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

Answer 1

Answer: (B)

$306\, km \,s^{-1}$

Answer 2

The relation between $\upsilon, c$ and $\lambda$ are, $\upsilon\lambda = c$
For small changes in $\upsilon$ and $\lambda$,
$\frac{\Delta\upsilon}{\upsilon} = \frac{-\Delta\lambda}{\lambda}$
As $\Delta\lambda = 589.6 - 589.0 = + 0.6\, nm$
Therefore, using doppler shift
$\frac{\Delta\upsilon}{\upsilon} = \frac{-\Delta\lambda}{\lambda} = \frac{-v_{radial}}{c}$
or $v_{radial} ? +c\left(\frac{0.6}{589.0}\right)$
$= + 3.06 \times10^{5} m \,s^{-1}$
$= 306 \,km\, s^{-1}$