Question

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

• A. $343\, km\, s ^{-1}$
• B. $686\, km\, s ^{-1}$
• C. $1372\, km\, s ^{-1}$
• D. $1715\, km\, s ^{-1}$

Answer 1

Answer: (B)

$\frac{\Delta u}{v}=\frac{\Delta \lambda}{\lambda}=\frac{v_{\text {radial }}}{c}$
$\Rightarrow \frac{15\, \mathring{A}}{6563\, \mathring{A}}=\frac{v_{\text {radial }}}{3 \times 10^{8} m / s }$
or $v_{\text {Radial }}=686\, km\, s ^{-1}$