Question

In Hydrogen spectrum, the wavelength of $H_{\alpha }$ line is 656 nm, whereas in the spectrum of a distant galaxy, $H_{\alpha }$ line wavelength is 706 nm. Estimated speed of the galaxy with respect to 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

Answer: (B)

$2\times {10}^7$m/s

$\frac{1}{{\lambda }^{\prime }}=\frac{1}{\lambda }\sqrt{\frac{c-v}{c+v}}$
Here, ${\lambda }^{\prime }=706nm,\lambda =656nm$
$\therefore \frac{c-v}{c+v}={\left(\frac{\lambda }{{\lambda }^{\prime }}\right)}^2={\left(\frac{656}{706}\right)}^2=0.86$
$\Rightarrow \frac{v}{c}=\frac{0.14}{1.86}\Rightarrow v=0.075\times 3\times {10}^8=2.25\times {10}^7$m/s