Question

A hydrogen line in a star's spectrum

has a frequency of 6.17x1014 Hz
when stationary. In Rigel's spectrum,
it is shifted downward by 4.26x1010
Hz. What is Rigel's velocity relative
to us?

Answer 1

The answer is 20713.13.

Step-by-step explanation:

The previous answerer did everything correctly but left the answer in its unexpanded form. For Acellus, this is the correct answer.

Answer 2

Riegel's velocity relative to us is:
`v_(r) = 2.07 * 10^4 m/s`

Step-by-step explanation:

Frequency of Riegel's spectrum,
`f_(r) = f - f'`

`f' = f - f_(r) = 4.26 * 10^(10) Hz`

From the relativistic doppler effect, the wavelength of Riegel's spectrum is:

`\lambda = \lambda_(r) (1 - (v_(r) )/(c) )\\(c)/(f) = (c)/(f_r) (1 - (v_(r) )/(c) )\\v_(r) = ((f - f_r)/(f) )c\\Since, f' = f - f_r\\v_(r) = ((f')/(f) )c\\v_(r) = ((4.26 * 10^(10))/(6.17 * 10^(14)) ) * (3 * 10^8)\\v_(r) = 2.07 * 10^4 m/s`