The 6563 Å $\mathrm{H}_{a}$ 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.
Wavelength of $\mathrm{H}_{a}$ line emitted by hydrogen,
λ = 6563 Å
= 6563 × 10−10 m.
Star’s red-shift, 
Speed of light, $c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
Let the velocity of the star receding away from the Earth be v.
The red shift is related with velocity as:
$\lambda^{\prime}-\lambda=\frac{v}{c} \lambda$
$v=\frac{c}{\lambda} \times\left(\lambda^{\prime}-\lambda\right)$
$=\frac{3 \times 10^{8} \times 15 \times 10^{-10}}{6563 \times 10^{-10}}=6.87 \times 10^{5} \mathrm{~m} / \mathrm{s}$
Therefore, the speed with which the star is receding away from the Earth is 6.87 × 105 m/s.