Three discs, A, B and C having radii 2m, 4m and6m respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are `300nm, 400nm` 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`

Options

A. `Q_(A)` is maximum
B. `Q_(B)` is maximum
C. `Q_(C)` is maximum
D. `Q_(A) = Q_(B) = Q_(C)`

Answer

B

Explanation

Power radiated `Q = esigmaAT^(4)"and" lambda_(m)T= b`So `(300) T_(1) = (400)T_(2) = (500)T_(3)`
`implies 3T_(1) = 4T_(2) = 5T_(3)` and`A_(1) : A_(2) : A_(3) = 4 : 16 : 36 = 1: 4: 9`
`Q_(A) : Q_(B) : Q_(C) = (1)/(81) : (4)/(256) : (9)/(625) implies Q_(B) "is maximum"`.