luminosity.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"(a) \\\\(\\\\lambda_{max} = \\\\dfrac{2.898\\\\times10^{-3}}{6000} = \\\\mathbf{4.83\\\\times10^{-7}\\\\ \\\\text{m}}\\\\) (483 nm) \\n (b) \\\\(L = 4\\\\pi \\\\times (8.0\\\\times10^8)^2 \\\\times 5.67\\\\times10^{-8} \\\\times (6000)^4 = \\\\mathbf{5.9\\\\times10^{26}\\\\ \\\\text{W}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q5. Hydrogen spectral line at rest: \\\\(\\\\lambda_0 = 656\\\\ \\\\text{nm}\\\\); observed: \\\\(\\\\lambda = 669\\\\ \\\\text{nm}\\\\). Find the recession speed and estimate the distance. (\\\\(H_0 = 70\\\\ \\\\text{km s}^{-1}\\\\text{Mpc}^{-1}\\\\))\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(\\\\Delta\\\\lambda = 13\\\\ \\\\text{nm}\\\\) \\n \\\\(v = 3.0\\\\times10^8 \\\\times \\\\dfrac{13}{656} = \\\\mathbf{5.95\\\\times10^6\\\\ \\\\text{m\/s}}\\\\) \\n \\\\(d = 5950 \\\\div 70 = \\\\mathbf{85\\\\ \\\\text{Mpc}}\\\\)\"\n }\n }\n ]\n}\n<\/script>\n\n<script>\nMathJax = {\n tex: { inlineMath: [['\\\\(','\\\\)']], displayMath: [['\\\\[','\\\\]']] },\n svg: { fontCache: 'global' }\n};\n<\/script>\n<script async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-svg.js\"><\/script>\n\n<style>\n:root{--accent:#2563eb;--warn-bg:#fef9c3;--warn-border:#ca8a04;--formula-bg:#eff6ff;--formula-border:#2563eb;}\nbody{font-family:system-ui,sans-serif;max-width:860px;margin:0 auto;padding:1.5rem;line-height:1.7;color:#1e293b;}\nh1{font-size:2rem;border-bottom:3px solid var(--accent);padding-bottom:.4rem;}\nh2{font-size:1.4rem;color:var(--accent);margin-top:2rem;}\nh3{font-size:1.1rem;margin-top:1.4rem;}\ntable{border-collapse:collapse;width:100%;margin:1rem 0;}\nth,td{border:1px solid #cbd5e1;padding:.5rem .75rem;text-align:left;}\nth{background:#e2e8f0;}\npre,code{background:#f1f5f9;border-radius:4px;}\npre{padding:1rem;overflow-x:auto;}\ncode{padding:.1rem .3rem;font-size:.9em;}\n.seo-warning-box{background:var(--warn-bg);border-left:4px solid var(--warn-border);padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\n.seo-note-box{background:#f0fdf4;border-left:4px solid #16a34a;padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\nsection.formula-card{background:var(--formula-bg);border:1px solid var(--formula-border);border-radius:8px;padding:1rem 1.25rem;margin:1.5rem 0;}\ndetails{border:1px solid #e2e8f0;border-radius:6px;padding:.5rem 1rem;margin:.75rem 0;}\nsummary{cursor:pointer;font-weight:600;}\n.answer-block{margin-top:.5rem;padding-top:.5rem;border-top:1px solid #e2e8f0;overflow-x:auto;}\n.answer-block p{margin:.25rem 0;}\n.numbered-step{padding-left:1.5rem;position:relative;}\nhr{border:none;border-top:1px solid #e2e8f0;margin:2rem 0;}\n.toc{background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;padding:1rem 1.5rem;margin-bottom:2rem;}\n.toc h2{margin-top:0;font-size:1.1rem;}\n.toc ul{margin:0;padding-left:1.2rem;}\n.toc a{color:var(--accent);text-decoration:none;}\n.site-footer{margin-top:3rem;padding-top:1rem;border-top:2px solid var(--accent);font-size:.9rem;color:#64748b;}\n<\/style>\n<\/head>\n<body>\n<nav class=\"toc\"><h2>Contents<\/h2><ul>\n <li><a href=\"#topic-1-simple-harmonic-motion-frequent-6mark-question\">Topic 1: Simple Harmonic Motion (frequent 6-mark question)<\/a><\/li>\n <li><a href=\"#topic-2-kinetic-theory-of-gases-frequent-6mark-question\">Topic 2: Kinetic Theory of Gases (frequent 6-mark question)<\/a><\/li>\n <li><a href=\"#topic-3-nuclear-decay-and-halflife\">Topic 3: Nuclear Decay and Half-Life<\/a><\/li>\n <li><a href=\"#topic-4-binding-energy-and-mass-defect\">Topic 4: Binding Energy and Mass Defect<\/a><\/li>\n <li><a href=\"#topic-5-gravitational-fields\">Topic 5: Gravitational Fields<\/a><\/li>\n <li><a href=\"#topic-6-thermodynamics-specific-heat-capacity-and-latent-heat\">Topic 6: Thermodynamics \u2014 Specific Heat Capacity and Latent Heat<\/a><\/li>\n <li><a href=\"#topic-7-damping-and-resonance\">Topic 7: Damping and Resonance<\/a><\/li>\n <li><a href=\"#topic-8-astrophysics-stellar-physics-and-the-hr-diagram\">Topic 8: Astrophysics \u2014 Stellar Physics and the H-R Diagram<\/a><\/li>\n <li><a href=\"#topic-9-astrophysics-cosmic-distances-and-hubbles-law\">Topic 9: Astrophysics \u2014 Cosmic Distances and Hubble’s Law<\/a><\/li>\n <li><a href=\"#practice-questions\">Practice Questions<\/a><\/li>\n<\/ul><\/nav>\n<h1>Unit 5 High-Yield Topics<\/h1>\n<p><strong>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<\/strong><\/p>\n<p><em>Not everything. Just what’s on the paper. High-frequency topics only \u2014 covering ~80% of exam marks.<\/em><\/p>\n<p>Edexcel A-level Physics | Thermal, Nuclear, SHM & Astrophysics | WPH14 & WPH15<\/p>\n<hr>\n<h2 id=\"topic-1-simple-harmonic-motion-frequent-6mark-question\">Topic 1: Simple Harmonic Motion (frequent 6-mark question)<\/h2>\n<p><strong>Question types:<\/strong> Identify SHM; describe phase relationships; calculate velocity\/acceleration; energy graphs.<\/p>\n<h3 id=\"two-conditions-for-shm-both-required\">Two Conditions for SHM (both required)<\/h3>\n<p class=\"numbered-step\">Acceleration is <strong>proportional to displacement<\/strong> from equilibrium<\/p>\n<p class=\"numbered-step\">Acceleration is always <strong>directed towards the equilibrium position<\/strong> (opposite to displacement)<\/p>\n<p>\\[a = -\\omega^2 x\\]<\/p>\n<h3 id=\"formulae\">Formulae<\/h3>\n<p>\\[x = A\\cos(\\omega t) \\qquad v = -A\\omega\\sin(\\omega t) \\qquad a = -A\\omega^2\\cos(\\omega t)\\]<\/p>\n<p>\\[v_{max} = \\omega A \\text{ (at equilibrium)} \\qquad a_{max} = \\omega^2 A \\text{ (at maximum displacement)}\\]<\/p>\n<h3 id=\"phase-relationships\">Phase Relationships<\/h3>\n<table>\n<thead><tr><th>Position<\/th><th>Displacement \\(x\\)<\/th><th>Velocity \\(v\\)<\/th><th>Acceleration \\(a\\)<\/th><\/tr><\/thead>\n<tr><td>Equilibrium<\/td><td>0<\/td><td><strong>maximum<\/strong><\/td><td>0<\/td><\/tr>\n<tr><td>Maximum displacement<\/td><td>\\(\\pm A\\)<\/td><td>0<\/td><td><strong>maximum<\/strong> (opposite direction)<\/td><\/tr>\n<\/table>\n\n<ul>\n<li>\\(v\\) leads \\(x\\) by 90\u00b0<\/li>\n<li>\\(a\\) is in antiphase with \\(x\\) (180\u00b0 phase difference)<\/li>\n<\/ul>\n<h3 id=\"period-formulae\">Period Formulae<\/h3>\n<p>\\[T_{spring} = 2\\pi\\sqrt{\\frac{m}{k}} \\qquad T_{pendulum} = 2\\pi\\sqrt{\\frac{L}{g}}\\]<\/p>\n<h3 id=\"shm-energy\">SHM Energy<\/h3>\n<p>\\[E_k = \\frac{1}{2}m\\omega^2(A^2 – x^2) \\qquad E_p = \\frac{1}{2}m\\omega^2 x^2 \\qquad E_{total} = \\frac{1}{2}m\\omega^2 A^2\\]<\/p>\n<p>Total energy is constant; \\(E_k + E_p = \\text{constant}\\).<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Both conditions must be stated: proportional to displacement <strong>AND<\/strong> directed towards equilibrium<\/li>\n<li>\u274c At equilibrium: maximum <strong>velocity<\/strong>, zero acceleration<\/li>\n<li>\u274c Pendulum period is independent of mass \u2014 depends only on \\(L\\) and \\(g\\)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-2-kinetic-theory-of-gases-frequent-6mark-question\">Topic 2: Kinetic Theory of Gases (frequent 6-mark question)<\/h2>\n<p><strong>Question types:<\/strong> Explain how gas pressure changes with temperature or volume.<\/p>\n<h3 id=\"answer-chain-temperature-pressure\">Answer Chain \u2014 Temperature \u2191 \u2192 Pressure \u2191<\/h3>\n<p class=\"numbered-step\">Temperature increases \u2192 mean kinetic energy of molecules increases<\/p>\n<p class=\"numbered-step\">Mean speed of molecules increases<\/p>\n<p class=\"numbered-step\">Greater change in momentum per collision with the wall<\/p>\n<p class=\"numbered-step\">Molecules collide with the wall more frequently<\/p>\n<p class=\"numbered-step\">Greater resultant force on the wall<\/p>\n<p class=\"numbered-step\">Area unchanged \u2192 <strong>pressure increases<\/strong><\/p>\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f Both steps 3 and 5 are required \u2014 neither can be omitted.<\/p>\n<\/div>\n<h3 id=\"ideal-gas-law\">Ideal Gas Law<\/h3>\n<p>\\[\\frac{pV}{T} = \\text{constant} \\qquad pV = nRT \\qquad R = 8.31\\ \\text{J mol}^{-1} \\text{K}^{-1}\\]<\/p>\n<p><strong>Temperature must be in Kelvin<\/strong>: \\(T = \\theta + 273\\)<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Using \u00b0C instead of K \u2014 most common error<\/li>\n<li>\u274c Must mention <strong>both<\/strong>: greater force per collision <strong>and<\/strong> higher collision frequency<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-3-nuclear-decay-and-halflife\">Topic 3: Nuclear Decay and Half-Life<\/h2>\n<p><strong>Question types:<\/strong> Balance nuclear equations; half-life calculations; explain randomness and spontaneity.<\/p>\n<h3 id=\"three-types-of-radiation\">Three Types of Radiation<\/h3>\n<table>\n<thead><tr><th>Radiation<\/th><th>Nature<\/th><th>Example equation<\/th><th>Ionisation & penetration<\/th><\/tr><\/thead>\n<tr><td>\\(\\alpha\\)<\/td><td>Helium nucleus \\(^4_2\\text{He}\\)<\/td><td>\\(^A_ZX \\to ^{A-4}_{Z-2}Y + ^4_2\\alpha\\)<\/td><td>Strongly ionising; stopped by paper<\/td><\/tr>\n<tr><td>\\(\\beta^-\\)<\/td><td>Electron \\(^0_{-1}e\\)<\/td><td>\\(^A_ZX \\to ^A_{Z+1}Y + ^0_{-1}\\beta + \\bar{\\nu}_e\\)<\/td><td>Moderately ionising; stopped by aluminium<\/td><\/tr>\n<tr><td>\\(\\gamma\\)<\/td><td>High-energy EM radiation<\/td><td>Accompanies \u03b1\/\u03b2 decay<\/td><td>Weakly ionising; requires lead shielding<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f \u03b2\u207b decay: neutron \u2192 proton + electron + <strong>electron antineutrino<\/strong> \u2014 do not omit the antineutrino.<\/p>\n<\/div>\n<h3 id=\"balancing-nuclear-equations\">Balancing Nuclear Equations<\/h3>\n<ul>\n<li>Mass number \\(A\\) (top): sum must be equal on both sides<\/li>\n<li>Atomic number \\(Z\\) (bottom): sum must be equal on both sides<\/li>\n<\/ul>\n<h3 id=\"halflife-calculations\">Half-Life Calculations<\/h3>\n<p>\\[N = N_0 \\left(\\frac{1}{2}\\right)^{t\/T_{1\/2}} \\qquad A = \\lambda N \\qquad T_{1\/2} = \\frac{\\ln 2}{\\lambda} = \\frac{0.693}{\\lambda}\\]<\/p>\n<h3 id=\"randomness-and-spontaneity\">Randomness and Spontaneity<\/h3>\n<ul>\n<li><strong>Random<\/strong>: It is impossible to predict which specific nucleus will decay or at what time<\/li>\n<li><strong>Spontaneous<\/strong>: Decay is unaffected by external conditions such as temperature, pressure or chemical state<\/li>\n<\/ul>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Omitting the electron antineutrino \\(\\bar{\\nu}_e\\) in \u03b2\u207b decay<\/li>\n<li>\u274c Both activity \\(A\\) and number of nuclei \\(N\\) follow the same exponential decay law<\/li>\n<li>\u274c Must subtract <strong>background radiation<\/strong> count rate \u2014 measure it first<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-4-binding-energy-and-mass-defect\">Topic 4: Binding Energy and Mass Defect<\/h2>\n<p><strong>Question types:<\/strong> Calculate binding energy; judge whether fission\/fusion releases energy; read binding energy per nucleon graph.<\/p>\n<h3 id=\"calculation-steps\">Calculation Steps<\/h3>\n<p class=\"numbered-step\">Mass defect: \\(\\Delta m = \\text{sum of individual nucleon masses} – \\text{actual nuclear mass}\\)<\/p>\n<p class=\"numbered-step\">Binding energy: \\(E = \\Delta mc^2\\)<\/p>\n<p class=\"numbered-step\">If \\(\\Delta m\\) in atomic mass units: \\(E\\text{(MeV)} = \\Delta m\\text{(u)} \\times 931.5\\)<\/p>\n<h3 id=\"binding-energy-per-nucleon-curve\">Binding Energy Per Nucleon Curve<\/h3>\n<ul>\n<li>Iron-56 (\\(^{56}\\)Fe) is at the <strong>peak<\/strong> \u2014 most stable nucleus<\/li>\n<li><strong>Fission<\/strong>: heavy nucleus splits from right side (low) to middle (higher) \u2192 energy <strong>released<\/strong><\/li>\n<li><strong>Fusion<\/strong>: light nuclei fuse from left side (low) to middle (higher) \u2192 energy <strong>released<\/strong><\/li>\n<\/ul>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c If \\(\\Delta m\\) in kg: use \\(E = \\Delta mc^2\\); if \\(\\Delta m\\) in u: multiply by 931.5 MeV\/u<\/li>\n<li>\u274c Energy is released when binding energy per nucleon <strong>increases<\/strong><\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-5-gravitational-fields\">Topic 5: Gravitational Fields<\/h2>\n<p><strong>Question types:<\/strong> Calculate gravitational field strength and potential; satellite orbits; comparison with electric fields.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[g = \\frac{GM}{r^2} \\qquad \\phi = -\\frac{GM}{r} \\qquad g = -\\frac{\\Delta\\phi}{\\Delta r}\\]<\/p>\n<ul>\n<li>Gravitational potential \\(\\phi\\) is <strong>always negative<\/strong> (zero at infinity, more negative closer to source)<\/li>\n<li>Field strength = negative of potential gradient<\/li>\n<\/ul>\n<h3 id=\"satellite-orbits\">Satellite Orbits<\/h3>\n<p>\\[\\frac{GMm}{r^2} = \\frac{mv^2}{r} \\implies v = \\sqrt{\\frac{GM}{r}} \\implies T^2 = \\frac{4\\pi^2}{GM}r^3\\]<\/p>\n<p>Higher orbit \u2192 smaller speed, longer period.<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Gravitational potential increases (becomes less negative) as distance from source increases<\/li>\n<li>\u274c Orbital speed <strong>decreases<\/strong> as orbital radius increases<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-6-thermodynamics-specific-heat-capacity-and-latent-heat\">Topic 6: Thermodynamics \u2014 Specific Heat Capacity and Latent Heat<\/h2>\n<p><strong>Question types:<\/strong> Calculate energy for heating; explain molecular reason why temperature stays constant during change of state.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[Q = mc\\Delta\\theta \\quad \\text{(temperature change \u2014 specific heat capacity, J kg}^{-1}\\text{ K}^{-1}\\text{)}\\]<\/p>\n<p>\\[Q = mL \\quad \\text{(change of state \u2014 temperature constant \u2014 specific latent heat, J kg}^{-1}\\text{)}\\]<\/p>\n<p>\\[\\Delta U = Q + W \\quad \\text{(first law of thermodynamics)}\\]<\/p>\n<h3 id=\"why-temperature-stays-constant-during-a-change-of-state\">Why Temperature Stays Constant During a Change of State<\/h3>\n<p>Energy supplied goes into increasing <strong>molecular potential energy<\/strong> (overcoming intermolecular forces), not kinetic energy. Temperature is proportional to mean kinetic energy \u2014 which does not change \u2192 temperature stays constant.<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Temperature constant does NOT mean internal energy constant \u2014 internal energy increases (as potential energy)<\/li>\n<li>\u274c Heat loss to surroundings \u2192 smaller measured temperature rise \u2192 calculated \\(c\\) is <strong>too large<\/strong><\/li>\n<li>\u274c Temperature difference may use K or \u00b0C (same magnitude); absolute temperature must use K<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-7-damping-and-resonance\">Topic 7: Damping and Resonance<\/h2>\n<p><strong>Question types:<\/strong> Describe features of different oscillations; explain resonance; sketch resonance curves for different damping.<\/p>\n<h3 id=\"types-of-oscillation\">Types of Oscillation<\/h3>\n<table>\n<thead><tr><th>Type<\/th><th>Amplitude<\/th><th>Frequency<\/th><th>Graph<\/th><\/tr><\/thead>\n<tr><td>Free<\/td><td>Constant<\/td><td>Natural frequency \\(f_0\\)<\/td><td>Constant-amplitude sine wave<\/td><\/tr>\n<tr><td>Light damping<\/td><td>Gradually decreases<\/td><td>Approximately \\(f_0\\)<\/td><td>Exponentially decaying sine wave<\/td><\/tr>\n<tr><td>Heavy damping<\/td><td>Monotonically \u2192 0<\/td><td>No oscillation<\/td><td>Slowly returns to equilibrium<\/td><\/tr>\n<tr><td>Critical damping<\/td><td>Fastest return<\/td><td>No oscillation<\/td><td>Fastest return with no oscillation<\/td><\/tr>\n<\/table>\n\n<h3 id=\"forced-oscillation-and-resonance\">Forced Oscillation and Resonance<\/h3>\n<ul>\n<li><strong>Forced oscillation<\/strong>: system driven at driving frequency \\(f_d\\) \u2014 oscillates at \\(f_d\\), not \\(f_0\\)<\/li>\n<li><strong>Resonance<\/strong>: when \\(f_d = f_0\\) \u2192 <strong>maximum amplitude<\/strong><\/li>\n<\/ul>\n<h3 id=\"effect-of-damping-on-resonance-curve\">Effect of Damping on Resonance Curve<\/h3>\n<ul>\n<li>More damping \u2192 lower, broader resonance peak; peak shifts slightly below \\(f_0\\)<\/li>\n<li>Light damping \u2192 tall, sharp peak<\/li>\n<\/ul>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Resonance occurs when driving frequency = <strong>natural frequency<\/strong><\/li>\n<li>\u274c Damping reduces amplitude \u2014 it does <strong>not<\/strong> change the natural frequency<\/li>\n<li>\u274c Frequency of forced oscillation = driving frequency, not natural frequency<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-8-astrophysics-stellar-physics-and-the-hr-diagram\">Topic 8: Astrophysics \u2014 Stellar Physics and the H-R Diagram<\/h2>\n<p><strong>Question types:<\/strong> Use Wien’s law to find temperature; Stefan-Boltzmann law to compare luminosity; identify star types on H-R diagram.<\/p>\n<h3 id=\"two-key-laws\">Two Key Laws<\/h3>\n<p>\\[\\lambda_{max} T = 2.898 \\times 10^{-3}\\ \\text{m K} \\quad \\text{(Wien’s displacement law)}\\]<\/p>\n<p>\\[L = 4\\pi R^2 \\sigma T^4 \\qquad \\sigma = 5.67\\times10^{-8}\\ \\text{W m}^{-2}\\text{K}^{-4}\\]<\/p>\n<ul>\n<li>Smaller \\(\\lambda_{max}\\) \u2192 higher temperature \u2192 bluer colour<\/li>\n<li>Luminosity is extremely sensitive to temperature (\\(T^4\\))<\/li>\n<\/ul>\n<h3 id=\"four-regions-of-the-hr-diagram\">Four Regions of the H-R Diagram<\/h3>\n<table>\n<thead><tr><th>Region<\/th><th>Position<\/th><th>Temperature<\/th><th>Luminosity<\/th><th>Example<\/th><\/tr><\/thead>\n<tr><td>Main Sequence<\/td><td>Diagonal (top-left \u2192 bottom-right)<\/td><td>High \u2192 low<\/td><td>High \u2192 low<\/td><td>Sun<\/td><\/tr>\n<tr><td>Red Giant<\/td><td>Top-right<\/td><td>Low (red)<\/td><td>Very high<\/td><td>Betelgeuse<\/td><\/tr>\n<tr><td>White Dwarf<\/td><td>Bottom-left<\/td><td>High (white)<\/td><td>Very low<\/td><td>Sirius B<\/td><\/tr>\n<tr><td>Supergiant<\/td><td>Top-right (above red giant)<\/td><td>Low<\/td><td>Highest<\/td><td>\u2014<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-note-box\">\n<p>H-R diagram temperature axis increases from <strong>right to left<\/strong> \u2014 opposite to the usual convention.<\/p>\n<\/div>\n<h3 id=\"stellar-evolution\">Stellar Evolution<\/h3>\n<p><strong>Low-mass stars<\/strong> (\\(< 8M_\\odot\\), e.g. Sun): Main sequence \u2192 Red giant \u2192 Planetary nebula \u2192 <strong>White dwarf<\/strong><\/p>\n<p><strong>High-mass stars<\/strong> (\\(> 10M_\\odot\\)): Main sequence \u2192 Red supergiant \u2192 <strong>Supernova<\/strong> \u2192 Neutron star (\\(M_{remnant} < 3M_\\odot\\)) or <strong>Black hole<\/strong> (\\(M_{remnant} > 3M_\\odot\\))<\/p>\n<div class=\"seo-note-box\">\n<p>Chandrasekhar limit: \\(1.4M_\\odot\\) \u2014 upper mass limit for a white dwarf.<\/p>\n<\/div>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Right side of H-R diagram = low temperature (cool, red stars)<\/li>\n<li>\u274c White dwarf: high \\(T\\), low \\(L\\) \u2192 very small radius. Red giant: low \\(T\\), high \\(L\\) \u2192 very large radius<\/li>\n<li>\u274c Main sequence stars fuse <strong>hydrogen<\/strong>, not helium<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-9-astrophysics-cosmic-distances-and-hubbles-law\">Topic 9: Astrophysics \u2014 Cosmic Distances and Hubble’s Law<\/h2>\n<p><strong>Question types:<\/strong> Stellar parallax; Hubble’s law for recession speed or age of universe; Doppler redshift calculation.<\/p>\n<h3 id=\"distance-ladder\">Distance Ladder<\/h3>\n<table>\n<thead><tr><th>Method<\/th><th>Range<\/th><th>Key formula<\/th><\/tr><\/thead>\n<tr><td>Stellar parallax<\/td><td>\\(< 1000\\ \\text{pc}\\) (within galaxy)<\/td><td>\\(d\\text{(pc)} = 1\/p\\text{(arcsec)}\\)<\/td><\/tr>\n<tr><td>Standard candle (Cepheid \/ Type Ia supernova)<\/td><td>\\(< 100\\ \\text{Mpc}\\)<\/td><td>\\(I = L \/ 4\\pi d^2\\)<\/td><\/tr>\n<tr><td>Hubble’s law<\/td><td>Very distant galaxies<\/td><td>\\(v = H_0 d\\)<\/td><\/tr>\n<\/table>\n\n<h3 id=\"doppler-redshift\">Doppler Redshift<\/h3>\n<p>\\[\\frac{\\Delta\\lambda}{\\lambda} \\approx \\frac{v}{c} \\quad (v \\ll c)\\]<\/p>\n<ul>\n<li>Galaxy receding \u2192 wavelength increases (redshift)<\/li>\n<li>Galaxy approaching \u2192 wavelength decreases (blueshift)<\/li>\n<\/ul>\n<h3 id=\"hubbles-law\">Hubble’s Law<\/h3>\n<p>\\[v = H_0 d \\qquad H_0 \\approx 70\\ \\text{km s}^{-1}\\text{Mpc}^{-1}\\]<\/p>\n<p>Age of universe estimate: \\(t \\approx 1\/H_0\\) (convert \\(H_0\\) to s\u207b\u00b9 first)<\/p>\n<h3 id=\"evidence-for-the-big-bang\">Evidence for the Big Bang<\/h3>\n<p class=\"numbered-step\"><strong>Hubble redshift<\/strong>: All distant galaxies are receding \u2192 universe is expanding \u2192 implies a beginning<\/p>\n<p class=\"numbered-step\"><strong>CMBR<\/strong>: Uniform 2.7 K microwave radiation from all directions \u2192 relic of the hot early universe<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Parallax angle must be in <strong>arcseconds<\/strong>, not degrees<\/li>\n<li>\u274c \\(d\\) must be in <strong>Mpc<\/strong> to match the units of \\(H_0\\)<\/li>\n<li>\u274c \\(\\Delta\\lambda = \\lambda_{observed} – \\lambda_{rest}\\) (positive for receding source)<\/li>\n<li>\u274c Convert \\(H_0\\) to s\u207b\u00b9 first: \\(1\\ \\text{Mpc} = 3.09\\times10^{22}\\ \\text{m}\\)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"practice-questions\">Practice Questions<\/h2>\n<p><strong>Q1.<\/strong> SHM: amplitude \\(A = 0.1\\ \\text{m}\\), \\(\\omega = 10\\ \\text{rad\/s}\\). Find maximum speed and maximum acceleration.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(v_{max} = \\omega A = 10 \\times 0.1 = \\mathbf{1.0\\ \\text{m\/s}}\\)<\/p>\n<p>\\(a_{max} = \\omega^2 A = 100 \\times 0.1 = \\mathbf{10\\ \\text{m\/s}^2}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q2.<\/strong> Mass defect \\(\\Delta m = 0.00318\\ \\text{u}\\). Find the energy released in MeV.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(E = 0.00318 \\times 931.5 = \\mathbf{2.96\\ \\text{MeV}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q3.<\/strong> Initial activity \\(A_0 = 800\\ \\text{Bq}\\), half-life \\(T_{1\/2} = 2\\ \\text{h}\\). Find the activity after \\(6\\ \\text{h}\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(6\/2 = 3\\) half-lives:<\/p>\n<p>\\(A = 800 \\times (1\/2)^3 = \\mathbf{100\\ \\text{Bq}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q4.<\/strong> A star has surface temperature \\(T = 6000\\ \\text{K}\\) and radius \\(R = 8.0\\times10^8\\ \\text{m}\\). Find: (a) peak wavelength; (b) total luminosity.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>(a) \\(\\lambda_{max} = \\dfrac{2.898\\times10^{-3}}{6000} = \\mathbf{4.83\\times10^{-7}\\ \\text{m}}\\) (483 nm)<\/p>\n<p>(b) \\(L = 4\\pi \\times (8.0\\times10^8)^2 \\times 5.67\\times10^{-8} \\times (6000)^4 = \\mathbf{5.9\\times10^{26}\\ \\text{W}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q5.<\/strong> Hydrogen spectral line at rest: \\(\\lambda_0 = 656\\ \\text{nm}\\); observed: \\(\\lambda = 669\\ \\text{nm}\\). Find the recession speed and estimate the distance. (\\(H_0 = 70\\ \\text{km s}^{-1}\\text{Mpc}^{-1}\\))<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(\\Delta\\lambda = 13\\ \\text{nm}\\)<\/p>\n<p>\\(v = 3.0\\times10^8 \\times \\dfrac{13}{656} = \\mathbf{5.95\\times10^6\\ \\text{m\/s}}\\)<\/p>\n<p>\\(d = 5950 \\div 70 = \\mathbf{85\\ \\text{Mpc}}\\)<\/p><\/div><\/details>\n<hr>\n<p><em>Want more? Visit <a href=\"https:\/\/flowxiom.com\">flowxiom.com<\/a><\/em><\/p>\n<footer class=\"site-footer\">\n <p>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<br>\n High-frequency topics only, covering ~80% of exam marks.<\/p>\n<\/footer>\n<\/body>\n<\/html>\n\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This high-yield revision guide covers the core topics of Edexcel A-level Physics Unit 5, spanning Thermodynamics, Nuclear Physics, Oscillations, and Astrophysics. It provides a detailed analysis of Simple Harmonic Motion (SHM), kinetic theory of gases, and radioactive decay laws. The resource also explores gravitational fields, stellar evolution via the H-R diagram, and cosmological evidence for the Big Bang. With a focus on frequent 6-mark questions, essential formulas, and common exam pitfalls, this guide is an indispensable tool for students mastering the 80% of content most likely to appear in the WPH15 exam.<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-48","post","type-post","status-publish","format-standard","hentry","category-exam-sprint-pack-physics-exam-sprint-pack"],"_links":{"self":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/comments?post=48"}],"version-history":[{"count":1,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/48\/revisions"}],"predecessor-version":[{"id":49,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/48\/revisions\/49"}],"wp:attachment":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/media?parent=48"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/categories?post=48"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/tags?post=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":48,"date":"2026-04-17T16:26:18","date_gmt":"2026-04-17T16:26:18","guid":{"rendered":"https:\/\/flowxiom.com\/?p=48"},"modified":"2026-04-17T16:26:48","modified_gmt":"2026-04-17T16:26:48","slug":"unit5-high-yield-topics","status":"publish","type":"post","link":"https:\/\/flowxiom.com\/index.php\/2026\/04\/17\/unit5-high-yield-topics\/","title":{"rendered":"Unit5 High-Yield Topics"},"content":{"rendered":"\n\n\n\n\n\nUnit 5 High-Yield Topics | Flowxiom<\/title>\n<meta name=\"description\" content=\"Unit 5 High-Yield Topics \u2014 Edexcel A-level Physics WPH. Question types: Identify SHM; describe phase relationships; calculate velocity\/acceleration; energy g...\">\n<link rel=\"canonical\" href=\"https:\/\/flowxiom.com\/edexcel-physics-unit-5-high-yield-topics\/\">\n<script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@type\": \"FAQPage\",\n \"mainEntity\": [\n {\n \"@type\": \"Question\",\n \"name\": \"Q1. SHM: amplitude \\\\(A = 0.1\\\\ \\\\text{m}\\\\), \\\\(\\\\omega = 10\\\\ \\\\text{rad\/s}\\\\). Find maximum speed and maximum acceleration.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(v_{max} = \\\\omega A = 10 \\\\times 0.1 = \\\\mathbf{1.0\\\\ \\\\text{m\/s}}\\\\) \\n \\\\(a_{max} = \\\\omega^2 A = 100 \\\\times 0.1 = \\\\mathbf{10\\\\ \\\\text{m\/s}^2}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q2. Mass defect \\\\(\\\\Delta m = 0.00318\\\\ \\\\text{u}\\\\). Find the energy released in MeV.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(E = 0.00318 \\\\times 931.5 = \\\\mathbf{2.96\\\\ \\\\text{MeV}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q3. Initial activity \\\\(A_0 = 800\\\\ \\\\text{Bq}\\\\), half-life \\\\(T_{1\/2} = 2\\\\ \\\\text{h}\\\\). Find the activity after \\\\(6\\\\ \\\\text{h}\\\\).\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(6\/2 = 3\\\\) half-lives: \\n \\\\(A = 800 \\\\times (1\/2)^3 = \\\\mathbf{100\\\\ \\\\text{Bq}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q4. A star has surface temperature \\\\(T = 6000\\\\ \\\\text{K}\\\\) and radius \\\\(R = 8.0\\\\times10^8\\\\ \\\\text{m}\\\\). Find: (a) peak wavelength; (b) total luminosity.\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"(a) \\\\(\\\\lambda_{max} = \\\\dfrac{2.898\\\\times10^{-3}}{6000} = \\\\mathbf{4.83\\\\times10^{-7}\\\\ \\\\text{m}}\\\\) (483 nm) \\n (b) \\\\(L = 4\\\\pi \\\\times (8.0\\\\times10^8)^2 \\\\times 5.67\\\\times10^{-8} \\\\times (6000)^4 = \\\\mathbf{5.9\\\\times10^{26}\\\\ \\\\text{W}}\\\\)\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Q5. Hydrogen spectral line at rest: \\\\(\\\\lambda_0 = 656\\\\ \\\\text{nm}\\\\); observed: \\\\(\\\\lambda = 669\\\\ \\\\text{nm}\\\\). Find the recession speed and estimate the distance. (\\\\(H_0 = 70\\\\ \\\\text{km s}^{-1}\\\\text{Mpc}^{-1}\\\\))\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"\\\\(\\\\Delta\\\\lambda = 13\\\\ \\\\text{nm}\\\\) \\n \\\\(v = 3.0\\\\times10^8 \\\\times \\\\dfrac{13}{656} = \\\\mathbf{5.95\\\\times10^6\\\\ \\\\text{m\/s}}\\\\) \\n \\\\(d = 5950 \\\\div 70 = \\\\mathbf{85\\\\ \\\\text{Mpc}}\\\\)\"\n }\n }\n ]\n}\n<\/script>\n\n<script>\nMathJax = {\n tex: { inlineMath: [['\\\\(','\\\\)']], displayMath: [['\\\\[','\\\\]']] },\n svg: { fontCache: 'global' }\n};\n<\/script>\n<script async src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-svg.js\"><\/script>\n\n<style>\n:root{--accent:#2563eb;--warn-bg:#fef9c3;--warn-border:#ca8a04;--formula-bg:#eff6ff;--formula-border:#2563eb;}\nbody{font-family:system-ui,sans-serif;max-width:860px;margin:0 auto;padding:1.5rem;line-height:1.7;color:#1e293b;}\nh1{font-size:2rem;border-bottom:3px solid var(--accent);padding-bottom:.4rem;}\nh2{font-size:1.4rem;color:var(--accent);margin-top:2rem;}\nh3{font-size:1.1rem;margin-top:1.4rem;}\ntable{border-collapse:collapse;width:100%;margin:1rem 0;}\nth,td{border:1px solid #cbd5e1;padding:.5rem .75rem;text-align:left;}\nth{background:#e2e8f0;}\npre,code{background:#f1f5f9;border-radius:4px;}\npre{padding:1rem;overflow-x:auto;}\ncode{padding:.1rem .3rem;font-size:.9em;}\n.seo-warning-box{background:var(--warn-bg);border-left:4px solid var(--warn-border);padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\n.seo-note-box{background:#f0fdf4;border-left:4px solid #16a34a;padding:.75rem 1rem;margin:1rem 0;border-radius:0 6px 6px 0;}\nsection.formula-card{background:var(--formula-bg);border:1px solid var(--formula-border);border-radius:8px;padding:1rem 1.25rem;margin:1.5rem 0;}\ndetails{border:1px solid #e2e8f0;border-radius:6px;padding:.5rem 1rem;margin:.75rem 0;}\nsummary{cursor:pointer;font-weight:600;}\n.answer-block{margin-top:.5rem;padding-top:.5rem;border-top:1px solid #e2e8f0;overflow-x:auto;}\n.answer-block p{margin:.25rem 0;}\n.numbered-step{padding-left:1.5rem;position:relative;}\nhr{border:none;border-top:1px solid #e2e8f0;margin:2rem 0;}\n.toc{background:#f8fafc;border:1px solid #e2e8f0;border-radius:8px;padding:1rem 1.5rem;margin-bottom:2rem;}\n.toc h2{margin-top:0;font-size:1.1rem;}\n.toc ul{margin:0;padding-left:1.2rem;}\n.toc a{color:var(--accent);text-decoration:none;}\n.site-footer{margin-top:3rem;padding-top:1rem;border-top:2px solid var(--accent);font-size:.9rem;color:#64748b;}\n<\/style>\n<\/head>\n<body>\n<nav class=\"toc\"><h2>Contents<\/h2><ul>\n <li><a href=\"#topic-1-simple-harmonic-motion-frequent-6mark-question\">Topic 1: Simple Harmonic Motion (frequent 6-mark question)<\/a><\/li>\n <li><a href=\"#topic-2-kinetic-theory-of-gases-frequent-6mark-question\">Topic 2: Kinetic Theory of Gases (frequent 6-mark question)<\/a><\/li>\n <li><a href=\"#topic-3-nuclear-decay-and-halflife\">Topic 3: Nuclear Decay and Half-Life<\/a><\/li>\n <li><a href=\"#topic-4-binding-energy-and-mass-defect\">Topic 4: Binding Energy and Mass Defect<\/a><\/li>\n <li><a href=\"#topic-5-gravitational-fields\">Topic 5: Gravitational Fields<\/a><\/li>\n <li><a href=\"#topic-6-thermodynamics-specific-heat-capacity-and-latent-heat\">Topic 6: Thermodynamics \u2014 Specific Heat Capacity and Latent Heat<\/a><\/li>\n <li><a href=\"#topic-7-damping-and-resonance\">Topic 7: Damping and Resonance<\/a><\/li>\n <li><a href=\"#topic-8-astrophysics-stellar-physics-and-the-hr-diagram\">Topic 8: Astrophysics \u2014 Stellar Physics and the H-R Diagram<\/a><\/li>\n <li><a href=\"#topic-9-astrophysics-cosmic-distances-and-hubbles-law\">Topic 9: Astrophysics \u2014 Cosmic Distances and Hubble’s Law<\/a><\/li>\n <li><a href=\"#practice-questions\">Practice Questions<\/a><\/li>\n<\/ul><\/nav>\n<h1>Unit 5 High-Yield Topics<\/h1>\n<p><strong>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<\/strong><\/p>\n<p><em>Not everything. Just what’s on the paper. High-frequency topics only \u2014 covering ~80% of exam marks.<\/em><\/p>\n<p>Edexcel A-level Physics | Thermal, Nuclear, SHM & Astrophysics | WPH14 & WPH15<\/p>\n<hr>\n<h2 id=\"topic-1-simple-harmonic-motion-frequent-6mark-question\">Topic 1: Simple Harmonic Motion (frequent 6-mark question)<\/h2>\n<p><strong>Question types:<\/strong> Identify SHM; describe phase relationships; calculate velocity\/acceleration; energy graphs.<\/p>\n<h3 id=\"two-conditions-for-shm-both-required\">Two Conditions for SHM (both required)<\/h3>\n<p class=\"numbered-step\">Acceleration is <strong>proportional to displacement<\/strong> from equilibrium<\/p>\n<p class=\"numbered-step\">Acceleration is always <strong>directed towards the equilibrium position<\/strong> (opposite to displacement)<\/p>\n<p>\\[a = -\\omega^2 x\\]<\/p>\n<h3 id=\"formulae\">Formulae<\/h3>\n<p>\\[x = A\\cos(\\omega t) \\qquad v = -A\\omega\\sin(\\omega t) \\qquad a = -A\\omega^2\\cos(\\omega t)\\]<\/p>\n<p>\\[v_{max} = \\omega A \\text{ (at equilibrium)} \\qquad a_{max} = \\omega^2 A \\text{ (at maximum displacement)}\\]<\/p>\n<h3 id=\"phase-relationships\">Phase Relationships<\/h3>\n<table>\n<thead><tr><th>Position<\/th><th>Displacement \\(x\\)<\/th><th>Velocity \\(v\\)<\/th><th>Acceleration \\(a\\)<\/th><\/tr><\/thead>\n<tr><td>Equilibrium<\/td><td>0<\/td><td><strong>maximum<\/strong><\/td><td>0<\/td><\/tr>\n<tr><td>Maximum displacement<\/td><td>\\(\\pm A\\)<\/td><td>0<\/td><td><strong>maximum<\/strong> (opposite direction)<\/td><\/tr>\n<\/table>\n\n<ul>\n<li>\\(v\\) leads \\(x\\) by 90\u00b0<\/li>\n<li>\\(a\\) is in antiphase with \\(x\\) (180\u00b0 phase difference)<\/li>\n<\/ul>\n<h3 id=\"period-formulae\">Period Formulae<\/h3>\n<p>\\[T_{spring} = 2\\pi\\sqrt{\\frac{m}{k}} \\qquad T_{pendulum} = 2\\pi\\sqrt{\\frac{L}{g}}\\]<\/p>\n<h3 id=\"shm-energy\">SHM Energy<\/h3>\n<p>\\[E_k = \\frac{1}{2}m\\omega^2(A^2 – x^2) \\qquad E_p = \\frac{1}{2}m\\omega^2 x^2 \\qquad E_{total} = \\frac{1}{2}m\\omega^2 A^2\\]<\/p>\n<p>Total energy is constant; \\(E_k + E_p = \\text{constant}\\).<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Both conditions must be stated: proportional to displacement <strong>AND<\/strong> directed towards equilibrium<\/li>\n<li>\u274c At equilibrium: maximum <strong>velocity<\/strong>, zero acceleration<\/li>\n<li>\u274c Pendulum period is independent of mass \u2014 depends only on \\(L\\) and \\(g\\)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-2-kinetic-theory-of-gases-frequent-6mark-question\">Topic 2: Kinetic Theory of Gases (frequent 6-mark question)<\/h2>\n<p><strong>Question types:<\/strong> Explain how gas pressure changes with temperature or volume.<\/p>\n<h3 id=\"answer-chain-temperature-pressure\">Answer Chain \u2014 Temperature \u2191 \u2192 Pressure \u2191<\/h3>\n<p class=\"numbered-step\">Temperature increases \u2192 mean kinetic energy of molecules increases<\/p>\n<p class=\"numbered-step\">Mean speed of molecules increases<\/p>\n<p class=\"numbered-step\">Greater change in momentum per collision with the wall<\/p>\n<p class=\"numbered-step\">Molecules collide with the wall more frequently<\/p>\n<p class=\"numbered-step\">Greater resultant force on the wall<\/p>\n<p class=\"numbered-step\">Area unchanged \u2192 <strong>pressure increases<\/strong><\/p>\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f Both steps 3 and 5 are required \u2014 neither can be omitted.<\/p>\n<\/div>\n<h3 id=\"ideal-gas-law\">Ideal Gas Law<\/h3>\n<p>\\[\\frac{pV}{T} = \\text{constant} \\qquad pV = nRT \\qquad R = 8.31\\ \\text{J mol}^{-1} \\text{K}^{-1}\\]<\/p>\n<p><strong>Temperature must be in Kelvin<\/strong>: \\(T = \\theta + 273\\)<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Using \u00b0C instead of K \u2014 most common error<\/li>\n<li>\u274c Must mention <strong>both<\/strong>: greater force per collision <strong>and<\/strong> higher collision frequency<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-3-nuclear-decay-and-halflife\">Topic 3: Nuclear Decay and Half-Life<\/h2>\n<p><strong>Question types:<\/strong> Balance nuclear equations; half-life calculations; explain randomness and spontaneity.<\/p>\n<h3 id=\"three-types-of-radiation\">Three Types of Radiation<\/h3>\n<table>\n<thead><tr><th>Radiation<\/th><th>Nature<\/th><th>Example equation<\/th><th>Ionisation & penetration<\/th><\/tr><\/thead>\n<tr><td>\\(\\alpha\\)<\/td><td>Helium nucleus \\(^4_2\\text{He}\\)<\/td><td>\\(^A_ZX \\to ^{A-4}_{Z-2}Y + ^4_2\\alpha\\)<\/td><td>Strongly ionising; stopped by paper<\/td><\/tr>\n<tr><td>\\(\\beta^-\\)<\/td><td>Electron \\(^0_{-1}e\\)<\/td><td>\\(^A_ZX \\to ^A_{Z+1}Y + ^0_{-1}\\beta + \\bar{\\nu}_e\\)<\/td><td>Moderately ionising; stopped by aluminium<\/td><\/tr>\n<tr><td>\\(\\gamma\\)<\/td><td>High-energy EM radiation<\/td><td>Accompanies \u03b1\/\u03b2 decay<\/td><td>Weakly ionising; requires lead shielding<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-warning-box\">\n<p>\u26a0\ufe0f \u03b2\u207b decay: neutron \u2192 proton + electron + <strong>electron antineutrino<\/strong> \u2014 do not omit the antineutrino.<\/p>\n<\/div>\n<h3 id=\"balancing-nuclear-equations\">Balancing Nuclear Equations<\/h3>\n<ul>\n<li>Mass number \\(A\\) (top): sum must be equal on both sides<\/li>\n<li>Atomic number \\(Z\\) (bottom): sum must be equal on both sides<\/li>\n<\/ul>\n<h3 id=\"halflife-calculations\">Half-Life Calculations<\/h3>\n<p>\\[N = N_0 \\left(\\frac{1}{2}\\right)^{t\/T_{1\/2}} \\qquad A = \\lambda N \\qquad T_{1\/2} = \\frac{\\ln 2}{\\lambda} = \\frac{0.693}{\\lambda}\\]<\/p>\n<h3 id=\"randomness-and-spontaneity\">Randomness and Spontaneity<\/h3>\n<ul>\n<li><strong>Random<\/strong>: It is impossible to predict which specific nucleus will decay or at what time<\/li>\n<li><strong>Spontaneous<\/strong>: Decay is unaffected by external conditions such as temperature, pressure or chemical state<\/li>\n<\/ul>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Omitting the electron antineutrino \\(\\bar{\\nu}_e\\) in \u03b2\u207b decay<\/li>\n<li>\u274c Both activity \\(A\\) and number of nuclei \\(N\\) follow the same exponential decay law<\/li>\n<li>\u274c Must subtract <strong>background radiation<\/strong> count rate \u2014 measure it first<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-4-binding-energy-and-mass-defect\">Topic 4: Binding Energy and Mass Defect<\/h2>\n<p><strong>Question types:<\/strong> Calculate binding energy; judge whether fission\/fusion releases energy; read binding energy per nucleon graph.<\/p>\n<h3 id=\"calculation-steps\">Calculation Steps<\/h3>\n<p class=\"numbered-step\">Mass defect: \\(\\Delta m = \\text{sum of individual nucleon masses} – \\text{actual nuclear mass}\\)<\/p>\n<p class=\"numbered-step\">Binding energy: \\(E = \\Delta mc^2\\)<\/p>\n<p class=\"numbered-step\">If \\(\\Delta m\\) in atomic mass units: \\(E\\text{(MeV)} = \\Delta m\\text{(u)} \\times 931.5\\)<\/p>\n<h3 id=\"binding-energy-per-nucleon-curve\">Binding Energy Per Nucleon Curve<\/h3>\n<ul>\n<li>Iron-56 (\\(^{56}\\)Fe) is at the <strong>peak<\/strong> \u2014 most stable nucleus<\/li>\n<li><strong>Fission<\/strong>: heavy nucleus splits from right side (low) to middle (higher) \u2192 energy <strong>released<\/strong><\/li>\n<li><strong>Fusion<\/strong>: light nuclei fuse from left side (low) to middle (higher) \u2192 energy <strong>released<\/strong><\/li>\n<\/ul>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c If \\(\\Delta m\\) in kg: use \\(E = \\Delta mc^2\\); if \\(\\Delta m\\) in u: multiply by 931.5 MeV\/u<\/li>\n<li>\u274c Energy is released when binding energy per nucleon <strong>increases<\/strong><\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-5-gravitational-fields\">Topic 5: Gravitational Fields<\/h2>\n<p><strong>Question types:<\/strong> Calculate gravitational field strength and potential; satellite orbits; comparison with electric fields.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[g = \\frac{GM}{r^2} \\qquad \\phi = -\\frac{GM}{r} \\qquad g = -\\frac{\\Delta\\phi}{\\Delta r}\\]<\/p>\n<ul>\n<li>Gravitational potential \\(\\phi\\) is <strong>always negative<\/strong> (zero at infinity, more negative closer to source)<\/li>\n<li>Field strength = negative of potential gradient<\/li>\n<\/ul>\n<h3 id=\"satellite-orbits\">Satellite Orbits<\/h3>\n<p>\\[\\frac{GMm}{r^2} = \\frac{mv^2}{r} \\implies v = \\sqrt{\\frac{GM}{r}} \\implies T^2 = \\frac{4\\pi^2}{GM}r^3\\]<\/p>\n<p>Higher orbit \u2192 smaller speed, longer period.<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Gravitational potential increases (becomes less negative) as distance from source increases<\/li>\n<li>\u274c Orbital speed <strong>decreases<\/strong> as orbital radius increases<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-6-thermodynamics-specific-heat-capacity-and-latent-heat\">Topic 6: Thermodynamics \u2014 Specific Heat Capacity and Latent Heat<\/h2>\n<p><strong>Question types:<\/strong> Calculate energy for heating; explain molecular reason why temperature stays constant during change of state.<\/p>\n<h3 id=\"key-formulae\">Key Formulae<\/h3>\n<p>\\[Q = mc\\Delta\\theta \\quad \\text{(temperature change \u2014 specific heat capacity, J kg}^{-1}\\text{ K}^{-1}\\text{)}\\]<\/p>\n<p>\\[Q = mL \\quad \\text{(change of state \u2014 temperature constant \u2014 specific latent heat, J kg}^{-1}\\text{)}\\]<\/p>\n<p>\\[\\Delta U = Q + W \\quad \\text{(first law of thermodynamics)}\\]<\/p>\n<h3 id=\"why-temperature-stays-constant-during-a-change-of-state\">Why Temperature Stays Constant During a Change of State<\/h3>\n<p>Energy supplied goes into increasing <strong>molecular potential energy<\/strong> (overcoming intermolecular forces), not kinetic energy. Temperature is proportional to mean kinetic energy \u2014 which does not change \u2192 temperature stays constant.<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Temperature constant does NOT mean internal energy constant \u2014 internal energy increases (as potential energy)<\/li>\n<li>\u274c Heat loss to surroundings \u2192 smaller measured temperature rise \u2192 calculated \\(c\\) is <strong>too large<\/strong><\/li>\n<li>\u274c Temperature difference may use K or \u00b0C (same magnitude); absolute temperature must use K<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-7-damping-and-resonance\">Topic 7: Damping and Resonance<\/h2>\n<p><strong>Question types:<\/strong> Describe features of different oscillations; explain resonance; sketch resonance curves for different damping.<\/p>\n<h3 id=\"types-of-oscillation\">Types of Oscillation<\/h3>\n<table>\n<thead><tr><th>Type<\/th><th>Amplitude<\/th><th>Frequency<\/th><th>Graph<\/th><\/tr><\/thead>\n<tr><td>Free<\/td><td>Constant<\/td><td>Natural frequency \\(f_0\\)<\/td><td>Constant-amplitude sine wave<\/td><\/tr>\n<tr><td>Light damping<\/td><td>Gradually decreases<\/td><td>Approximately \\(f_0\\)<\/td><td>Exponentially decaying sine wave<\/td><\/tr>\n<tr><td>Heavy damping<\/td><td>Monotonically \u2192 0<\/td><td>No oscillation<\/td><td>Slowly returns to equilibrium<\/td><\/tr>\n<tr><td>Critical damping<\/td><td>Fastest return<\/td><td>No oscillation<\/td><td>Fastest return with no oscillation<\/td><\/tr>\n<\/table>\n\n<h3 id=\"forced-oscillation-and-resonance\">Forced Oscillation and Resonance<\/h3>\n<ul>\n<li><strong>Forced oscillation<\/strong>: system driven at driving frequency \\(f_d\\) \u2014 oscillates at \\(f_d\\), not \\(f_0\\)<\/li>\n<li><strong>Resonance<\/strong>: when \\(f_d = f_0\\) \u2192 <strong>maximum amplitude<\/strong><\/li>\n<\/ul>\n<h3 id=\"effect-of-damping-on-resonance-curve\">Effect of Damping on Resonance Curve<\/h3>\n<ul>\n<li>More damping \u2192 lower, broader resonance peak; peak shifts slightly below \\(f_0\\)<\/li>\n<li>Light damping \u2192 tall, sharp peak<\/li>\n<\/ul>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Resonance occurs when driving frequency = <strong>natural frequency<\/strong><\/li>\n<li>\u274c Damping reduces amplitude \u2014 it does <strong>not<\/strong> change the natural frequency<\/li>\n<li>\u274c Frequency of forced oscillation = driving frequency, not natural frequency<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-8-astrophysics-stellar-physics-and-the-hr-diagram\">Topic 8: Astrophysics \u2014 Stellar Physics and the H-R Diagram<\/h2>\n<p><strong>Question types:<\/strong> Use Wien’s law to find temperature; Stefan-Boltzmann law to compare luminosity; identify star types on H-R diagram.<\/p>\n<h3 id=\"two-key-laws\">Two Key Laws<\/h3>\n<p>\\[\\lambda_{max} T = 2.898 \\times 10^{-3}\\ \\text{m K} \\quad \\text{(Wien’s displacement law)}\\]<\/p>\n<p>\\[L = 4\\pi R^2 \\sigma T^4 \\qquad \\sigma = 5.67\\times10^{-8}\\ \\text{W m}^{-2}\\text{K}^{-4}\\]<\/p>\n<ul>\n<li>Smaller \\(\\lambda_{max}\\) \u2192 higher temperature \u2192 bluer colour<\/li>\n<li>Luminosity is extremely sensitive to temperature (\\(T^4\\))<\/li>\n<\/ul>\n<h3 id=\"four-regions-of-the-hr-diagram\">Four Regions of the H-R Diagram<\/h3>\n<table>\n<thead><tr><th>Region<\/th><th>Position<\/th><th>Temperature<\/th><th>Luminosity<\/th><th>Example<\/th><\/tr><\/thead>\n<tr><td>Main Sequence<\/td><td>Diagonal (top-left \u2192 bottom-right)<\/td><td>High \u2192 low<\/td><td>High \u2192 low<\/td><td>Sun<\/td><\/tr>\n<tr><td>Red Giant<\/td><td>Top-right<\/td><td>Low (red)<\/td><td>Very high<\/td><td>Betelgeuse<\/td><\/tr>\n<tr><td>White Dwarf<\/td><td>Bottom-left<\/td><td>High (white)<\/td><td>Very low<\/td><td>Sirius B<\/td><\/tr>\n<tr><td>Supergiant<\/td><td>Top-right (above red giant)<\/td><td>Low<\/td><td>Highest<\/td><td>\u2014<\/td><\/tr>\n<\/table>\n\n<div class=\"seo-note-box\">\n<p>H-R diagram temperature axis increases from <strong>right to left<\/strong> \u2014 opposite to the usual convention.<\/p>\n<\/div>\n<h3 id=\"stellar-evolution\">Stellar Evolution<\/h3>\n<p><strong>Low-mass stars<\/strong> (\\(< 8M_\\odot\\), e.g. Sun): Main sequence \u2192 Red giant \u2192 Planetary nebula \u2192 <strong>White dwarf<\/strong><\/p>\n<p><strong>High-mass stars<\/strong> (\\(> 10M_\\odot\\)): Main sequence \u2192 Red supergiant \u2192 <strong>Supernova<\/strong> \u2192 Neutron star (\\(M_{remnant} < 3M_\\odot\\)) or <strong>Black hole<\/strong> (\\(M_{remnant} > 3M_\\odot\\))<\/p>\n<div class=\"seo-note-box\">\n<p>Chandrasekhar limit: \\(1.4M_\\odot\\) \u2014 upper mass limit for a white dwarf.<\/p>\n<\/div>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Right side of H-R diagram = low temperature (cool, red stars)<\/li>\n<li>\u274c White dwarf: high \\(T\\), low \\(L\\) \u2192 very small radius. Red giant: low \\(T\\), high \\(L\\) \u2192 very large radius<\/li>\n<li>\u274c Main sequence stars fuse <strong>hydrogen<\/strong>, not helium<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"topic-9-astrophysics-cosmic-distances-and-hubbles-law\">Topic 9: Astrophysics \u2014 Cosmic Distances and Hubble’s Law<\/h2>\n<p><strong>Question types:<\/strong> Stellar parallax; Hubble’s law for recession speed or age of universe; Doppler redshift calculation.<\/p>\n<h3 id=\"distance-ladder\">Distance Ladder<\/h3>\n<table>\n<thead><tr><th>Method<\/th><th>Range<\/th><th>Key formula<\/th><\/tr><\/thead>\n<tr><td>Stellar parallax<\/td><td>\\(< 1000\\ \\text{pc}\\) (within galaxy)<\/td><td>\\(d\\text{(pc)} = 1\/p\\text{(arcsec)}\\)<\/td><\/tr>\n<tr><td>Standard candle (Cepheid \/ Type Ia supernova)<\/td><td>\\(< 100\\ \\text{Mpc}\\)<\/td><td>\\(I = L \/ 4\\pi d^2\\)<\/td><\/tr>\n<tr><td>Hubble’s law<\/td><td>Very distant galaxies<\/td><td>\\(v = H_0 d\\)<\/td><\/tr>\n<\/table>\n\n<h3 id=\"doppler-redshift\">Doppler Redshift<\/h3>\n<p>\\[\\frac{\\Delta\\lambda}{\\lambda} \\approx \\frac{v}{c} \\quad (v \\ll c)\\]<\/p>\n<ul>\n<li>Galaxy receding \u2192 wavelength increases (redshift)<\/li>\n<li>Galaxy approaching \u2192 wavelength decreases (blueshift)<\/li>\n<\/ul>\n<h3 id=\"hubbles-law\">Hubble’s Law<\/h3>\n<p>\\[v = H_0 d \\qquad H_0 \\approx 70\\ \\text{km s}^{-1}\\text{Mpc}^{-1}\\]<\/p>\n<p>Age of universe estimate: \\(t \\approx 1\/H_0\\) (convert \\(H_0\\) to s\u207b\u00b9 first)<\/p>\n<h3 id=\"evidence-for-the-big-bang\">Evidence for the Big Bang<\/h3>\n<p class=\"numbered-step\"><strong>Hubble redshift<\/strong>: All distant galaxies are receding \u2192 universe is expanding \u2192 implies a beginning<\/p>\n<p class=\"numbered-step\"><strong>CMBR<\/strong>: Uniform 2.7 K microwave radiation from all directions \u2192 relic of the hot early universe<\/p>\n<div class=\"seo-warning-box\" id=\"common-mistakes\">\n<h3>Common Mistakes<\/h3>\n<ul>\n<li>\u274c Parallax angle must be in <strong>arcseconds<\/strong>, not degrees<\/li>\n<li>\u274c \\(d\\) must be in <strong>Mpc<\/strong> to match the units of \\(H_0\\)<\/li>\n<li>\u274c \\(\\Delta\\lambda = \\lambda_{observed} – \\lambda_{rest}\\) (positive for receding source)<\/li>\n<li>\u274c Convert \\(H_0\\) to s\u207b\u00b9 first: \\(1\\ \\text{Mpc} = 3.09\\times10^{22}\\ \\text{m}\\)<\/li>\n<\/ul>\n<\/div>\n<hr>\n<h2 id=\"practice-questions\">Practice Questions<\/h2>\n<p><strong>Q1.<\/strong> SHM: amplitude \\(A = 0.1\\ \\text{m}\\), \\(\\omega = 10\\ \\text{rad\/s}\\). Find maximum speed and maximum acceleration.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(v_{max} = \\omega A = 10 \\times 0.1 = \\mathbf{1.0\\ \\text{m\/s}}\\)<\/p>\n<p>\\(a_{max} = \\omega^2 A = 100 \\times 0.1 = \\mathbf{10\\ \\text{m\/s}^2}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q2.<\/strong> Mass defect \\(\\Delta m = 0.00318\\ \\text{u}\\). Find the energy released in MeV.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(E = 0.00318 \\times 931.5 = \\mathbf{2.96\\ \\text{MeV}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q3.<\/strong> Initial activity \\(A_0 = 800\\ \\text{Bq}\\), half-life \\(T_{1\/2} = 2\\ \\text{h}\\). Find the activity after \\(6\\ \\text{h}\\).<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(6\/2 = 3\\) half-lives:<\/p>\n<p>\\(A = 800 \\times (1\/2)^3 = \\mathbf{100\\ \\text{Bq}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q4.<\/strong> A star has surface temperature \\(T = 6000\\ \\text{K}\\) and radius \\(R = 8.0\\times10^8\\ \\text{m}\\). Find: (a) peak wavelength; (b) total luminosity.<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>(a) \\(\\lambda_{max} = \\dfrac{2.898\\times10^{-3}}{6000} = \\mathbf{4.83\\times10^{-7}\\ \\text{m}}\\) (483 nm)<\/p>\n<p>(b) \\(L = 4\\pi \\times (8.0\\times10^8)^2 \\times 5.67\\times10^{-8} \\times (6000)^4 = \\mathbf{5.9\\times10^{26}\\ \\text{W}}\\)<\/p><\/div><\/details>\n<hr>\n<p><strong>Q5.<\/strong> Hydrogen spectral line at rest: \\(\\lambda_0 = 656\\ \\text{nm}\\); observed: \\(\\lambda = 669\\ \\text{nm}\\). Find the recession speed and estimate the distance. (\\(H_0 = 70\\ \\text{km s}^{-1}\\text{Mpc}^{-1}\\))<\/p>\n<details><summary>Answer<\/summary><div class=\"answer-block\"><p>\\(\\Delta\\lambda = 13\\ \\text{nm}\\)<\/p>\n<p>\\(v = 3.0\\times10^8 \\times \\dfrac{13}{656} = \\mathbf{5.95\\times10^6\\ \\text{m\/s}}\\)<\/p>\n<p>\\(d = 5950 \\div 70 = \\mathbf{85\\ \\text{Mpc}}\\)<\/p><\/div><\/details>\n<hr>\n<p><em>Want more? Visit <a href=\"https:\/\/flowxiom.com\">flowxiom.com<\/a><\/em><\/p>\n<footer class=\"site-footer\">\n <p>Free resource by <a href=\"https:\/\/flowxiom.com\">Flowxiom<\/a> \u2014 Edexcel A-level Physics<br>\n High-frequency topics only, covering ~80% of exam marks.<\/p>\n<\/footer>\n<\/body>\n<\/html>\n\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This high-yield revision guide covers the core topics of Edexcel A-level Physics Unit 5, spanning Thermodynamics, Nuclear Physics, Oscillations, and Astrophysics. It provides a detailed analysis of Simple Harmonic Motion (SHM), kinetic theory of gases, and radioactive decay laws. The resource also explores gravitational fields, stellar evolution via the H-R diagram, and cosmological evidence for the Big Bang. With a focus on frequent 6-mark questions, essential formulas, and common exam pitfalls, this guide is an indispensable tool for students mastering the 80% of content most likely to appear in the WPH15 exam.<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-48","post","type-post","status-publish","format-standard","hentry","category-exam-sprint-pack-physics-exam-sprint-pack"],"_links":{"self":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/comments?post=48"}],"version-history":[{"count":1,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/48\/revisions"}],"predecessor-version":[{"id":49,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/posts\/48\/revisions\/49"}],"wp:attachment":[{"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/media?parent=48"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/categories?post=48"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/flowxiom.com\/index.php\/wp-json\/wp\/v2\/tags?post=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}