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. Stationary with respect to the earth
• B. Approaching the earth with velocity of light
• C. Receding from the earth with the velocity of light
• D. Receding from the earth with a velocity equal to $1.5 \times 10^{6}m/s$

Answer 1

Answer: (D)

Receding from the earth with a velocity equal to $1.5 \times 10^{6}m/s$

Answer 2

$\frac{\Delta\lambda}{\lambda} = \frac{v}{c},$ Now $\Delta\lambda = \frac{0.5}{100}\lambda \Rightarrow \frac{\Delta\lambda}{\lambda} = \frac{0.5}{100}$

$\therefore v = \frac{0.5}{100} \times c = \frac{0.5}{100} \times 3 \times 10^{8} = 1.5 \times 10^{6}m/s$

Increase in λ indicates that the star is receding.