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  • In Hydrogen spectrum, the wavelength of  line is 656 nm, whereas in the spectrum of a distant

In Hydrogen spectrum, the wavelength of H_{\alpha } line is 656 nm, whereas in the spectrum of a distant galaxy, H_{\alpha } line wavelength is 706 nm, Estimated speed of the galaxy with respect to
earth is

Option: 1

2 \times 10^8 \mathrm{~m} / \mathrm{s}


Option: 2

2 \times 10^7 \mathrm{~m} / \mathrm{s}


Option: 3

2 \times 10^6 \mathrm{~m} / \mathrm{s}


Option: 4

2 \times 10^5 \mathrm{~m} / \mathrm{s}


Answers (1)

best_answer

\frac{1}{\lambda^{\prime}}=\frac{1}{\lambda} \sqrt{\frac{\mathrm{c}-\mathrm{v}}{\mathrm{c}+\mathrm{v}}}

Here, \lambda^{\prime}=706 \mathrm{~nm}, \lambda=656 \mathrm{~nm}

\therefore \frac{\mathrm{c}-\mathrm{v}}{\mathrm{c}+\mathrm{v}}=\left(\frac{\lambda}{\lambda^{\prime}}\right)=\left(\frac{656}{706}\right)^2=0.86

\Rightarrow \quad \frac{\mathrm{v}}{\mathrm{c}}=\frac{0.14}{1.86} \Rightarrow \mathrm{v}=0.075 \times 3 \times 10^8=2.25 \times 10^7 \mathrm{~m} / \mathrm{s}

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vinayak

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