Question

The $6563A^0{H}_{\alpha }$ line emitted by hydrogen in a star is found to be red-shifted by $15A^0$. 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)

$6.87\times {10}^{5}m{s}^{-1}$

Wavelength of $H_{\alpha }$ line,
$\lambda =6563A^o$
$=6563\times {10}^{-10}$

Redshift observed in star $\left(\acute{\lambda -\lambda }\right)=15A^o=15\times {10}^{-10}$

Let the velocity of the star with which it is receding away from the earth be v.

Red shift relation, $\acute{\lambda }-\lambda$=$\frac{v}{c}\lambda$

$=\frac{c}{\lambda }\times (\acute{\lambda }-\lambda )$

$=\frac{3\times {10}^8\times 15\times {10}^{-10}}{6563\times {10}^{-10}}$

$=6.87\times {10}^{5}m{s}^{-1}$