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Three black discs A, B and C have radii 2 m, 4 m and 6 m respectively. Their emission spectra peak (maximum-intensity wavelength) at 300 nm, 400 nm and 500 nm respectively. If the powers they radiate are Q_A, Q_B and Q_C, which disc radiates the most power?

1. Q_A is maximum
2. Q_B is maximum
3. Q_C is maximum
4. Q_A = Q_B = Q_C

Correct answer: Q_B is maximum

Solution

Since T ~ 1/lambda_max and P ~ r² T⁴ ~ r²/lambda_max⁴, computing r²/lambda⁴ gives B the largest value.

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