With what speed should a galaxy move with respect to us to that the sodium line at `589.0 nm` is observed at `589.6 nm` ?

Options

A. 206 km `s^(-1)`
B. 306 km `s^(-1)`
C. 103 km `s^(-1)`
D. 51 km `s^(-1)`

Answer

B

Explanation

The relation between v, c and `lambda` are ,`v lambda=c`
For small change in v and `lambda`,
`(triangle v)/(v)=(-triangle lambda)/(lambda)`
As `triangle lambda =589.6-589.0=+0.6 nm`
Therefore, using doppler shift
`(triangle v)/(v)=(-triangle lambda)/(lambda)=(-v_("radial"))/(c)`
or `-v_("radial")~=+c((0.6)/(589.0))=+3.06xx10^(5)ms^(-1)`
` " " =306kms^(- 1)`
Therefore, the galaxy is moving away from us.