Question

A star of emitting radiation 5000 $\stackrel{o}{A}$ 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 $\stackrel{o}{A}$
• B. 25 $\stackrel{o}{A}$
• C. 2.5 $\stackrel{o}{A}$
• D. zero

Answer 1

Answer: (B)

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