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Discuss briefly energy distribution of black body radiation. Hence deduce Wien’s displacement law and Stefan’s law.

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Wein’s displacement law: The wavelength (λm) Corresponding to maximum energy emitted by a black body is inversely proportional to its absolute temperature. i.e. λm\(\frac{1}{T}\) or λm T = b. where b is a constant, called Wein’s constant. The radiation emitted by a black body is called black body radiation. The distribution of energy of a black body radiation at different temperatures is as shown in the figure.

The energy distribution is not uniform. There is a particular wavelength λm at which the energy emitted is maximum. The wavelength λm for which the intensity is maximum decreases with increase in temperature.

Stefan’s law: The total radiation emitted by a perfect black body per second per unit area of the surface is directly proportional to the fourth power of its absolute temperature. If E is radiation emitted per second per unit area of a perfect black body at temperature T then, E ∝ T4 or E = σT4 where s is called Stefan’s constant.

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