Question

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

• A. \(\frac{9}{4}\)
• B. \(\frac{81}{16}\)
• C. \(\frac{3}{2}\)
• D. \(\frac{27}{8}\)

Hint:

Wien's law gives the new temperature; power goes as T^4.

Answer 1

The Correct Option is B

Step 1: Link wavelength and power:
$P\propto T^4\propto\lambda_m^{-4}$ from Wien's law.

Step 2: Substitute:
$\dfrac{P_2}{P_1} = \left(\dfrac{\lambda}{2\lambda/3}\right)^4 = \left(\dfrac32\right)^4$.

Step 3: Evaluate:
$\dfrac{81}{16}$, option (B).

Final Answer:
Power increases by a factor of 81/16. \[ \boxed{\text{(B) }\dfrac{81}{16}} \]