A) \[\sigma {{r}^{2}}{{T}^{4}}/{{R}^{2}}\]
B) \[\sigma {{r}^{2}}{{T}^{4}}/4\pi {{r}^{2}}\]
C) \[\sigma {{r}^{4}}{{T}^{4}}/{{r}^{4}}\]
D) \[4\pi \,\sigma {{r}^{4}}{{T}^{4}}/{{R}^{2}}\]
Correct Answer: A
Solution :
If r is the radius of the star and T its temperature, then the energy emitted by the star per second through radiation in accordance with Stefan's law will be given by \[A\sigma {{T}^{4}}=4\pi {{r}^{2}}\sigma {{T}^{4}}\]In reaching a distance R this energy will spread over a sphere of radius R; so the intensity of radiation will be given by \[S=\frac{p}{4\pi {{R}^{2}}}=\frac{4\pi {{r}^{2}}\sigma {{T}^{4}}}{4\pi {{R}^{2}}}\]
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