Physics • Year 12 • Module 8 • Lesson 2
Evidence for the Big Bang
Lock in the three pillars of Big Bang evidence — cosmological redshift, the CMB, and primordial nucleosynthesis — before tackling data and extended-response tasks.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: redshift, Hubble’s law, cosmological redshift, lookback time, cosmic microwave background (CMB), primordial nucleosynthesis, black-body spectrum, isotropy, baryon, recession velocity. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The increase in wavelength (shift toward the red end of the spectrum) of light from a source moving away from the observer. | |
| 1.2 | The statement that a galaxy’s recession velocity is proportional to its distance: $v = H_0 d$. | |
| 1.3 | The stretching of photon wavelengths caused by the expansion of space itself, rather than by motion through space. | |
| 1.4 | The time light has been travelling from a distant object to reach us; equals the distance divided by $c$ for nearby objects. | |
| 1.5 | Uniform thermal radiation arriving from all directions, with a temperature of approximately 2.725 K; a relic of the early hot universe. | |
| 1.6 | The production of hydrogen, helium-4, deuterium, helium-3, and trace lithium in the first few minutes after the Big Bang. | |
| 1.7 | A continuous thermal spectrum whose shape depends only on temperature; the CMB is an almost perfect example at 2.725 K. | |
| 1.8 | The property of being the same in all directions; the CMB is isotropic to about 1 part in 100 000. | |
| 1.9 | A type of subatomic particle, such as a proton or neutron, that makes up ordinary (visible) matter. | |
| 1.10 | The speed at which a galaxy appears to be moving away from us, inferred from its redshift via $v \approx cz$. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 Cosmological redshift means that distant galaxies are moving through space away from us at high speed. T / F
2.2 The CMB has a black-body spectrum peaking at a temperature of approximately 2.725 K. T / F
2.3 The CMB was discovered in 1965 by Penzias and Wilson while they were deliberately searching for relic radiation from the Big Bang. T / F
2.4 The observed helium-4 mass fraction in old, unprocessed gas clouds is approximately 25%, which matches Big Bang nucleosynthesis predictions. T / F
2.5 Stars are capable of producing all the helium-4 observed in the universe if enough time has passed since the Big Bang. T / F
2.6 A galaxy at higher redshift is, on average, farther away and therefore we see it at an earlier time in cosmic history. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
black-body · CMB · expansion · helium · Hubble · nucleosynthesis · proportional · redshift
In the 1920s, Edwin ___________ observed that distant galaxies have their spectral lines shifted toward longer (redder) wavelengths — a phenomenon called ___________. The amount of redshift is ___________ to the galaxy’s distance, which is direct evidence for the ___________ of the universe. The second pillar of Big Bang evidence is the ___________, a relic thermal radiation that fills all of space with a near-perfect ___________ spectrum at 2.725 K. The third pillar is primordial ___________, which correctly predicts that approximately 25% of the mass of ordinary matter is in the form of ___________-4 — too abundant to have been produced solely by stars.
4. Short recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What is the key difference between cosmological redshift and the Doppler effect?
4.2 Why does the CMB have a near-perfect black-body spectrum?
4.3 Name the three main light nuclides produced during Big Bang nucleosynthesis and give the approximate mass fraction for each.
4.4 State one reason why the steady-state model of the universe cannot account for the CMB.
5. Formula recall & numerical substitution
Use the formula $z = (\lambda_{obs} - \lambda_{rest}) / \lambda_{rest}$ and Hubble’s law $v = H_0 d$ (with $H_0 = 70$ km/s/Mpc and $v \approx cz$ for small $z$). 6 marks (2 each)
5.1 A spectral line with rest wavelength 486 nm is observed at 510 nm from a distant galaxy. Calculate the redshift $z$.
5.2 Using Hubble’s law, estimate the distance (in Mpc) to the galaxy in Q5.1. (Use $c = 3 \times 10^5$ km/s.)
5.3 A different galaxy has $z = 0.10$. Estimate its recession velocity in km/s.
Q1 — Term–definition match
1.1 redshift • 1.2 Hubble’s law • 1.3 cosmological redshift • 1.4 lookback time • 1.5 cosmic microwave background (CMB) • 1.6 primordial nucleosynthesis • 1.7 black-body spectrum • 1.8 isotropy • 1.9 baryon • 1.10 recession velocity.
Q2 — True / false with correction
2.1 False. Cosmological redshift is caused by the expansion of space stretching the photon wavelengths as they travel, not by galaxies moving through space. The galaxies are largely at rest in their local frame; it is space itself that is expanding.
2.2 True. The CMB has a near-perfect black-body spectrum corresponding to a temperature of 2.725 K.
2.3 False. The CMB was discovered accidentally by Arno Penzias and Robert Wilson in 1965. They were not searching for relic radiation; they noticed an unexplained microwave noise in their radio antenna and only later realised its cosmological significance.
2.4 True. The observed helium-4 mass fraction (~24–25%) in old, metal-poor gas clouds is consistent with the Big Bang nucleosynthesis prediction of approximately 25%.
2.5 False. Stars cannot account for all the observed helium. Stellar nucleosynthesis would overproduce heavy elements relative to the observed abundances, and the deuterium abundance in particular could not survive stellar processing. The high helium fraction is a signature of the hot, dense early universe, not stars.
2.6 True. A higher redshift corresponds to a longer light-travel time, meaning we observe the galaxy at an earlier epoch of cosmic history.
Q3 — Cloze paragraph
In order: Hubble / redshift / proportional / expansion / CMB / black-body / nucleosynthesis / helium.
Q4.1 — Cosmological vs Doppler redshift
The Doppler effect is caused by relative motion of the source through space toward or away from the observer, and redshifts/blueshifts depend on the velocity of the source. Cosmological redshift is caused by the expansion of space itself stretching the wavelength of photons as they travel; the galaxy is not moving through space but being carried apart by the expansion.
Q4.2 — Why the CMB is a black-body spectrum
In the early universe, matter and radiation were in thermal equilibrium: photons were absorbed and re-emitted so frequently that the radiation field took on a perfect black-body (Planck) spectrum characteristic of the temperature. When the universe cooled enough for electrons and protons to combine into neutral hydrogen (recombination, ~380 000 years after the Big Bang), photons decoupled and streamed freely. The cosmic expansion has since cooled them to 2.725 K, preserving the black-body shape.
Q4.3 — Light nuclides from Big Bang nucleosynthesis
Hydrogen-1 (protium): ~75% by mass. Helium-4: ~25% by mass. Trace amounts of deuterium (hydrogen-2), helium-3, and lithium-7 combined: ~0.01% by mass.
Q4.4 — Why the steady-state model fails to explain the CMB
The steady-state model proposes that the universe has always existed in the same state, with matter being continuously created to maintain a constant density. It has no mechanism to produce a uniform, isotropic thermal background at a specific temperature. The CMB requires a hot, dense early phase (the Big Bang) in which radiation and matter were in thermal equilibrium; the steady-state model never has such a phase.
Q5 — Redshift calculations
5.1 $z = (510 - 486)/486 = 24/486 \approx 0.049$. Marking criteria: 1 mark for correct substitution; 1 mark for correct answer (accept $z = 0.049$ or $z \approx 0.05$).
5.2 $v \approx cz = 3 \times 10^5 \times 0.049 = 1.48 \times 10^4$ km/s. $d = v/H_0 = 14\,700/70 \approx 210$ Mpc. Marking criteria: 1 mark for correct calculation of $v$; 1 mark for correct distance (accept 200–215 Mpc).
5.3 $v \approx cz = 3 \times 10^5 \times 0.10 = 3.0 \times 10^4$ km/s = 30 000 km/s. Marking criteria: 1 mark for correct formula; 1 mark for correct answer.