Three discs A, B and C having radii 2 m, 4m, and 6 m, respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are 3 m, 4 m and 5 m respectively. The power radiated by them are `P_(A),P_(B)andP_(C )` respectively. Find the ratio of powers emitted by the three discs.

Explanation

To find the ratio of powers emitted by the three discs A, B, and C, we can use Stefan-Boltzmann Law and Wien's Displacement Law. Let's break it down step by step.

### Step 1: Understand the Laws
According to **Stefan-Boltzmann Law**, the power emitted by a black body is proportional to the fourth power of its temperature (T):
\[ P \propto A \cdot T^4 \]
where \( A \) is the area.

According to **Wien's Displacement Law**, the product of the wavelength of maximum intensity (\( \lambda_m \)) and the temperature is constant:
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