Question

Two metal spheres have radii $r$ and $2r$ and they emit thermal radiation with maximum intensities at wavelengths $\lambda$ and $2\lambda$ respectively. The respective ratio of the radiant energy emitted by them per second will be

• A. $4:1$
• B. $1:4$
• C. $16:1$
• D. $8:1$

Answer 1

Answer: (A)

$T\propto \frac{1}{\lambda }$
[wien's displacement law]
So, $\frac{T_1}{T_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{2\lambda }{\lambda }=2$
and $H=eA\sigma T^4$
$\Rightarrow H\propto A{T}^4$
$\frac{H_1}{H_2}=\frac{4\pi r^2}{4\pi (2r{)}^2}\times \frac{T_1^4}{T_2^4}=\frac{1}{4}\times (2{)}^4=4$
$\therefore H_1:H_2::4:1$