The radiation emitted by a star A is 10,000 t | vedclass

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(C) According to Stefan-Boltzmann Law,the power radiated by a star is given by $Q = \sigma A T^4 = \sigma (4 \pi r^2) T^4$,where $r$ is the radius and

Vedclass · Accepted Answer

$900$

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(C) According to Stefan-Boltzmann Law,the power radiated by a star is given by $Q = \sigma A T^4 = \sigma (4 \pi r^2) T^4$,where $r$ is the radius and $T$ is the surface temperature.Therefore,$Q \propto r^2 T^4$.Given: $\frac{Q_{	ext{star}}}{Q_{	ext{sun}}} = 10,000$,$T_{	ext{sun}} = 6000 \ K$,and $T_{	ext{star}} = 2000 \ K$.Using the ratio formula: $\frac{Q_{	ext{star}}}{Q_{	ext{sun}}} = \left( \frac{r_{	ext{star}}}{r_{	ext{sun}}} ight)^2 	imes \left( \frac{T_{	ext{star}}}{T_{	ext{sun}}} ight)^4$.Substituting the values: $10,000 = \left( \frac{r_{	ext{star}}}{r_{	ext{sun}}} ight)^2 	imes \left( \frac{2000}{6000} ight)^4$.$10,000 = \left( \frac{r_{	ext{star}}}{r_{	ext{sun}}} ight)^2 	imes \left( \frac{1}{3} ight)^4$.$10,000 = \left( \frac{r_{	ext{star}}}{r_{	ext{sun}}} ight)^2 	imes \frac{1}{81}$.$\left( \frac{r_{	ext{star}}}{r_{	ext{sun}}} ight)^2 = 10,000 	imes 81 = 810,000$.$\frac{r_{	ext{star}}}{r_{	ext{sun}}} = \sqrt{810,000} = 900$.Thus,the ratio of the radii is $900:1$.

The radiation emitted by a star $A$ is $10,000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is (in $:1$)

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