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 $x \times 10^{-10} \mathrm{~m}$. The value of $x$, to the nearest integer, is_______.
[Take the value of speed of light c, as $3 \times 10^{8}$ $\mathrm{ms}^{-1}$ ]
Solution:
$\frac{\Delta \lambda}{\lambda} \mathrm{c}=\mathrm{v}$
$\Delta \lambda=\frac{\mathrm{v}}{\mathrm{c}} \times \lambda=\frac{286}{3 \times 10^{5}} \times 630 \times 10^{-9}=6 \times 10^{-10}$