Question

A spectral line of wave length $5000A.U$, in the light coming from a distant star is observed to be shifted to $5004A.U$ The component of the recessional velocity of the star along the line of sight is:

• A. $1.4\times {10}^{5}m/s$
• B. $1.8\times {10}^{5}m/s$
• C. $2.0\times {10}^{5}m/s$
• D. $2.4\times {10}^{5}m/s$
• E. $1.4\times {10}^{4}m/s$

Answer 1

The correct option is D $2.4\times {10}^{5}m/s$

We have $v=zc$ where $z=({\lambda }^{\prime }-\lambda )/\lambda$.

Therefore, the recessional velocity $=\frac{5004-5000}{5000}\times (3\times {10}^8)=\frac{4\times 3\times {10}^8}{5000}=2.4\times {10}^{5}m/s$
Note that we can substitute the wave length in the given unit itself since $z$ is a ratio of wave lengths.