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(B) According to Wien's displacement law,the wavelength $\lambda_m$ at which a black body radiates maximum energy is inversely proportional to its abs

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$6$

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(B) According to Wien's displacement law,the wavelength $\lambda_m$ at which a black body radiates maximum energy is inversely proportional to its absolute temperature $T$,i.e.,$\lambda_m T = b$ (constant).Let $\lambda_A$ and $\lambda_B$ be the wavelengths of maximum emission for bodies $A$ and $B$ respectively,and $T_A$ and $T_B$ be their temperatures.Given: $T_A = 3T_B$.From Wien's law: $\lambda_A T_A = \lambda_B T_B$.Substituting $T_A$: $\lambda_A (3T_B) = \lambda_B T_B$,which implies $\lambda_B = 3\lambda_A$.Given the difference in wavelengths: $\lambda_B - \lambda_A = 4 \mu m$.Substituting $\lambda_B = 3\lambda_A$: $3\lambda_A - \lambda_A = 4 \mu m$,so $2\lambda_A = 4 \mu m$,which gives $\lambda_A = 2 \mu m$.Therefore,$\lambda_B = 3 	imes 2 \mu m = 6 \mu m$.

Black bodies $A$ and $B$ radiate maximum energy with wavelength difference $4 \mu m$. The absolute temperature of body $A$ is $3$ times that of $B$. The wavelength at which body $B$ radiates maximum energy is (in $\mu m$)

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