The black discs \(x, y\) and \(z\) have radii \(1 \mathrm{~m}, 2 \mathrm{~m}\) and 3 m respectively. The wavelengths corresponding to maximum intensity are \(200 \mathrm{~nm}, 300 \mathrm{~nm}\) and 400 nm respectively. The relation between emissive power \(\mathrm{E}_{\mathrm{x}}, \mathrm{E}_{\mathrm{y}}\) and \(\mathrm{E}_{\mathrm{z}}\) is

\(\begin{array}{ll}
\text { Emissive power } E=\sigma A T^4 & \Rightarrow E \propto A T^4 \\
A=\pi R^2 & \Rightarrow A \propto R^2
\end{array}\)
Given, \(\mathrm{R}_1=1 \mathrm{~m}, \mathrm{R}_2=2 \mathrm{~m}, \mathrm{R}_3=3 \mathrm{~m}\)
\(\Rightarrow A_x: A_y: A_z:: 1: 4: 9\)
By Wien's displacement law
\(\lambda_{\max } \mathrm{T}=\text { constant } \quad \Rightarrow \mathrm{T} \propto \frac{1}{\lambda}\)
Given,
\(\begin{aligned}
& \lambda_{\max 1}=200 \mathrm{~nm}, \lambda_{\max 2}=300 \mathrm{~nm}, \lambda_{\max 3}=400 \mathrm{~nm} \\
& \Rightarrow \lambda_x: \lambda_y: \lambda_z:: 2: 3: 4 \\
& \frac{1}{\mathrm{~T}_x}: \frac{1}{\mathrm{~T}_{\mathrm{y}}}: \frac{1}{\mathrm{~T}_{\mathrm{z}}}:: 2: 3: 4
\end{aligned}\)
\(\begin{aligned}
\therefore \quad & T_x: T_y: T_z:: \frac{1}{2}: \frac{1}{3}: \frac{1}{4} \\
& \text { or } T_x: T_y: T_z:: 6: 4: 3...(ii)
\end{aligned}\)
Comparing the product \(\mathrm{AT}^4\) for the 3 discs From (i) and (ii), we have, for disc \(\mathrm{x}: \mathrm{A}_{\mathrm{x}} \mathrm{T}_{\mathrm{x}}^4=1 \times(6)^4=1296\)
for disc \(\mathrm{y}: \mathrm{A}_{\mathrm{y}} \mathrm{T}_{\mathrm{y}}^4=4 \times(4)^4=1024\)
for disc \(z: A_z T_z^4=9 \times(3)^4=729\)
\(\therefore \quad \mathrm{E}_{\mathrm{x}}\gt\mathrm{E}_{\mathrm{y}}\gt\mathrm{E}_{\mathrm{z}}\).