Question

A star, which is emitting radiation at a wavelength of $5000\mathring{A}$ is approaching the earth with a velocity of $1.5\times 10^{5}m/s.$ The change in wavelength of the radiation as received on the earth is

• A. $25\mathring{A}$
• B. $100\mathring{A}$
• C. zero
• D. $2.5\mathring{A}$

Answer 1

Answer: (A)

${\lambda }_0=\sqrt{\frac{1+\beta }{1-\beta }}{\lambda }_s$
${\lambda }_0$ is observed wave length. $\lambda$ is emitted wave length and $\beta =\frac{v}{c}$
where $c$ is speed of light and $v=1.5\times 10^{6}m/s$
$\delta \lambda ={\lambda }_0-{\lambda }_s={\lambda }_C\left(1-\sqrt{\frac{1+\beta }{1-\beta }}\right)$
$=\lambda \left(1-\sqrt{\frac{1+1.5\times 10^6/3\times 10^8}{1-1.5\times 10^6/3\times 10^8}}\right)=25\mathring{A}$