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In the spectrum of light of a luminous heavenly body the wavelength of a spectral line is measured to be 4747 $Å$ while actual wavelength of the line is 4700 $Å$ . Tre relative velocity of the heavenly body with respect to earth will be (velocity of light is $3 \times 10^{8}$ m/s)

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3 $\times$ 10⁵m/s moving towards the earth

3 $\times$ 10⁵ m/s moving away from the earth

3 $\times$ 10⁶ m/s moving away from the earth

3 $\times$ 10⁶ m/s moving towards the earth

answer is D.

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Detailed Solution

$\begin{array}{l} Δλ = \frac{v_{s}}{c} λ \\ \Rightarrow v_{s} = \frac{Δλ . c}{λ} = \frac{47 \times 3 \times 10^{8}}{4700} = 3 \times 10^{6} m / s \end{array}$

away from earth

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