Chapter 44, Problem 32P

The various spectral lines observed in the light from a distant quasar have longer wavelengths λ′_n than the wavelengths λ_n measured in light from a stationary source. Here n is an index taking different values for different spectral lines. The fractional change in wavelength toward the red is the same for all spectral lines. That is, the Doppler redshift parameter Z defined by

$Z=\frac{{{\lambda }^{\prime }}_n-{\lambda }_n}{{\lambda }_n}$

is common to all spectral lines for one object. In terms of Z, use Hubble’s law to determine (a) the speed of recession of the quasar and (b) the distance from the Earth to this quasar.