Q.The $6563\ \text{Å}$ H$_\alpha$ line emitted by hydrogen in a star is found to be red-shifted by $15\ \text{Å}$. Estimate the speed with which the star is receding from the Earth.

A redshift means the wavelength has increased, which by the Doppler effect signals the source is moving away from us; the fractional wavelength shift directly gives the recession speed as a fraction of the speed of light.

Step 1: The Doppler shift relation for light

For speeds much smaller than $c$, the fractional change in wavelength due to relative radial motion between source and observer is:

A redshift ($\Delta\lambda > 0$, wavelength increases) corresponds to the source receding from the observer.

Step 2: Substitute the given values

Step 3: Evaluate

Since the line is red-shifted (wavelength increased), the star is receding from the Earth.