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)T="constant"lambda_(A)T_(A)=lambda_(A)T_(A)=lambda_(B)T_(B)`
Now rate of total energy radiated `propAT^(4)rArr(E_(A))/(E_(B))=((T_(A))/(T_(B)))^(4)xx((R_(A))/(R_(B)))^(2)=(3)^(4)xx((6)/(18))^(2)=9`