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

C

Explanation

(3) `lambda_(1) T_(1) = lambda_(2) T_(2) = lambda_(3) T_(3)`
`300 T_(1) = 400 T_(2) = 500 T_(3)`
`3 T_(1) = 4 T_(2) = 5 T_(3) = k, k:` constant
`Q = sigma A T^(4) = sigma. Pi r^(2) T^(4)`
`Q prop r^(2) T^(4)`
`Q_(a) : Q_(b) : Q_(c ) = (2)^(2) ((k)/(3))^(4) : (4)^(2) ((k)/(4))^(4) : (6)^(2) ((k)/(5))^(4)`
`= (1)/(81) : (1)/(16) : (36)/(25)`
`Q_(C ) gt Q_(b) gt Q_(a)`