The fractional change in the wavelength λ of light from the galaxy Hydra is \(\frac{{\Delta \lambda }}{\lambda }\)=0.204. The distance to Hydra is 820 Mpc.

Estimate in km s^–1 Mpc^–1 a value for the Hubble constant.

An estimate of the age of the universe is \(\frac{1}{H}\) where H is the Hubble constant. Suggest why \(\frac{1}{H}\) overestimates the age of the universe.

\(\frac{{\Delta \lambda }}{\lambda } = 0.204 = \frac{v}{c} \Rightarrow v = 6.12 \times {10^4}{\rm{km}}{{\rm{s}}^{ - 1}}\);
so \(H = \frac{v}{d} = \frac{{6.12 \times {{10}^4}}}{{820}} = 74.6{\rm{km}}{{\rm{s}}^{ - 1}}{\rm{Mp}}{{\rm{c}}^{ - 1}}\);
Award [2] for a bald correct answer.
Award [1 max] if power of ten error in first marking point is carried forward.

present value of expansion rate is used for estimate;
but in the past the expansion rate was greater;