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Nuclear Fission

The radiation...

Question

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperature of the sun and star $A$ are $6000 K$ and $2000 K$ , respectively, the ratio of the radii of the star $A$ and the sun is

A

300 : 1

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B

600 : 1

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C

900 : 1

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D

1200 : 1

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Solution

The correct option is A $900 : 1$
Stars can be approximated as black bodies.
Hence by stefan's law, power emitted=P= $σ A T^{4}$
Thus, $\frac{P_{A}}{P_{s u n}} = \frac{r_{A}^{2} T_{A}^{4}}{r_{s u n}^{2} T_{s u n}^{4}}$
$\Rightarrow (\frac{r_{A}}{r_{s u n}})^{2} = 10000 \times (\frac{6000}{2000})^{4} \to \frac{r_{A}}{r_{s u n}} = 900$
So required ratio is 900:1

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