Question

Three discs $A, B$ and $C$ having radii $2\, m , 4 \,m$, and $6\, m$ respectively are coated with carbon black on their other surfaces. The wavelengths corresponding to maximum intensity are $300 \,nm , 400 \,nm$ and $500 \,nm$, 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 $P =A e \sigma T^{4} \Rightarrow P \propto A T^{4}$
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.