The 6563 Å H2 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.
Given that,
Wavelength of H2 line emitted by hydrogen, λ = 6563 Å = 6563 × 10-10 m.
Star’s red-shift can be obtain by, (λ' - λ) = 15 Å = 15 x 10-10 m
We know that, Speed of light, c = 3 x 108 m/s
Let the velocity of the star receding away from the Earth be v. Since the star is receding away, hence its velocity v is negative.
The red shift is related with velocity as: λ' - λ = v/c λ
∴ v = c/λ x (λ' - λ) = 3 x 108 x 15 x 10-10 / 6563 x 10-10 = 6.87 x 105 m/s
Therefore, the speed with which the star is receding away from the Earth is -6.87 × 105 m/s.
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