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

Answer 1

Answer: (B)

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