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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	1
Command term	Determine	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]

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]

« $z = \frac{v}{c} \Rightarrow$ » v = 0.16 × 3 × 10⁵«= 0.48 × 10⁵km $\,$ 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]

c.i.

[N/A]

c.ii.

Syllabus sections

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

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20N.3.SL.TZ0.16a:
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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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Markscheme

Examiners report

Syllabus sections

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