A hydrogen atom, when vigorously perturbed, can emit light with a frequency of 6.16 × 1014 Hz. When the same light from hydrogen atoms in a distant galaxy is observed on earth, the frequency is 5.21 × 1014 Hz. Calculate the speed at which the galaxy is receding from the earth (in units of the speed of light, c).

Answer 1

Since v is much less than c, you can use the approximate formula

(delta f)/fo = 0.95*10^14/6.16*10^14
= 0.154 = v/c

v = 0.154 c = 4.6*10^7 m/s

There is an exact formula for the relativistic Doppler shift of light, but I don't believe they expect you to know it. You can find it at

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/reldop2.html