Question

A black disc has a radius 'R' and wavelength corresponding to the maximum intensity is '\(λ\)'. The emissive power (E) for the different radii and maximum wavelengths is directly proportional to

• A. \(R,λ\)
• B. \(R^2,λ^{-4}\)
• C. \(R^2,λ^{-2}\)
• D. \(R^2,λ\)

Hint:

Stefan law gives T^4, Wien law gives T proportional to 1/lambda.

Answer 1

The Correct Option is B

Step 1: Stefan:
Power $P=\sigma AT^4$, with $A=\pi R^2$.

Step 2: Wien:
$T=\dfrac b{\lambda_m}$.

Step 3: Substitute:
$P=\sigma\pi R^2\dfrac{b^4}{\lambda_m^4}$, so $P\propto R^2\lambda_m^{-4}$. Option (B).

Final Answer:
Use Stefan law with area R^2 and Wien law for T. \[ \boxed{B} \]