Question

The observed wavelength of light coming from a distant galaxy is found to be increased by $0.5\%$ as compared with that coming from a terrestrial source. The galaxy is

• A. receding earth with a speed equal to $5\times {10}^5\text{m/s}$.
• B. approaching earth with a speed equal to $5\times {10}^5\text{m/s}$.
• C. approaching earth with a speed equal to $1.5\times {10}^6\text{m/s}$.
• D. receding earth with a speed equal to $1.5\times {10}^6\text{m/s}$.

Answer 1

The correct option is D receding earth with a speed equal to $1.5\times {10}^6\text{m/s}$.

The Doppler shift in wavelength is given by,

$\frac{\Delta \lambda }{\lambda }=\frac{v_r}{c}$

Here, $\lambda$ increases by $0.5\%$

i.e. $\frac{\Delta \lambda }{\lambda }\times 100=0.5$

$\Rightarrow \frac{\Delta \lambda }{\lambda }=5\times {10}^{-3}$

And $c=3\times {10}^8$

$\therefore 5\times {10}^{-3}=\frac{v_r}{3\times {10}^8}$

$v_r=1.5\times {10}^6\text{m/s}$

As the apparent wavelength is increasing, the galaxy is receding earth.

Hence, $\left(D\right)$ is the correct answer.