The apparent wavelength of the light from a star, moving away from the earth is $0.01\%$ more than its real…

The apparent wavelength of the light from a star, moving away from the earth is $0.01\%$ more than its real wavelength. The speed of the star with respect to earth is
  1. (a) $10\text{ km/s}$
  2. (b) $15\text{ km/s}$
  3. (c) $30\text{ km/s}$
  4. (d) $60\text{ km/s}$

Solution

$\frac{\Delta \lambda}{\lambda} = \frac{v}{c} \Rightarrow \frac{0.01}{100} = \frac{v}{3 \times 10^8}$ $\Rightarrow v = 3 \times 10^4\text{ m/s} = 30\text{ km/s}$

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