Question

The spectral line for a given element of light received from a distant star is shifted towards longer wavelength side by 0.025%. The velocity of star in the line of light is then

• A. $7.5\times {10}^{4}m{s}^{-1}$
• B. $-7.5\times {10}^{4}m{s}^{-1}$
• C. $3.7\times {10}^{4}m{s}^{-1}$
• D. $-3.7\times {10}^{4}m{s}^{-1}$

Answer 1

Answer: (B)

$-7.5\times {10}^{4}m{s}^{-1}$

Given: The shift occurred in the wavelength of the light received from the star is $0.025\%$

To find: The velocity of the star in the line of light.

Since the wavelength of the light received is increased, it means that the star is traveling towards the observer.

Velocity of star in line of light is

$v=\frac{-\Delta \lambda }{\lambda }\times c$

The changed in wavelength is $0.025\%$ of the actual wavelength. So, $\frac{\Delta \lambda }{\lambda }$ will be $\frac{0.025}{100}$.

$=-\frac{0.025}{100}\times 3\times {10}^8=-7.5\times {10}^{4}m{s}^{-1}$.