| Date | May 2017 | Marks available | 1 | Reference code | 17M.3.SL.TZ1.10 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Calculate | Question number | 10 | Adapted from | N/A |
Question
A spectral line in the light received from a distant galaxy shows a redshift of z = 0.16.
State two characteristics of the cosmic microwave background (CMB) radiation.
The present temperature of the CMB is 2.8 K. Calculate the peak wavelength of the CMB.
Describe how the CMB provides evidence for the Hot Big Bang model of the universe.
Determine the distance to this galaxy using a value for the Hubble constant of H0 = 68 km s–1\(\,\)Mpc–1.
Estimate the size of the Universe relative to its present size when the light was emitted by the galaxy in (c).
Markscheme
black body radiation / 3 K
highly isotropic / uniform throughout
OR
filling the universe
Do not accept: CMB provides evidence for the Big Bang model.
[2 marks]
«\(\lambda = \frac{{2.9 \times {{10}^{ - 3}}}}{{2.8}}\)» ≈ 1.0 «mm»
[1 mark]
the universe is expanding and so the wavelength of the CMB in the past was much smaller
indicating a very high temperature at the beginning
[2 marks]
«\(z = \frac{v}{c} \Rightarrow \)» v = 0.16 × 3 × 105 «= 0.48 × 105 km\(\,\)s−1»
«\(d = \frac{v}{{{H_0}}} \Rightarrow v = \frac{{0.48 \times {{10}^5}}}{{68}} = 706\)» ≈ 710 «Mpc»
Award [1 max] for POT error.
[2 marks]
\(z = \frac{R}{{{R_0}}} - 1 \Rightarrow \frac{R}{{{R_0}}} = 1.16\)
\(\frac{{{R_0}}}{R} = 0.86\)
[2 marks]
