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

Raidated power `P=A epsilon sigma T^(4) rArr P prop AT^(4)`
From Wein's law `lambda_(m)T = consta nt rArr T prop 1/(lambda_m)`
`:. P prop (A)/((lambda_m)^(4)) prop (r^2)/((lambda_m)^(4))`
`rArr Q_(A):Q_(B):Q_(C) = (2^2)/((300)^(4)) : (4^2)/((400)^(4)):(6^2)/((500)^(4))`
`:. Q_(B)` will be maximum`.