Physics • Year 12 • Module 8 • Lesson 2
Evidence for the Big Bang
Apply your understanding of the three pillars of Big Bang evidence to real spectroscopic data, CMB observations, and nucleosynthesis arguments.
1. Interpret spectroscopic data — galaxy recession velocities
A student measured the observed wavelengths of a single spectral line (rest wavelength $\lambda_{rest} = 656.3$ nm, hydrogen Hα) in four galaxies. The Hubble constant is $H_0 = 70$ km/s/Mpc and $c = 3.0 \times 10^5$ km/s. 10 marks
| Galaxy | $\lambda_{obs}$ (nm) | $z = (\lambda_{obs} - \lambda_{rest})/\lambda_{rest}$ | $v \approx cz$ (km/s) | Distance $d = v/H_0$ (Mpc) |
|---|---|---|---|---|
| NGC-Alpha | 659.9 | |||
| NGC-Beta | 669.4 | |||
| NGC-Gamma | 689.1 | |||
| NGC-Delta | 722.0 |
1.1 Complete all four columns in the table. Show your working for NGC-Beta below. 8 marks (2 per galaxy)
1.2 Describe the trend between $\lambda_{obs}$ and distance $d$ in the table. State which law this trend illustrates. 2 marks
2. Interpret CMB data — Planck satellite results
The Planck satellite measured the CMB temperature across the entire sky. The graph below shows a simplified version of the CMB black-body intensity spectrum. 8 marks
Figure 2.1. Simplified CMB black-body spectrum. Data consistent with Planck Collaboration (2018). Illustrative curve.
2.1 Describe the shape of the CMB spectrum shown in the graph. What type of spectrum is this? 2 marks
2.2 Explain why the CMB being isotropic (uniform in all directions to 1 part in 100 000) is evidence that the early universe was in thermal equilibrium. 2 marks
2.3 A student says: “The CMB proves the Big Bang happened because we can see the explosion.” Identify the flaw in this reasoning and write a scientifically correct explanation. 4 marks
3. Compare the three pillars of Big Bang evidence
Complete the table below by describing each pillar across three evaluation criteria. 9 marks (1 per cell)
| Criterion | Cosmological redshift | CMB | Primordial nucleosynthesis |
|---|---|---|---|
| Key observation | |||
| What it proves about the early universe | |||
| Why the steady-state model fails to explain it |
4. Predict and justify — a galaxy survey scenario
The Parkes radio telescope in NSW detects a galaxy “PKS-X” whose Hα spectral line (rest wavelength 656.3 nm) is observed at 698.4 nm. A second galaxy “PKS-Y” is detected at the same observed frequency but is known to be twice as far away. 6 marks
4.1 Calculate the redshift of PKS-X and estimate its distance from Earth (use $H_0 = 70$ km/s/Mpc, $c = 3.0 \times 10^5$ km/s). 3 marks
4.2 PKS-Y is twice as far away as PKS-X. Use Hubble’s law to predict the recession velocity of PKS-Y and calculate the observed wavelength of its Hα line. 3 marks
Q1.1 — Galaxy recession velocity table
Using $z = (\lambda_{obs} - 656.3)/656.3$, $v = cz$, $d = v/H_0$:
- NGC-Alpha: $z = (659.9-656.3)/656.3 = 3.6/656.3 = 0.00549$; $v = 1647$ km/s; $d = 23.5$ Mpc.
- NGC-Beta: $z = (669.4-656.3)/656.3 = 13.1/656.3 = 0.01995$; $v = 5985$ km/s; $d = 85.5$ Mpc.
- NGC-Gamma: $z = (689.1-656.3)/656.3 = 32.8/656.3 = 0.04997$; $v = 14\,991$ km/s; $d = 214.2$ Mpc.
- NGC-Delta: $z = (722.0-656.3)/656.3 = 65.7/656.3 = 0.10011$; $v = 30\,034$ km/s; $d = 429.1$ Mpc.
Accept rounding to 3 significant figures throughout. Marking criteria: 2 marks per galaxy row (1 for $z$, 1 for $v$ and $d$).
Q1.2 — Trend and law
As the observed wavelength $\lambda_{obs}$ increases (greater redshift), the estimated distance $d$ also increases proportionally [1]. This is Hubble’s law: recession velocity (and hence redshift) is proportional to distance [1].
Q2.1 — CMB spectrum shape
The CMB spectrum rises from low frequency, peaks near 160 GHz, then falls off at higher frequencies [1]. It has a smooth, characteristic bell-like shape consistent with a black-body (Planck) spectrum at $T = 2.725$ K [1].
Q2.2 — Isotropy and thermal equilibrium
If the early universe were not in thermal equilibrium, different regions would have different temperatures, producing a highly anisotropic CMB [1]. The extreme uniformity (to 1 part in 100 000) means that all regions of the early universe — even those now far apart — were at the same temperature, which is only possible if the universe was once very small and in thermal contact throughout [1].
Q2.3 — Flaw and correction (4 marks)
Flaw 1 (1 mark): The CMB is not a picture of the Big Bang explosion itself. The CMB was emitted about 380 000 years after the Big Bang, not at the moment of the event.
Flaw 2 (1 mark): The Big Bang was not an “explosion” in the conventional sense — it was not an explosion of matter into existing space, but an expansion of space itself from an extremely hot, dense state.
Correct explanation (2 marks): The CMB is relic thermal radiation released at the epoch of recombination, when the universe cooled enough (~3000 K) for electrons and protons to combine into neutral hydrogen. Photons decoupled from matter and streamed freely. The expansion of the universe has since cooled this radiation to 2.725 K. The CMB is evidence for the Big Bang because the Big Bang model specifically predicts a uniform thermal background at this temperature; no alternative cosmological model can account for it [2].
Q3 — Three pillars comparison table (sample)
Key observation: Redshift: distant galaxies have spectral lines shifted to longer wavelengths, with $z \propto d$. CMB: uniform microwave radiation at 2.725 K arrives from all directions with a perfect black-body spectrum. Nucleosynthesis: ~75% H / ~25% He-4 (plus trace D, He-3, Li-7) in old, unprocessed gas clouds.
What it proves: Redshift: space is expanding (the universe was once smaller and denser). CMB: the early universe was hot and dense, in thermal equilibrium, then cooled. Nucleosynthesis: the early universe was hot and dense enough for nuclear fusion, lasting only a few minutes.
Why steady-state fails: Redshift: a static or steady-state universe would not show systematic redshift proportional to distance. CMB: a steady-state universe has no mechanism to produce a uniform thermal background at a specific temperature. Nucleosynthesis: a steady-state universe cannot produce the observed H/He ratio because it never had a hot, dense early phase.
Award 1 mark per cell for a correct, concise description.
Q4.1 — PKS-X redshift and distance (3 marks)
$z = (698.4 - 656.3)/656.3 = 42.1/656.3 = 0.0641$ [1]. $v = cz = 3.0 \times 10^5 \times 0.0641 = 19\,230$ km/s [1]. $d = v/H_0 = 19\,230/70 = 274.7$ Mpc $\approx 275$ Mpc [1].
Q4.2 — PKS-Y prediction (3 marks)
PKS-Y is twice as far: $d_{Y} = 2 \times 275 = 550$ Mpc [1]. By Hubble’s law, $v_{Y} = H_0 d_{Y} = 70 \times 550 = 38\,500$ km/s; hence $z_{Y} = v/c = 38\,500/(3.0 \times 10^5) = 0.1283$ [1]. $\lambda_{obs} = 656.3 \times (1 + 0.1283) = 656.3 \times 1.1283 \approx 740.5$ nm [1].