Q.

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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a

34

b

43

c

25681

d

81256

answer is C.

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Detailed Solution

From Wien's law, λmaxT= constant  So, λmax1T1=λmax2T2⇒λ0T=3λ04T'⇒T'=43According to Stefan-Boltzmann law, energy emitted unit time by a black body is AeσT4, i.e., power radiated.∴  P∝T4 So, P2P1=T'T4⇒n=434=25681
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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