The hα line (sec. 2.6) of a certain star is received on earth at a wavelength of 682 nm. what is the star's radial velocity with respect to earth?

We have that

wavelength of H-alpha (hα) is > 656.3 nm
measured wavelenght > 682 nm

Let
V> radial velocity
C > is the speed of light which is equal to 300,000km/sec.

Doppler formula:
 [(measured wavelenght - wavelength of hα)/ wavelength of hα] = V/C

V=C*[(measured wavelenght - wavelength of hα)/ wavelength of hα]
V=300000*[(682 - 656.3)/ 656.3]=11747.67 km/sec

the answer is 11747.67 km/sec

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