A galaxy moves with respect to the earth, so that sodium line of 589.0 ~nm is observed at 589.6 ~nm . The speed of the galaxy is

Step-by-step solution

Given, wavelength of sodium line, =589.0 ~nm =5.89 10⁻⁷ ~m Observed wavelength, ^ =589.6 ~nm =5.896 10⁻⁷ ~m Change in wavelength, aligned &= ^ - &=5.896 10⁻⁷-5.89 10⁻⁷ &=0.006 10⁻⁷ ~m =6 10⁻¹⁰ ~m aligned According to Doppler's shift equation, Speed of galaxy is given as aligned v &= c &= 6 10⁻¹⁰ 5.89 10⁻⁷ 3 10⁸ &=3.06 10⁵ ~m / s &=306 10³ ~m / s =306 ~km / s aligned