Question

The energy spectrum of a black body exhibits a maximum around a wavelength \(λ\). The temperature of a black body is now changed such that the energy is maximum at wavelength \(2λ/3\). The power radiated by the black body will now increase by a factor of

• A. \(\frac{256}{81}\)
• B. \(\frac{81}{16}\)
• C. \(\frac{162}{41}\)
• D. \(\frac{16}{81}\)

Hint:

Wien law gives T inversely proportional to the peak wavelength; power goes as T^4.

Answer 1

The Correct Option is B

Step 1: Wien
$T \propto 1/\lambda_m$, so shrinking the wavelength to $2/3$ raises $T$ by $3/2$.

Step 2: Stefan
$P \propto T^4$.

Step 3: Factor
$(3/2)^4 = 81/16$. Option (B).

Final Answer:
Option (B). \[ \boxed{\frac{81}{16}} \]