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A black body has maximum wavelength λₘ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be:

1. 2/3 λₘ
2. λₘ / 3
3. 4/9 λₘ
4. 9/4 λₘ

Correct answer: 2/3 λₘ

Solution

According to Wien's displacement law, the product of the wavelength at which the intensity is maximum (λₘ) and the absolute temperature (T) is constant: λₘT = constant. For T₁ = 2000 K and T₂ = 3000 K, λₘ₂ = λₘ₁ × (T₁/T₂) = λₘ × (2000/3000) = 2/3 λₘ.

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