Question

In hydrogen spectrum, the wavelength of $H\alpha$ line is $656nm,$ whereas in the spectrum of a distant galaxy, $H\alpha$ line wavelength is $706nm$. Estimated speed of the galaxy with respect to earth is

• A. $2\times {10}^{8}m{s}^{-1}$
• B. $2\times {10}^{7}m{s}^{-1}$
• C. $2\times {10}^{6}m{s}^{-1}$
• D. $2\times {10}^{5}m{s}^{-1}$

Answer 1

The correct option is B $2\times {10}^{7}m{s}^{-1}$

Speed of galaxy $v=c\frac{{\lambda }_{observed}-{\lambda }_{actual}}{{\lambda }_{actual}}=3\times {10}^8\frac{50}{656}=2.28\times {10}^7\cong 2\times {10}^{7}m/s$