Question

A star, which is emitting radiation at a wavelength of $5000\stackrel{0}{\text{A}}$ , is approaching the earth with a velocity of $1.5\times {10}^{5}m/s$ . The change in the wavelength of the radiation as received on the earth is

• A. $25\stackrel{0}{\text{A}}$
• B. $100\stackrel{0}{\text{A}}$
• C. Zero
• D. $2.5\stackrel{0}{\text{A}}$

Answer 1

Answer: (A)

$25\stackrel{0}{\text{A}}$

${\lambda }_0=\sqrt{\frac{1+\beta }{1-\beta }}{\lambda }_s$

${\lambda }_0$ is observed wave length. $\lambda$ is emitted wave length and

$\beta =\frac{v}{c}$ where c is speed of light and $v=1.5\times {10}^{6}m/s$

$\begin{array}{c}\delta \lambda ={\lambda }_0-{\lambda }_s={\lambda }_c\left(1-\sqrt{\frac{1+\beta }{1-\beta }}\right)\\ =\lambda \left(1-\sqrt{\frac{1+1.5\times {10}^6/3\times {10}^8}{1-1.5\times {10}^6/3\times {10}^8}}\right)={25}^{\circ }A\end{array}$

Option A.