Q. The velocity of a moving galaxy is $300\ km\ s^{- 1}$ and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as $0.5\ nm$. Then, the actual wavelength of the spectral line is
A) $3000\ \mathring{\mathrm{A}}$
B) $5000\ \mathring{\mathrm{A}}$
C) $6000\ \mathring{\mathrm{A}}$
D) $4500\ \mathring{\mathrm{A}}$
Explanation
(b) Here, $\mathrm{\Delta}\lambda = 0.5nm = 0.5 \times 10^{- 9}m$
$v = 300kms^{- 1} = 300 \times 10^{3}ms^{- 1}$
As $\frac{\mathrm{\Delta}\lambda}{\lambda} = \frac{v}{c} \Rightarrow \lambda = \frac{\mathrm{\Delta}\lambda c}{v}$
$\therefore\lambda = \frac{(0.5 \times 10^{- 9}m)(3 \times 10^{8}ms^{- 1})}{(300 \times 10^{3}ms^{- 1})} = 5 \times 10^{- 7}m$
$= 5000 \times 10^{- 10}m = 5000\ \mathring{\mathrm{A}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.