At what speed should a galaxy move with respect to earth so that spectral line of 600.0 nm appears as 600.6 nm?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 3 \times 10^{5}\,\mathrm{m\,s^{-1}} \)
By the Doppler effect for light, a source moving with speed \( v \) (much less than \( c \)) along the line of sight shifts each wavelength by
\( \displaystyle \frac{\Delta\lambda}{\lambda} = \frac{v}{c} \)
The line appears at a longer wavelength, a red shift, so the galaxy is moving away from the earth.
\( \Delta\lambda = 600.6 - 600.0 = 0.6\,\mathrm{nm} \)
\( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle v = c\,\frac{\Delta\lambda}{\lambda} = 3\times10^{8} \times \frac{0.6}{600.0} = 3\times10^{5}\,\mathrm{m\,s^{-1}} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
The Doppler Effect – …
