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A black body at 1227°C emits radiations with maximum intensity at a wavelength of 5000Å. If the temperature of the body is increased by 1000°C, the maximum intensity will be observed at:

1. 5000Å
2. 6000Å
3. 3000Å
4. 4000Å

Correct answer: 4000Å

Solution

According to Wien's displacement law, the wavelength of maximum intensity is inversely proportional to the absolute temperature (λ_max ∝ 1/T). Converting temperatures to Kelvin, initial T1 = 1227 + 273 = 1500 K and final T2 = 2227 + 273 = 2500 K. Using λ_max1 * T1 = λ_max2 * T2, we find λ_max2 = (λ_max1 * T1) / T2 = (5000 * 1500) / 2500 = 3000 Å.

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