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Date May 2017 Marks available 2 Reference code 17M.3.SL.TZ1.10
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Estimate 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.

[2]
a.i.

The present temperature of the CMB is 2.8 K. Calculate the peak wavelength of the CMB.

[1]
a.ii.

Describe how the CMB provides evidence for the Hot Big Bang model of the universe.

[2]
b.

Determine the distance to this galaxy using a value for the Hubble constant of H0 = 68 km s–1\(\,\)Mpc–1.

[2]
c.i.

Estimate the size of the Universe relative to its present size when the light was emitted by the galaxy in (c).

[2]
c.ii.

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]

a.i.

«\(\lambda  = \frac{{2.9 \times {{10}^{ - 3}}}}{{2.8}}\)» ≈ 1.0 «mm»

[1 mark]

a.ii.

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]

b.

«\(z = \frac{v}{c} \Rightarrow \)» v = 0.16 × 3 × 10«= 0.48 × 10km\(\,\)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]

c.i.

\(z = \frac{R}{{{R_0}}} - 1 \Rightarrow \frac{R}{{{R_0}}} = 1.16\)

\(\frac{{{R_0}}}{R} = 0.86\)

[2 marks]

c.ii.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.3 – Cosmology
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