The 6563 Å Hα line emitted by hydrogen in a star is found to be red shifted by 15 Å. Estimate the speed with which the star is receding from the Earth.
Redshift is a Doppler’s effect phenomena seen in the case of electromagnetic waves, It happens whenever the light source moves away from the observer or vice versa and the light or other electromagnetic radiation from an object seems to be increased in wavelength, or shifted to the red end of the spectrum. The wavelength of the light is observed increased because of the change in the frequency of the light observed, since the departing source will give an impression of decreased frequency or increased wavelength, the light observed will shift towards red spectrum or the larger wavelength.
The relation of red shift with velocity is
Where,
λ’ is the apparent increased wavelength,
λ is the original wavelength
δλ is the difference between apparent and original wavelength.
Given:
Wavelength of Hα line emitted by hydrogen
λ = 6563 Å = 6563 × 10 -10 m.
Red shift of the star, δλ = (λ’ - λ) = 15 Å = 15 × 10- 10 m
Speed of Light, c = 3 × 108 m/s
We suppose the velocity of the star receding away from the Earth as v.
Since, the ratio of apparent change in the wavelength is equal to the ratio of velocity of receding body and the standard speed of light.
⇒ v = 6.87 × 105 m/s
The estimated speed with which the star is receding from the Earth is 6.87 × 105 m/s