Two spheres A and B having radii 3 cm and 5 cm respectively are coated with carbon black on their outer surfaces. The wavelengths of maximum intensity of emitted radiation are 300 nm and 500 nm respectively. If the powers radiated are `Q_A` and `Q_B` respectively, then `(Q_A)/(Q_B)` is

Options

A. `(5/3)^(2)`
B. `5/3`
C. `(5/3)^(4)`
D. `sqrt(5/3)`

Answer

A

Explanation

According to Wien's law `lamda_(m)`T = constant (b)
or `T=b/lamda_(m)" "...(1)`
as per Stefan's law `Q=sigmaAT^(4)" "...(2)`
and for a sphere `A=4pir^(2)`
`therefore` from (2), `Q=sigma*4pir^(2)*b^(4)/lamda_(m)^(4)=(Kr^(2))/((lamda_(m))^(4)`
where `K=4pisigmab^(4)` is a constant
`thereforeQ_(1)/Q_(2)=(r_(1)/r_(2))^(2)(((lamda_(m))_(2))/(lamda_(m))_(1))^(4)`
`thereforeQ_(1)/Q_(2)=(3/5)^(2)xx(500/300)^(4)=(5/3)^(2)`