Suggest why the two wavelengths are different.

Determine the distance to this galaxy from Earth using a Hubble constant of \({\text{74 km}}\,{{\text{s}}^{ - 1}}{\text{Mp}}{{\text{c}}^{ - {\text{1}}}}\).

the galaxy is moving away from the Earth and so the wavelength is Doppler/Red shifted;

or

the universe is expanding and so the space between galaxies is stretched/increases and this means that the wavelength of the received light will also be stretched/increased;

Do not accept answers such as “the galaxy is red-shifted”.

\(v = \left( {\frac{{\Delta \lambda }}{\lambda }c = \frac{{682 - 656}}{{656}} \times 3 \times {{10}^8} = 3.96 \times {{10}^{ - 2}} \times 3 \times {{10}^8} = } \right){\text{ }}1.2 \times {10^4}{\text{ (km}}\,{{\text{s}}^{ - 1}}{\text{)}}\);

\(d = \left( {\frac{v}{{{H_0}}} = \frac{{1.2 \times {{10}^4}}}{{74}} = } \right){\text{ }}160{\text{ (Mpc)}}\); (allow 5 \( \times \) 10²⁴ (m))

Allow ECF from first marking point for [1 max].

For example use of 682 in denominator also giving 160/155 (Mpc).

Award [0] for second marking point if 160 pc, 160 kpc and 160 Gpc are given. These are power of ten errors, not unit errors.

In (a) there were far too many vague responses that just stated 'galaxies are red-shifted'.

Many correct answers were seen in (b), but there were also many power of ten errors where \({\text{km}}\,{{\text{s}}^{ - 1}}\) were not used in the calculation of distance. Another common mistake was to use the observed frequency in the denominator.