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The power radiated by a black body is P and it radiates maximum energy at wavelength λ₀. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 3/4 λ₀, the power radiated by it becomes nP. The value of n is

1. 3/4
2. 4/3
3. 81
4. 256

Correct answer: 256

Solution

Using Wien's displacement law, λ₀T = constant, so if λ decreases to 3/4 λ₀, the temperature T increases by a factor of 4/3. The power radiated is proportional to T⁴ (Stefan-Boltzmann law), so the new power is (4/3)⁴ = 256 times the original power. Thus, n = 256.

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