At what speed should a galaxy move with respect to earth so that spectral line of 600.0 nm appears as 600.6 nm?

$3×10^5 m s^{-1}$

The correct answer is Option (2) → $3×10^5 m s^{-1}$

Using the doppler effect for light, the relationship between the observed wavelength and emitted wavelength is-

$λ_{observed}=λ_{emitted}\left(1+\frac{v}{c}\right)$

where,

$λ_{observed} = 600.3 nm$ (Observed wavelength)

$λ_{emitted} = 600.0 nm$ (Emitted wavelength)

$v$ = relative velocity

$c = 3×10^8m/s$

$∴v=c\left(\frac{λ_{observed}}{λ_{emitted}}-1\right)$

$=3×10^8\left(\frac{600.6}{600.0}-1\right)$

$=3×10^8×0.001=3.0×10^5m/s$