This comprehensive quiz covers all four inquiry questions from Module 8: the Big Bang and evolution of the universe, the origin of elements through stellar nucleosynthesis, the structure of the atom from Rutherford to quantum mechanics, and the Standard Model of particle physics. It is designed to simulate exam conditions and test your ability to integrate knowledge across the entire module.
Big Bang, evidence, Hubble's law, expanding universe
Stellar evolution, nucleosynthesis, HR diagram, supernovae
Rutherford, Bohr, quantum mechanics, strong force, radioactive decay
Quarks, leptons, forces, accelerators, beyond the Standard Model
20 questions covering all four inquiry questions
Q1. The Cosmic Microwave Background provides evidence for the Big Bang because it:
Correct: B. The CMB is relic black-body radiation from recombination (~380,000 years after the Big Bang), currently at 2.725 K.
Q2. A galaxy at 400 Mpc has recession velocity approximately:
Correct: C. $v = H_0 d = 70 \\times 400 = 28,000$ km/s.
Q3. Current best measurements indicate the universe is:
Correct: A. Current measurements indicate the universe is spatially flat with accelerating expansion.
Q4. A star with initial mass $15 M_{\\odot}$ will end its life as:
Correct: D. Massive stars ($> 8 M_{\\odot}$) undergo core-collapse supernovae, leaving neutron stars or black holes.
Q5. Elements heavier than iron are produced primarily by:
Correct: B. The r-process in supernovae and neutron star mergers builds nuclei beyond iron.
Q6. On the HR diagram, a star that is cool but very luminous must be:
Correct: C. Cool but luminous implies enormous radius — the defining feature of red giants/supergiants.
Q7. In Rutherford's scattering experiment, large-angle alpha deflection indicated:
Correct: A. Only a concentrated positive charge can repel alphas through large angles.
Q8. The wavelength of the H$\\alpha$ line ($n=3 \\rightarrow n=2$) in hydrogen is approximately:
Correct: D. H$\\alpha$ is the first Balmer line at ~656 nm (red).
Q9. The Heisenberg uncertainty principle states that:
Correct: B. $\\Delta x \\Delta p \\geq \\hbar/2$ is a fundamental quantum limit.
Q10. The binding energy per nucleon peaks at:
Correct: C. Fe-56 has maximum binding energy per nucleon (~8.8 MeV).
Q11. A sample with half-life 6 hours has activity 1,600 Bq. After 18 hours, its activity is:
Correct: A. 18 h = 3 half-lives. $1600 \\times (1/2)^3 = 200$ Bq.
Q12. In beta-minus decay, the atomic number $Z$:
Correct: D. A neutron becomes a proton: $Z$ increases by 1, $A$ unchanged.
Q13. A proton is classified as a:
Correct: B. Protons are baryons (three quarks: $uud$).
Q14. The charge of a strange quark is:
Correct: C. Down-type quarks (d, s, b) have charge $-1/3$.
Q15. The strong nuclear force is mediated by:
Correct: A. Gluons mediate the strong force between quarks and between nucleons.
Q16. The weak force has a short range because:
Correct: D. $R \\approx \\hbar/(mc)$; massive mediators have short range.
Q17. The Higgs boson gives mass to:
Correct: B. The Higgs mechanism generates mass for $W$, $Z$, and fermions. Force carriers of EM and strong remain massless.
Q18. Neutrino oscillations demonstrate that neutrinos:
Correct: C. Oscillations require mass differences between flavours — beyond the Standard Model.
Q19. The Standard Model does NOT include:
Correct: A. The Standard Model describes the strong, weak and electromagnetic forces, but does not include gravity.
Q20. Which statement correctly describes a key difference between Bohr's model and quantum mechanics?
Correct: D. Bohr orbits are deterministic paths; quantum orbitals are probability distributions with no definite trajectory.
5 integrated questions — model answers revealed
SAQ 1. (a) Describe the three main lines of evidence supporting the Big Bang theory. (b) Explain how Hubble's law ($v = H_0 d$) provides evidence for an expanding universe. (c) Calculate the distance to a galaxy with recession velocity 21,000 km/s using $H_0 = 70$ km/s/Mpc. (d) Explain the significance of the uniformity of the cosmic microwave background for the Big Bang model. (e) Describe the process of primordial nucleosynthesis and identify which elements were produced. (6 marks)
Model answer (6 marks):
(a) (1) Cosmological redshift — galaxies recede with $v \\propto d$. (2) CMB — uniform black-body at 2.725 K. (3) Primordial nucleosynthesis — H/He/Li abundance matches predictions (1.5 marks).
(b) Linear $v-d$ relation implies space itself expands uniformly. Every observer sees the same pattern (1 mark).
(c) $d = v/H_0 = 21,000/70 = 300$ Mpc (1 mark).
(d) The CMB is highly uniform (to 1 part in 100,000), indicating the early universe was homogeneous and isotropic. Small anisotropies are the seeds of large-scale structure (1 mark).
(e) In the first ~3 minutes, protons and neutrons fused to form deuterium, helium-4, and trace lithium-7. The observed primordial abundances match Big Bang predictions (1.5 marks).
SAQ 2. (a) Distinguish between the evolution of a low-mass star ($1 M_{\\odot}$) and a massive star ($25 M_{\\odot}$). (b) Explain why massive stars produce heavier elements than low-mass stars. (c) Describe the process of Big Bang nucleosynthesis and explain why it produced only hydrogen, helium, and trace lithium. (d) Explain why fusion cannot produce elements heavier than iron. (e) Describe the r-process and identify where it occurs. (6 marks)
Model answer (6 marks):
(a) Low-mass: main sequence → red giant → planetary nebula → white dwarf. Massive: main sequence → supergiant → supernova → neutron star/black hole (1 mark).
(b) Massive stars reach higher core temperatures, enabling fusion through to iron. Low-mass stars never ignite carbon (1 mark).
(c) First ~3 minutes: $p + n \\rightarrow$ D, then fusion to He. Universe cooled below fusion temperature before heavier nuclei could form (1.5 marks).
(d) Fe-56 has maximum binding energy per nucleon. Fusion beyond Fe is endothermic — requires energy input rather than releasing it (1.5 marks).
(e) r-process: rapid neutron capture in supernovae and neutron star mergers. Builds very heavy, neutron-rich nuclei that decay to stable heavy elements (1 mark).
SAQ 3. (a) Describe the Geiger-Marsden experiment and explain how it led to Rutherford's nuclear model. (b) State Bohr's three postulates for the hydrogen atom. (c) Calculate the wavelength emitted when an electron transitions from $n = 4$ to $n = 2$ in hydrogen. Identify the spectral series. (d) Explain how de Broglie's hypothesis accounts for Bohr's angular momentum quantisation. (e) Distinguish between a Bohr orbit and a quantum orbital. (6 marks)
Model answer (6 marks):
(a) Alpha particles fired at gold foil. Most passed through (empty space), some deflected (concentrated charge), few bounced back (small dense nucleus) (1.5 marks).
(b) (1) Electrons in allowed orbits don't radiate. (2) $L = n\\hbar$. (3) Photons emitted/absorbed with $E = hf = |\\Delta E|$ (1 mark).
(c) $1/\\lambda = 1.097\\times10^7(1/4 - 1/16) = 2.06\\times10^6$. $\\lambda = 486$ nm (Balmer series, H$\\beta$) (1.5 marks).
(d) Standing wave condition: $2\\pi r = n\\lambda = nh/(mv)$, giving $mvr = n\\hbar$ (1 mark).
(e) Bohr orbit = precise circular path; orbital = probability cloud ($||\\psi||^2$) with no definite trajectory (1 mark).
SAQ 4. (a) Define binding energy and mass defect. (b) Calculate the binding energy per nucleon for helium-4 ($m_p = 1.007276$ u, $m_n = 1.008665$ u, $m_{He} = 4.002602$ u, 1 u = 931.5 MeV/c²). (c) Explain why both fusion of light nuclei and fission of heavy nuclei release energy. (d) A radioactive sample has half-life 12 hours and initial activity 3,200 Bq. Calculate its activity after 36 hours. (e) Write the complete decay equation for $^{14}_6$ C undergoing beta-minus decay. (6 marks)
Model answer (6 marks):
(a) Mass defect = difference between separated nucleon mass and nucleus mass. Binding energy = $\\Delta m \\cdot c^2$ (0.5 mark).
(b) $\\Delta m = 2(1.007276) + 2(1.008665) - 4.002602 = 0.02928$ u. $E_b = 0.02928 \\times 931.5 = 27.3$ MeV. $E_b/A = 6.82$ MeV/nucleon (1.5 marks).
(c) Both processes move toward Fe-56 (peak of binding energy per nucleon curve), increasing binding energy per nucleon and releasing energy (1.5 marks).
(d) 36 h = 3 half-lives. $A = 3200 \\times (1/2)^3 = 400$ Bq (1 mark).
(e) $^{14}_6\\text{C} \\rightarrow \\; ^{14}_7\\text{N} + e^- + \\bar{\\nu}_e$ (1.5 marks).
SAQ 5. (a) Distinguish between hadrons and leptons, and between baryons and mesons. (b) State the quark composition of a proton and a neutron, and verify their charges. (c) Explain why quarks are never observed in isolation. (d) Compare the four fundamental forces in terms of relative strength and range. (e) Identify two major limitations of the Standard Model and propose how each might be addressed by physics beyond the Standard Model. (6 marks)
Model answer (6 marks):
(a) Hadrons experience strong force, composed of quarks. Leptons are fundamental, no strong force. Baryons = 3 quarks ($B = 1$). Mesons = quark-antiquark ($B = 0$) (1 mark).
(b) Proton = $uud$: $+2/3 + 2/3 - 1/3 = +1$. Neutron = $udd$: $+2/3 - 1/3 - 1/3 = 0$ (1 mark).
(c) Strong force energy increases with quark separation. At sufficient energy, new quark-antiquark pairs form rather than freeing isolated quarks (1 mark).
(d) Strong: 1, ~1 fm. EM: $10^{-2}$, infinite. Weak: $10^{-13}$, ~$10^{-18}$ m. Gravity: $10^{-38}$, infinite (1.5 marks).
(e) Any two valid limitations with proposed solutions. Examples: does not include gravity (string theory/loop quantum gravity), neutrino masses (seesaw mechanism), hierarchy problem (SUSY), CP violation not fully explained (1.5 marks).