Question

If a black body at a temperature T radiates the maximum energy at a wavelength \(\lambda_{m}\), then to radiate the maximum energy at the wavelength \(\frac{\lambda_{m}}{3}\), its temperature should be

• A. increased to \(3T\)
• B. increased to \(9T\)
• C. decreased to \(3T\)
• D. decreased to \(9T\)
• E. increased to \(\sqrt{3}T\)

Hint:

Wien's law: \(\lambda_{\text{max}} T = \text{constant} = 2.898 \times 10^{-3} \text{ m·K}\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Wien's displacement law: \(\lambda_m T = \text{constant}\).

Step 2: Detailed Explanation:
\(\lambda_m T = \lambda_m' T'\)
Given \(\lambda_m' = \frac{\lambda_m}{3}\)
\(\lambda_m T = \frac{\lambda_m}{3} \cdot T' \Rightarrow T' = 3T\)
Temperature must be increased to \(3T\).

Step 3: Final Answer:
Temperature should be increased to \(3T\).