Question

In hydrogen spectrum, the wavelength of the line is 656 nm, where as in the spectrum of a distant galaxy, the line wavelength is 706 nm. Estimated speed of galaxy with respect to the earth is :

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

Answer 1

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

$\frac{△\lambda }{\lambda }=\pm \frac{v}{c}$

Here (-) sign to be used for appraoching (+) sign to be used for receding.

$\frac{△\lambda }{\lambda }=\frac{706-656}{656}=\pm =v/c$

$\frac{v}{c}=\frac{50}{656}$

$v=\frac{50}{656}\times c$

$v=\frac{50}{656}\times 3\times {10}^8=2\times {10}^{7}m/s$