Question

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

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

Answer 1

The correct option is A $50km{s}^{-1}$

Here, $\lambda =600nm$
$\Delta \lambda =600.1nm-600nm=0.1nm$
$\frac{v_s}{c}=\frac{\Delta \lambda }{\lambda }$

$\therefore v_s=\frac{\Delta \lambda }{\lambda }c=\frac{0.1nm}{600nm}\times 3\times {10}^{8}m{s}^{-1}$

$V_s=50\times {10}^{3}m{s}^{-1}$
$V_s=50km{s}^{-1}$