Question

A sodium lamp in space was emitting waves of wavelength $2880Å$. When observed from a planet, its wavelength was recorded at $2886Å$. Find the speed of the planet?

• A. $4.25\times {10}^{5}m/s$
• B. $6.25\times {10}^{5}m/s$
• C. $2.75\times {10}^{5}m/s$
• D. $3.75\times {10}^{5}m/s$

Answer 1

The correct option is B

$6.25\times {10}^{5}m/s$

Step 1: Given data

Wavelength of lamp in space, $\lambda =2880Å$

Wavelength of lamp from planet, ${\lambda }_p=2886Å$

Speed of light, $C=3\times {10}^{8}m/s$

Step 2: Find the speed of the planet

By, doppler effect of light, the speed of planet is given by

$\frac{V_{rel}}{C}=\frac{∆\lambda }{\lambda }$

Where,

Relative velocity $=V_{rel}$

Change in wavelength $=∆\lambda ={\lambda }_p-\lambda$

$$\begin{gathered} V_{rel}=\frac{∆\lambda }{\lambda }\times C \\ {V}_{rel}=\frac{{\lambda }_p-\lambda }{\lambda }\times C \\ {V}_{rel}=\frac{6}{2880}\times 3\times {10}^8 \\ {V}_{rel}=6.25\times {10}^{5}m/s \end{gathered}$$

Hence, option B is correct.