A star is moving away from the earth with a velocity of $100\text{ km/s}$. If the velocity of light is $3…

A star is moving away from the earth with a velocity of $100\text{ km/s}$. If the velocity of light is $3 \times 10^8\text{ m/s}$, then the shift of its spectral line of wavelength $5700\text{ \AA}$ due to Doppler effect is
  1. (a) $0.63\text{ \AA}$
  2. (b) $1.90\text{ \AA}$
  3. (c) $3.80\text{ \AA}$
  4. (d) $5.70\text{ \AA}$

Solution

$\frac{\Delta \lambda}{\lambda} = \frac{v}{c} \Rightarrow \Delta \lambda = \frac{v}{c} \lambda = \frac{100 \times 10^3}{3 \times 10^8} \times 5700 = 1.90\text{ \AA}$

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