Two bodies A and B radiate maximum energy wit | vedclass

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(C) According to Wien's displacement law,the wavelength $\lambda_m$ corresponding to maximum energy emission is inversely proportional to the absolute

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$6$

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(C) According to Wien's displacement law,the wavelength $\lambda_m$ corresponding to maximum energy emission is inversely proportional to the absolute temperature $T$:$\lambda_m T = b$ (where $b$ is Wien's constant).Therefore,$\lambda_{mA} T_A = \lambda_{mB} T_B$.Given that $T_A = 3 T_B$,we substitute this into the equation:$\lambda_{mA} (3 T_B) = \lambda_{mB} T_B \implies \lambda_{mB} = 3 \lambda_{mA}$.We are also given the difference in wavelengths:$\lambda_{mB} - \lambda_{mA} = 4 \mu m$.Substituting $\lambda_{mB} = 3 \lambda_{mA}$ into the difference equation:$3 \lambda_{mA} - \lambda_{mA} = 4 \mu m \implies 2 \lambda_{mA} = 4 \mu m \implies \lambda_{mA} = 2 \mu m$.Now,calculate $\lambda_{mB}$:$\lambda_{mB} = 3 \lambda_{mA} = 3(2 \mu m) = 6 \mu m$.

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

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