Three discs A,B and C having radii 2,4 and 6 cm respectively are coated with carbon black. Wavelength for maximum intensity for the three discs are 300,400 and 500 nm respectively. If `Q_A,Q_B and Q_C`are power emitted by A,B and D respectively, then

Options

A. `Q_A` will be maximum
B. `Q_B` will be maximum
C. `Q_C` will be maximum
D. `Q_A=Q_B=Q_C`

Answer

B

Explanation

(b) We know that
`lambda_mT=constant`
`lambda_Altlambda_Bltlambda_C`
So, `T_AgtT_BgtT_C`
`{:' T_A=C/(3xx10^-7),T_B=C/(4xx10^-7),T_C=C/(5xx10^-7)}`
`Q=esigmaAT^4`
`e=1 black body`
`:. Q=sigmaAT^4`
`:. Q_A=sigma.pi(2xx10^-2)^2xxC^4/(27xx10^-28)`
`:. Q_B=sigma.pi(4xx10^-2)^2xxC^2/(64xx10^-28)`
and `Q_C=sigma.pi(6xx10^-2)^2xxC^2/(625xx10^-28)`
From comparison `Q_B` is maximum.