First slide

Radiation

Question

Three discs A, B and C having radii 2m, 4m, 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

Moderate

A

$Q_{a}$ is maximum
B

$Q_{b}$ is maximum
C

$Q_{c}$ is maximum
D

$Q_{a} = Q_{b} = Q_{c}$

Solution

Radiated power P = $A \in {σT}^{4} \Rightarrow P \propto {AT}^{4}$
From Weins's law, $λ_{m} T = constant \Rightarrow T \propto \frac{1}{λ_{m}}$
$∴ P \propto \frac{A}{{(λ_{m})}^{4}} \propto \frac{r^{2}}{{(λ_{m})}^{4}}$
$\Rightarrow Q_{a} : Q_{b} : Q_{c} = \frac{2^{2}}{{(300)}^{4}} : \frac{4^{2}}{{(400)}^{4}} : \frac{6^{2}}{{(500)}^{4}}$
$∴ Q_{b} will be maximum$

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