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

Options

A. 9
B. 9.5
C. 8
D. 8.5

Answer

A

Explanation

We know that ,
` (lambda_(A))/(lambda_(B)) = T_(B)/T_(A) = 500/1500 = 1/3`
Also, ` E prop T^(4)R^(2)`
(Where , A = surface area = ` 4piR^(2))`
` or E_(A)/E_(B) = (T_(A)/(T_(B))^(4)) (R_(A)/(R_(B))^(2))`
` =(3)^(4) (16/18)^(2) = 9`