Question

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 (where $\sigma$ is Stefan's constant)

• A. $\frac{\sigma r^2T^4}{R^2}$
• B. $\frac{\sigma r^2T^4}{4\pi r^2}$
• C. $\frac{\sigma r^4T^4}{r^4}$
• D. $\frac{4\pi\sigma r^2T^4}{R^2}$

Answer 1

Answer: (A)

By Stefan's law,
$
E =\sigma e AT ^{4}
$
For black body, e = 1
Energy, $E =\sigma\left(4 \pi r ^{2}\right) T ^{4}$
Intensity, $I =\frac{\sigma\left(4 \pi r ^{2} T ^{4}\right)}{4 \pi R ^{2}}=\frac{\sigma r ^{2} T ^{4}}{ R ^{2}}$