Two bodies $A$ and $B$ of equal surface area have thermal emissivities of $0.01$ and $0.81$ respectively. The two bodies are radiating energy at the same rate. Maximum energy is radiated from the two bodies A and B at wavelengths $\lambda _A$ and $\lambda_B$ respectively. Difference in these two wavelength is $1 \; \mu m$. If the temperature of the body A is $5802\;K,$ then value of $\lambda _B$ is

Question

$$(a)\;\frac{1}{2} \mu m \quad (b)\;1\;\mu m \quad (c)\;2\;\mu m \quad (d)\;\frac{3}{2} \;\ mu m$$