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Q.

The energy spectrum of a black body exihibits maximum around a wavelength λo. The temperature of the black body is now changed such that the energy is maximum around a wavelength 3λo/4. The power radiated by the black body will now increase by a factor of

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a

256/81

b

64/27

c

16/9

d

4/3

answer is A.

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Detailed Solution

According to Wien's displacement law, λm1T1=λm2T2∴ λ0T1=3λ0/4T2or       T1T2=34            ...(i)We know that    E1E2=T14T24∴   E2E1=T2T14        ....(ii)From eqns. (i) and (ii), We get            E2E1=434=25681
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The energy spectrum of a black body exihibits maximum around a wavelength λo. The temperature of the black body is now changed such that the energy is maximum around a wavelength 3λo/4. The power radiated by the black body will now increase by a factor of