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: Use a number
Take $T=300$ K. The new $T=200$ K. Then $\frac{200^4}{300^4}=\left(\frac23\right)^4=\frac{16}{81}$.

Final Answer:
Option (B). \[ \boxed{\text{(B)}} \]