Question

Three discs $A,B$ and $C$ having radii $2m,4m$, and $6m$ respectively are coated with carbon black on their other surfaces. The wavelengths corresponding to maximum intensity are $300nm,400nm$ and $500nm$, respectively. The power radiated by them are $Q_a,Q_b$, and $Q_c$, respectively,

• A. $Q_a$ is maximum
• B. $Q_b$ is maximum
• C. $Q_c$ is maximum
• D. $Q_a=Q_b=Q_c$.

Answer 1

Answer: (B)

Radiated power $P=Ae\sigma T^4\Rightarrow P\propto A{T}^4$
From Wein's law, ${\lambda }_{m}T=$ constant $\Rightarrow T\propto \frac{1}{{\lambda }_m}$
$\therefore P\propto \frac{A}{{\left({\lambda }_m\right)}^4}\propto \frac{r^2}{{\left({\lambda }_m\right)}^4}$
$\Rightarrow Q_A:Q_B:Q_C=\frac{2^2}{(300{)}^4}:\frac{4^2}{(400{)}^4}:\frac{6^2}{(500{)}^4}$
$\therefore Q_B$ will be maximum.