Question

A star radiates heat as a black body at temperature ' (T) '. The total radiant energy per unit area received at a distance ' (R) ' from the centre of a star of radius ' (r) ' is : ((\sigma =) Stefan's constant)

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

Hint:

Intensity follows the inverse square law ($I \propto 1/R^2$).

Answer 1

The Correct Option is A

Step 1: Power Radiated
Total power radiated by star $P = \sigma A T^4 = \sigma (4\pi r^2) T^4$.

Step 2: Intensity Formula
Intensity (energy per unit area) at distance $R$ is $I = \frac{P}{4\pi R^2}$.

Step 3: Calculation
$I = \frac{\sigma (4\pi r^2) T^4}{4\pi R^2} = \frac{\sigma r^2 T^4}{R^2}$.
Final Answer: (A)