Question

Three discs A, B and C having radii 2 m, 4m and 6m respectively are coated with carbon black on their outer
surfaces. The wavelengths corresponding to the maximum intensity are 300 nm, 400 nm, 500 nm respectively.
The power radiated by the are$Q_A,Q_B$ and $Q_C$respectively. Then

• A. $Q_A$ is masimum
• B. $Q_B$ is maximum
• C. $Q_C$ is masimum
• D. $Q_A=Q_B=Q_C$

Answer 1

The correct option is B $Q_B$ is maximum

Q= $\sigma A{T}^4$, Here $A=\pi r^2$
According to wien's law
${\lambda }_{m}T=b$
or, $T=\left(\frac{b}{{\lambda }_m}\right)\therefore Q=\sigma \left(\pi r^2\right){\left(\frac{b}{{\lambda }_m}\right)}^4$
or, $Q\alpha \frac{r^2}{{\lambda }_m^4}\therefore Q_B>Q_C>Q_A$