The ratio of radiant energy emitted by them per second is the ratio if power.

The intensities at wavelengths be \(=\lambda, 2 \lambda\)

Power \(P =\sigma A \varepsilon T ^4\)

\(\begin{array}{rl}\text { for } 1^{\text {st }} \text { metal sphere } & \text { second :- } \\ \lambda T=k & 2 \lambda T_2=k \\ \lambda T_1=k & T_2=\frac{T}{2} \\ T_1=T & \end{array}\)

\(\begin{aligned}\frac{P_1}{P_2} &=\frac{\sigma T_1^2 4 \pi r_1^2}{\sigma T_2^2 4 \pi r_2^2}=\frac{T_1^2 r^2}{T_2^2 r^2}=\frac{4}{1} \\& \therefore P_1: P_2=4: 1\end{aligned}\)