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).

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]