Question

A galaxy is moving away from the earth at a speed of $286{\text{kms}}^{-1}$. The shift in the wavelength of a red line at $630\text{nm}$ is $x\times {10}^{-10}\text{m}$. The value of $x$, to the nearest integer, is _______.

$(c=3\times {10}^8{\text{ms}}^{-1})$

Answer 1

Shift in wavelength is given by,

$\Delta \lambda =\left(\frac{v_r}{c}\right)\lambda$

$=\frac{286\times {10}^3}{3\times {10}^8}\times 630\times {10}^{-9}$

$=6\times {10}^{-10}\text{m}=x\times {10}^{-10}\text{m}$

$\therefore x=6$