Question

The energy spectrum of a black body exhibits a maximum of wavelength \(λ_0\). The temperature of the black body is now changed such that the energy is maximum at wavelength \(\frac{3λ_0}{2}\). The ratio of power radiated by the black body will be

• A. \(\frac{16}{9}\)
• B. \(\frac{16}{81}\)
• C. \(\frac{64}{27}\)
• D. \(\frac{4}{3}\)

Hint:

Wien law $\lambda_mT=$ constant, and power $\propto T^4$.

Answer 1

The Correct Option is B

Step 1: Wien displacement law
\(\lambda_mT=b\). When \(\lambda_m\) changes from \(\lambda_0\) to \(\frac{3\lambda_0}{2}\), \(T^{\prime}=T\cdot\frac{2}{3}\).

Step 2: Stefan law
Radiated power \(\propto T^4\).
\[ \frac{P^{\prime}}{P}=\left(\frac23\right)^4=\frac{16}{81} \]

Step 3: Result
The ratio of the new power to the old is \(\frac{16}{81}\). Option (B).

Final Answer:
The ratio is \(\frac{16}{81}\), option (B). \[ \boxed{\text{(B) } \frac{16}{81}} \]