A galaxy is moving away from the earth

Question:

A galaxy is moving away from the earth at a speed of $286 \mathrm{kms}^{-1}$. The shift in the wavelength of a red line at $630 \mathrm{~nm}$ is $\mathrm{x} \times 10^{-10} \mathrm{~m}$. The value of $\mathrm{x}$, to the nearest integer, is [Take the value of speed of light $c$, as $3 \times 10^{8}$ $\left.\mathrm{ms}^{-1}\right]$

Solution:

(6)

$\frac{\Delta \lambda}{\lambda} c=v$

$\Delta \lambda=\frac{v}{c} \times \lambda=\frac{286}{3 \times 10^{5}} \times 630 \times 10^{-9}=6 \times 10^{-10}$

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