The power radiated by a black body is P and it radiates maximum energy at wavelength, λ$$0$$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $$34$$λ$$0$$ the power radiated by it becomes nP. The value of n is

Question

The power radiated by a black body is P and it radiates maximum energy at wavelength, λ$$0$$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $$34$$λ$$0$$ the power radiated by it becomes nP. The value of n is

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From Wien's law, λ$$maxT=$$ constant  So, λ$$max1T1=$$λ$$max2T2$$⇒λ$$0T=3$$λ$$04T$$'⇒T'$$=43According$$ to $$Stefan-Boltzmann$$ law, energy emitted unit time by a black body is Aeσ$$T4$$, i.e., power radiated.∴  P∝$$T4$$ So, $$P2P1=T$$'$$T4$$⇒$$n=434=25681$$

The power radiated by a black body is P and it radiates maximum energy at wavelength, $λ_{0}$ . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4} λ_{0}$ the power radiated by it becomes nP. The value of n is

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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 34λ0 the power radiated by it becomes nP. The value of n is

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The power radiated by a black body is P and it radiates maximum energy at wavelength, $λ_{0}$ . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4} λ_{0}$ the power radiated by it becomes nP. The value of n is