Ncert Exercises & Solutions

10.11 The 6563 Å Hα line emitted by hydrogen in a star is found to be red-shifted by 15 Å. Estimate the speed with which the star is receding from the Earth.

Hint: Star’s red-shift, (λ′ − λ)
Step 1: Find red-shift.

The wavelength of Hα line emitted by hydrogen,
λ = 6563 Å= 6563 × 10^-10 m.
Star’s red-shift, (λ′ − λ) = 15 Å = 15 × 10^-10 m.
Step 2: Find the speed with which the star is receding from the Earth.
Speed of light, c = 3 × 10⁸ m.
Let the velocity of the star receding away from the Earth be v.
The redshift is related to velocity as:

$\begin{array}{l} λ^{'} - λ = \frac{v}{c} λ \\ v = \frac{c}{λ} \times (λ^{'} - λ) \\ = \frac{3 \times 10^{8} \times 15 \times 10^{- 10}}{6563 \times 10^{- 10}} = 6.87 \times 10^{5} m / s \end{array}$

Therefore, the speed of a star while receding away from the Earth is 6.87 × 10⁵ m/s.

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