The 6563 Å
Question:

The 6563 Å $\mathrm{H}_{a}$ 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.

Solution:

Wavelength of $\mathrm{H}_{a}$ line emitted by hydrogen,

λ = 6563 Å

= 6563 × 10−10 m.

Star’s red-shift, $\left(\lambda^{\prime}-\lambda\right)=15Å =15 \times 10^{-10} \mathrm{~m}$

Speed of light, $c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$

Let the velocity of the star receding away from the Earth be v.

The red shift is related with velocity as:

$\lambda^{\prime}-\lambda=\frac{v}{c} \lambda$

$v=\frac{c}{\lambda} \times\left(\lambda^{\prime}-\lambda\right)$

$=\frac{3 \times 10^{8} \times 15 \times 10^{-10}}{6563 \times 10^{-10}}=6.87 \times 10^{5} \mathrm{~m} / \mathrm{s}$

Therefore, the speed with which the star is receding away from the Earth is 6.87 × 105 m/s.

 

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