Question

The $6563 \,\mathring{A}$ $H_\alpha$ line emitted by hydrogen in a star is found to be red-shifted by $15\,\mathring{A}$. The speed with which the star is receding from the earth is

• A. $3.2\times 10^{5} ms^{-1}$
• B. $6.87\times 10^{5} ms^{-1}$
• C. $2\times 10^{5} ms^{-1}$
• D. $12.74\times 10^{5} ms^{-1}$

Answer 1

Answer: (B)

Wavelength of $H_{\alpha}$ line, $\lambda = 6563 \mathring{A} $
$= 6563 \times 10^{-10} m$
Red shift observed in star, $\left(\lambda' -\lambda\right) =15\mathring{A} $
$= 15 \times 10^{-10} m$
Let the velocity of the star with which it is receding away from the earth be $v$
$\therefore $ Red shift relation, $\lambda' - \lambda = \frac{v}{c} \lambda$
$\therefore v = \frac{c}{\lambda} \times\left(\lambda' -\lambda\right)$
$ = \frac{3\times 10^{8}\times 15\times 10^{-10}}{6563\times 10^{-10}}$
$= 6.86 \times 10^{5} ms^{-1}$