QJEEM21Ph5962: JEE Main 2021 Physics - Class 12 JEEM21Ph5962 Solution: With what speed should a galaxy move outward with respect to…

Question

Verified Solution • 2025–26 Session moderate

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890

\overset{o}{A}

is observed at 5896

\overset{o}{A}

?

Accepted Answer

f = f_{0} \sqrt{\frac{1 + β}{1 - β}}

β = \frac{v}{c}

\frac{f}{f_{0}} = \sqrt{\frac{1 + β}{1 - β}}

{(1 + \frac{Δ f}{f_{0}})}^{2} = (1 + β) (1 - β)^{- 1}

β

is small compared to 1

(1 + \frac{2 Δ f}{f_{0}}) = (1 + 2 β)

β = \frac{Δ f}{f_{0}} = \frac{v}{c}

v = 6 \times \frac{c}{5890} = 305.6

km/s

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