Question

The wavelength of spectral line coming from a distant star shifts from $600\, nm$ to $600.1\, nm$. The velocity of the star relative to earth is

• A. $50\, km s^{-1}$
• B. $100\, km s^{-1}$
• C. $25\, km s^{-1}$
• D. $200\, km s^{-1}$

Answer 1

The Correct Option is A

Here, $\lambda = 600\, nm$
$ \Delta\lambda = 600 .1\, nm - 600\, nm = 0.1 \,nm$
As $\frac{v_{s}}{c} = \frac{\Delta\lambda}{ \lambda }$;
$ \therefore v_{s} = \frac{\Delta\lambda}{\lambda } c $
$ =\frac{ 0.1 \,nm}{600 \,nm }\times 3\times 10^{8} \,ms^{-1}$
$\therefore v_{s} = 50 \times 10^{3} ms^{-1}$
$ = 50 \,km s^{-1}$