Lessons 1–3 cover the Big Bang theory, the evidence for it, and Hubble's law and the expanding universe. This checkpoint assesses your understanding of cosmological concepts and your ability to apply Hubble's law and interpret observational evidence.
Expansion of space, cosmic timeline, recombination, CMB
Three pillars: redshift, CMB, primordial nucleosynthesis
$v = H_0 d$, redshift, scale factor, lookback time
15 questions — instant feedback
Q1. The Big Bang is best described as:
Correct: B. The Big Bang is expansion of space, not an explosion into space.
Q2. The Cosmic Microwave Background was released when:
Correct: C. Recombination (~380,000 years) made the universe transparent, releasing the CMB.
Q3. Which of the following is NOT one of the three main pillars of Big Bang evidence?
Correct: A. The three pillars are: (1) expansion/redshift, (2) CMB, (3) primordial nucleosynthesis. Black holes are not direct evidence for the Big Bang.
Q4. A galaxy at 300 Mpc has recession velocity approximately:
Correct: B. $v = H_0 d = 70 \\times 300 = 21,000$ km/s.
Q5. A spectral line at rest wavelength 500 nm is observed at 525 nm. The redshift is:
Correct: C. $z = (525 - 500)/500 = 25/500 = 0.05$.
Q6. The Cosmic Microwave Background is best described as:
Correct: B. The CMB is black-body radiation from recombination (~380,000 years after the Big Bang), redshifted to microwave wavelengths with a temperature of approximately 2.725 K.
Q7. Primordial nucleosynthesis produced primarily:
Correct: B. In the first few minutes after the Big Bang, protons and neutrons fused to form mainly helium-4 (~25% by mass), with trace amounts of deuterium and lithium-7. Heavier elements formed later in stars.
Q8. A spectral line with rest wavelength 656 nm is observed at 720 nm from a distant galaxy. The redshift is approximately:
Correct: B. $z = (\\lambda_{obs} - \\lambda_{rest})/\\lambda_{rest} = (720 - 656)/656 = 64/656 \\approx 0.098$.
Q9. Using Hubble's law with $H_0 = 70$ km/s/Mpc, a galaxy with recession velocity 14,000 km/s is approximately:
Correct: B. $d = v/H_0 = 14{,}000/70 = 200$ Mpc. This assumes the velocity is due to cosmic expansion and not local gravitational motion.
Q10. The scale factor when light from a galaxy with $z = 3$ was emitted was:
Correct: D. $a_{then} = 1/(1+z) = 1/4 = 0.25$. The universe was one-quarter its present size.
Q11. Which observation provides the strongest evidence that the universe is expanding?
Correct: B. Hubble's observation that recession velocity increases linearly with distance ($v = H_0 d$) is direct evidence of cosmic expansion. More distant galaxies recede faster, consistent with uniform expansion.
Q12. The Hubble time ($1/H_0$) is approximately:
Correct: C. $t_H = 1/H_0 \\approx 14$ Gyr, close to the actual age of 13.8 Gyr.
Q13. Primordial nucleosynthesis produced mainly hydrogen and helium because:
Correct: B. Nucleosynthesis lasted only ~3 minutes. By then the universe had cooled below the temperature needed to overcome the Coulomb barrier for heavier nuclei.
Q14. The small anisotropies in the CMB (temperature fluctuations of ~1 part in 100,000) are significant because they:
Correct: D. The tiny temperature anisotropies correspond to density fluctuations in the early universe. These fluctuations grew via gravitational instability to form galaxies, clusters, and the large-scale structure we observe today.
Q15. The peak wavelength of the CMB is approximately:
Correct: B. Using Wien's law, $\\lambda_{max} = b/T = 2.898\\times10^{-3}/2.725 \\approx 1.06$ mm, in the microwave region of the spectrum.
5 questions — model answers revealed
SAQ 1. (a) Outline the three main lines of evidence supporting the Big Bang theory. (b) Explain why the CMB is described as a black-body spectrum and why this is significant. (3 marks)
Model answer (3 marks):
(a) (1) Cosmological redshift — galaxies recede with velocity proportional to distance, indicating expanding space (0.5 mark). (2) CMB — uniform black-body radiation at 2.725 K, relic from recombination (0.5 mark). (3) Primordial nucleosynthesis — observed H/He ratio matches Big Bang predictions (0.5 mark).
(b) The CMB has a perfect thermal spectrum with peak wavelength corresponding to 2.725 K (0.5 mark). A hot early universe that cooled by expansion naturally produces this spectrum; no other model predicts it (0.5 mark).
SAQ 2. (a) State Hubble's law. (b) A galaxy shows an emission line at 672 nm with rest wavelength 656 nm. Calculate redshift, recession velocity, and distance using $H_0 = 70$ km/s/Mpc. (c) Explain why Hubble's law implies space is expanding rather than galaxies moving through space. (4 marks)
Model answer (4 marks):
(a) $v = H_0 d$ — recession velocity proportional to distance (0.5 mark).
(b) $z = (672-656)/656 = 0.0244$ (0.5 mark). $v = cz = 0.0244 \\times 3\\times10^5 = 7320$ km/s (0.5 mark). $d = v/H_0 = 7320/70 = 105$ Mpc (0.5 mark).
(c) If galaxies moved through space, we would expect a centre of explosion with faster galaxies farther out. Instead, every observer in any galaxy sees the same expansion pattern (1 mark). This is consistent only with space itself stretching uniformly (1 mark).
SAQ 3. (a) Explain how the cosmic microwave background provides evidence for the Big Bang theory. (b) Describe what is meant by primordial nucleosynthesis and identify which elements were produced. (c) Explain why heavier elements such as carbon and iron could not have formed during primordial nucleosynthesis. (4 marks)
Model answer (4 marks):
(a) The CMB is black-body radiation with a temperature of ~2.7 K (0.5 mark). Its existence was predicted by the Big Bang theory as cooled radiation from when the universe became transparent (~380,000 years after the Big Bang) (0.5 mark). The observed spectrum matches the theoretical prediction precisely (0.5 mark).
(b) Primordial nucleosynthesis is the formation of light nuclei in the first few minutes after the Big Bang (0.5 mark). It produced mainly hydrogen and helium-4, with trace amounts of deuterium and lithium-7 (0.5 mark).
(c) Heavier elements require fusion reactions at higher temperatures and densities than existed in the early universe (0.5 mark). There was insufficient time before the universe cooled below the temperatures needed for fusion beyond helium (0.5 mark).
SAQ 4. (a) State Hubble's law and define each variable. (b) A galaxy has a recession velocity of 21,000 km/s. Calculate its distance using $H_0 = 70$ km/s/Mpc. (c) Explain why Hubble's law implies the universe is expanding rather than galaxies moving through static space. (d) The same galaxy shows a spectral line at 720 nm that has a rest wavelength of 600 nm. Calculate the redshift and verify that it is consistent with Hubble's law. (5 marks)
Model answer (5 marks):
(a) $v = H_0 d$, where $v$ is recession velocity (km/s), $H_0$ is Hubble's constant (km/s/Mpc), and $d$ is distance (Mpc) (1 mark).
(b) $d = v/H_0 = 21{,}000/70 = 300$ Mpc (1 mark).
(c) Hubble's law shows velocity proportional to distance for all galaxies (0.5 mark). If galaxies moved through space, there would be no such systematic relationship, and some galaxies would approach us (0.5 mark). Uniform expansion of space itself explains why all distant galaxies recede and why the recession velocity increases with distance (1 mark).
(d) $z = (\\lambda_{obs} - \\lambda_{rest})/\\lambda_{rest} = (720 - 600)/600 = 0.20$ (0.5 mark). For small $z$, $v \\approx cz = 0.20 \\times 3\\times10^5 = 60{,}000$ km/s. Then $d = 60{,}000/70 = 857$ Mpc (0.5 mark). Note: this is approximate since $z = 0.20$ is moderately large and the linear relation $v = cz$ is not exact.
SAQ 5. (a) Explain what is meant by cosmological redshift and distinguish it from Doppler redshift. (b) A quasar has $z = 4.0$. Calculate the scale factor when its light was emitted. (c) Calculate its approximate distance using $d = cz/H_0$ ($H_0 = 70$ km/s/Mpc). (d) Explain why this distance is only an approximation for large $z$. (e) Describe how the uniformity of the CMB temperature supports the Big Bang theory and outline what the small anisotropies tell us. (5 marks)
Model answer (5 marks):
(a) Cosmological redshift: stretching of wavelengths due to expansion of space itself (0.5 mark). Doppler redshift: shift due to relative motion through space (0.5 mark).
(b) $a_{then} = 1/(1+z) = 1/5 = $ 0.20 (0.5 mark).
(c) $v = cz = 4c = 1.2\\times10^6$ km/s. $d = 1.2\\times10^6/70 = 17,100$ Mpc (0.5 mark).
(d) For large $z$, $v = cz$ is only an approximation because the expansion rate has changed over time. The actual distance depends on the integral of $c/H(t)$ over cosmic time (1 mark).
(e) The CMB is highly uniform to 1 part in 100,000, indicating the early universe was homogeneous and isotropic (0.5 mark). This is consistent with the Big Bang prediction of a hot, dense initial state (0.5 mark). The small anisotropies represent density fluctuations that seeded the formation of galaxies and large-scale structure (0.5 mark).