Question

The 6563 Å Ha 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.

Answer 1

Hey Dear,

◆ Answer -

∆v = -6.857×10^5 m/s

● Explaination -

# Given -

λ = 6563 Å = 6563×10^-10 m

∆λ = 15 Å = 15×10^-10 m

# Solution -

Let ∆v be the relative speed of star receeding from earth -

∆v/c = -∆λ/λ

∆v = c × -∆λ/λ

∆v = 3×10^8 × (-15×10^-10) / (6563×10^-10)

∆v = -6.857×10^5 m/s

Hence, the star is receding from the earth with speed of 6.857×10^5 m/s.

Hope this helps you...

Answer 2

Explanation:

$\Large{\red{\underline{\underline{\tt{\green{Answer:}}}}}}$

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Wavelength of $\sf H_a$ line emitted by hydrogen, $\sf \lambda\:=\:6563\,Å$

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Star's red shift is $\sf (\grave{\lambda}- \lambda)\:=\:15\,Å\:=\:15\times 10^{-10}$

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

The red shift is related with velocity as:

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$\sf (\grave{\lambda}- \lambda)\:=\: \dfrac{v}{c} \lambda$

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$\sf v\:=\: \dfrac{c}{\lambda}\times (\grave{\lambda}- \lambda)$

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$\sf \:=\: \dfrac{3\times 10^8\times 15\times \cancel{10^{-10}}}{6563\times \cancel{10^{-10}}}$

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$\sf \:=\:6.87\times 10^5ms^{-1}$

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Therefore the speed with which the star is receding away from the earth is $\sf{\red{6.87\times 10^5ms^{-1}}}$