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Question

The power radiated by a black body is P and it radiates maximum energy around the wavelength λo . If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength 3λo/4 , the power radiated by it will increase by a factor of :

A
4/3
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B
16/9
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C
64/27
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D
256/81
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Solution

The correct option is D 256/81
From Wein's displacement law, we know that λmaxT=CONSTANT

So, let us assume that initial temperature of the body be T1
and by changing the temperature from T1 to T, wavelength will change from λ to 3λ4,so applying the above relation,

λ0T1=3λ04T

Hence, T=43T1

and we know that P=eT4

So, P=25681P

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