Question

A galaxy moves with respect to us so that sodium light of $589.0$ nm is observed at $589.6$nm. The speed of the galaxy is:

• A. $206km{s}^{-1}$
• B. $306km{s}^{-1}$
• C. $103km{s}^{-1}$
• D. $51km{s}^{-1}$

Answer 1

The correct option is B $306km{s}^{-1}$

The relation between $v$m c and $\lambda$ are, $v\lambda =c$
for small changes in v and $\lambda$,
$v=\frac{\Delta v}{v}=\frac{-\Delta \lambda }{\lambda }$

As $\Delta \lambda =589.6-589.0=+0.6nm$

Therefore using doppler shift $\frac{\delta v}{v}=\frac{-\Delta \lambda }{\lambda }=\frac{-v_{radial}}{c}$
$v_{radial}=+c\left(\frac{0.6}{589.0}\right)$

$+3.06\times {10}^{5}m{s}^{-1}$= $306km{s}^{-1}$

Therefore , the galaxy is moving away from us.