Two spherical black bodies A and B are emitting radiations at same rate. The radius of B is doubled keeping radius of A fixed. The wavelength corresponding to maximum intensity becomes half for A white it ramains same for B. Then, the ratio of rate radiation energy emitted by a and is B is

Options

A. 2
B. `1//2`
C. 4
D. `1//4`

Answer

C

Explanation

Initially `sigma4pir_(A)^(2)T_(A)^(4)=sigma4pir_(B)^(2)T_(B)^(4)`
Now `(Q_(A))/(Q_(B))=(sigma(4pi)(r_(A))^(2)(2T_(A))^(4))/(sigma4pi(2r_(B)^(2)(T_(B))^(4))=(4r_(A)^(2)T_(A)^(4))/(r_(B)^(2)T_(B)^(4))=4`