Q. A spectral line $\lambda = 5000\ \mathring{\mathrm{A}}$ in the light coming from a distant star is observed as a $5200\ \mathring{\mathrm{A}}$. What will be recession velocity of the star
A) $1.15 \times 10^{7}cm/s$
B) $1.15 \times 10^{7}m/s$
C) $1.15 \times 10^{7}km/s$
D) $1.15\ km/s$
Explanation
(b) $\mathrm{\Delta}\lambda = 5200 - 5000 = 200\mathring{\mathrm{A}}$
Now $\frac{\mathrm{\Delta}\lambda}{\lambda^{'}} = \frac{v}{c} \Rightarrow v = \frac{c\mathrm{\Delta}\lambda}{\lambda^{'}} = \frac{3 \times 10^{8} \times 200}{5000}$
$= 1.2 \times 10^{7}m/s \approx 1.15 \times 10^{7}m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.