NEET Physics Question - Thermal Physics

The total radiant energy per unit area, normal to the direction of incidence, received at a distance $R$ from the center of a star of radius $r$, whose outer surface radiates as a black body at a temperature $T$ $K$ is given by: (2010 Pre) (Where $\sigma$ is Stefan's Constant)

$\frac{4\pi\sigma r^2 T^4}{R^2}$

$\frac{\sigma r^2 T^4}{R^2}$

$\frac{\sigma r^2 T^4}{4\pi r^2}$

$\frac{\sigma r^4 T^4}{r^2}$

Solution:

Radiant energy per unit area per unit time (Intensity) at distance $R$ is $I = \frac{P}{4\pi R^2} = \frac{\sigma (4\pi r^2) T^4}{4\pi R^2} = \frac{\sigma r^2 T^4}{R^2}$.

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