State

(i) Hubble’s law.

(ii) the significance of the reciprocal of the Hubble constant.

The wavelength of a certain line in the hydrogen spectrum is measured to be 434 nm in the laboratory. The same line in the hydrogen spectrum of the galaxy 3C-273 is measured on Earth to be 504 nm.

Determine the distance of 3C-273 from Earth using a Hubble constant of 72 kms^–1 Mpc^–1.

(i) galaxies move away from each other/from Earth with a speed that is proportional to their separation/distance from Earth;
Accept answer in terms of equation with symbols defined.

(ii) it gives age of the universe/time since the Big Bang;

$\frac{v}{c} = \left( {\frac{{\Delta \lambda }}{{{\lambda _0}}} = \frac{{504 - 434}}{{434}} = } \right)0.161$;
$d = \left( {\frac{v}{H} = \frac{{0.161 \times 3 \times {{10}^5}}}{{72}} = } \right)672{\rm{Mpc}} \approx 670{\rm{Mpc}}$;
Alward [1] for 578(Mpc) if 504 used in the denominator.