Question

A star of emitting radiation 5000 $ \overset{o}{\mathop{\text{A}}}\, $ is coming towards the earth with velocity $ 1.5\times {{10}^{6}}m/s $ . The change of wavelength of radiation on earth will be

• A. 250 $ \overset{o}{\mathop{\text{A}}}\, $
• B. 25 $ \overset{o}{\mathop{\text{A}}}\, $
• C. 2.5 $ \overset{o}{\mathop{\text{A}}}\, $
• D. zero

Answer 1

Answer: (B)

$ \frac{\lambda '}{\lambda }=1-\frac{v}{c} $
$ \Rightarrow $ $ \lambda '=\left( 1-\frac{v}{c} \right)\lambda $
$ =\left( 1-\frac{1.5\times {{10}^{6}}}{3\times {{10}^{8}}} \right)\times 5000 $
$ =4975\overset{o}{\mathop{\text{A}}}\, $
Change in wavelength
$ =5000-4975=25\overset{o}{\mathop{\text{A}}}\, $