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A body at temperature T1 has its spectral emissive power E_λ plotted against wavelength, and the area under that curve is A. When the body's temperature changes to T2, the area under the corresponding curve becomes 9A. What is the ratio λ1/λ2 of the wavelengths of peak emission?

1. 3
2. 1/3
3. 1/√3
4. √3

Correct answer: √3

Solution

Area ∝ T⁴, so (T2/T1)⁴ = 9 -> T2/T1 = sqrt(3). By Wien's law λ ∝ 1/T, hence λ1/λ2 = T2/T1 = sqrt(3).

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