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Physics Question on huygens principle

The 6563 ?6563 \,? HαH_\alpha line emitted by hydrogen in a star is found to be red-shifted by 15 ?15\,?. The speed with which the star is receding from the earth is

A

3.2×105ms−13.2\times 10^{5} ms^{-1}

B

6.87×105ms−16.87\times 10^{5} ms^{-1}

C

2×105ms−12\times 10^{5} ms^{-1}

D

12.74×105ms−112.74\times 10^{5} ms^{-1}

Answer

6.87×105ms−16.87\times 10^{5} ms^{-1}

Explanation

Solution

Wavelength of HαH_{\alpha} line, λ=6563?\lambda = 6563 ? =6563×10−10m= 6563 \times 10^{-10} m Red shift observed in star, (λ′−λ)=15?\left(\lambda' -\lambda\right) =15? =15×10−10m= 15 \times 10^{-10} m Let the velocity of the star with which it is receding away from the earth be vv ∴\therefore Red shift relation, λ′−λ=vcλ\lambda' - \lambda = \frac{v}{c} \lambda ∴v=cλ×(λ′−λ)\therefore v = \frac{c}{\lambda} \times\left(\lambda' -\lambda\right) =3×108×15×10−106563×10−10 = \frac{3\times 10^{8}\times 15\times 10^{-10}}{6563\times 10^{-10}} =6.86×105ms−1= 6.86 \times 10^{5} ms^{-1}