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` . ?

Explanation

`lambda_(m)T ="constant" , (T_(A))/(T_(B)) = (lambda_(B))/(lambda_(A)) = (1500)/(500) =3`
Rate of total energy radiated `P prop AT^(4) prop R^(2) t^(4)`
`:.(P_(A))/(P_(B)) =((R_(A))/(R_(B))) xx ((T_(A))/(T_(B)))^(4) = ((6)/(18))^(2)xx(3)=9:1` .