Question

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.

Answer 1

Given: The wavelength of the light emitted by the Hydrogen is, λ=6563  A ∘ or λ=6563× 10 −10  m.

Star’s red shift is ( λ ′ −λ )=15  A ∘ =15× 10 −10  m.

Speed of the light, c=3× 10 8  m/s.

Let v be the velocity of the star receding away from the Earth.

The relation between the red shift and velocity is,

( λ ′ −λ )= v c λ

The velocity of the star is,

v= c×( λ ′ −λ ) λ = 3× 10 8 ×15× 10 −10 6563× 10 −10 = 45× 10 8 6563 =6.86× 10 5  m/s

Thus, the speed of the star receding away from the Earth is 6.86× 10 5  m/s.