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

6.18

Step-by-step explanation:

Answer 2

f - f '= 6.18*10^11 Hz

Step-by-step explanation:

The change in frequency is given by:

`(1)/(f')=(1)/(f)(√(1+v/c))/(√(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:

`(1)/(f')=(1)/(6.17x10^(14) Hz)(√(1+(3.01*10^5m/s)(3*10^8m/s)))/(√(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