Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature `T_(1)andT_(2)` respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?.

Answer

9

Explanation

`(lambda_(m))_(B) = 3(lambda_(m))_(A)`
`rArr T_(A) = 3T_(B)`
`E_(1) = 4pi (6)^(2) sigma T_(A)^(4) = 4pi(6)^(2) (3T_(B))^(4)`
`E_(2) = 4pi (18)^(2) sigma T_(B)^(4)`
`(E_(1))/(E_(2)) = 9`.