The periodic time of rotation of a certain st | vedclass

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Question

(A) The Doppler shift in wavelength is given by the formula $\Delta \lambda = \lambda \cdot \frac{v}{c}$.Here, $v$ is the tangential velocity of the s

Vedclass · Accepted Answer

$0.033 \ \mathring{A}$

Vedclass · Answer

(A) The Doppler shift in wavelength is given by the formula $\Delta \lambda = \lambda \cdot \frac{v}{c}$.Here, $v$ is the tangential velocity of the star's surface due to rotation, given by $v = r\omega = r 	imes \left( \frac{2\pi}{T} ight)$.Given values are: $\lambda = 4320 \ \mathring{A}$, $r = 7 	imes 10^8 \ m$, $T = 22 \ days = 22 	imes 86400 \ s$, and $c = 3 	imes 10^8 \ m/s$.Substituting these values into the formula:$\Delta \lambda = \frac{4320 	imes 7 	imes 10^8 	imes 2 	imes 3.14}{3 	imes 10^8 	imes 22 	imes 86400}$.$\Delta \lambda = \frac{4320 	imes 7 	imes 2 	imes 3.14}{3 	imes 22 	imes 86400} \ \mathring{A}$.$\Delta \lambda = \frac{190425.6}{5702400} \ \mathring{A} \approx 0.033 \ \mathring{A}$.

The periodic time of rotation of a certain star is $22$ days and its radius is $7 \times 10^8 \ m$. If the wavelength of light emitted by its surface is $4320 \ \mathring{A}$, the Doppler shift will be $(1 \ day = 86400 \ s)$

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