What speed should a galaxy move with respect to us so that the sodium line at $589.0nm$ is observed at $589.6nm$?

$\lambda =589.0nm$

$\therefore \Delta \lambda =589.6-589.0$

$=0.6nm$

Hence velocity of Galaxy ;

$=C\times \frac{\Delta \lambda }{\lambda }$

$=C\times \frac{0.6\times {10}^{-9}}{589\times {10}^{-9}}$

$=3\times {10}^8\times \frac{0.6}{589}$

$=3.06\times {10}^{5}m/s$