Question

The Andromeda galaxy is moving toward us at 3.01x10^5 m/s. By how much will the frequency of the 6.17x10^14 Hz hydrogen line be shifted in the galaxy's spectrum?
(Answer is ___x10^11 Hz)

Answer 1

Answer:

f - f '= 6.18*10^11 Hz

Explanation:

The change in frequency is given by:

$\frac{1}{f'}=\frac{1}{f}\frac{\sqrt{1+v/c}}{\sqrt{1-v/c}}$

f': observed frequency

f: source frequency = 6.17*10^14 Hz

v: speed of the source = 3.01*10^55 m/s

c: speed of light = 3*10^8 m/s

By replacing all these values you obtain:

$\frac{1}{f'}=\frac{1}{6.17x10^{14} Hz}\frac{\sqrt{1+(3.01*10^5m/s)(3*10^8m/s)}}{\sqrt{1-(3.01*10^5m/s)(3*10^8m/s)}}=1.62*10^{-15}\\\\f'=6.16*10^{14}Hz$

hence, the change in frequency f-f' will be:

f - f '= 6.18*10^11 Hz