The 6563,mathring{A} H_{alpha} line emitted b | vedclass

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Question

(A) Wavelength of the $H_{\alpha}$ line emitted by hydrogen,$\lambda = 6563\,\mathring{A} = 6563 	imes 10^{-10} \,m$.The redshift of the star is give

Vedclass · Accepted Answer

$6.87 	imes 10^{5} \,m/s$

Vedclass · Answer

(A) Wavelength of the $H_{\alpha}$ line emitted by hydrogen,$\lambda = 6563\,\mathring{A} = 6563 	imes 10^{-10} \,m$.The redshift of the star is given by $\Delta\lambda = \lambda' - \lambda = 15\,\mathring{A} = 15 	imes 10^{-10} \,m$.Speed of light,$c = 3 	imes 10^{8} \,m/s$.For a star receding from the Earth,the Doppler shift formula is $\frac{\Delta\lambda}{\lambda} = \frac{v}{c}$,where $v$ is the speed of the star.Rearranging for $v$,we get $v = c 	imes \frac{\Delta\lambda}{\lambda}$.Substituting the values: $v = (3 	imes 10^{8} \,m/s) 	imes \frac{15 	imes 10^{-10} \,m}{6563 	imes 10^{-10} \,m}$.$v = \frac{45 	imes 10^{8}}{6563} \approx 6.87 	imes 10^{5} \,m/s$.Thus,the speed with which the star is receding from the Earth is $6.87 	imes 10^{5} \,m/s$.

The $6563\,\mathring{A}$ $H_{\alpha}$ line emitted by hydrogen in a star is found to be redshifted by $15\,\mathring{A}$. Estimate the speed with which the star is receding from the Earth.

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