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. 8
B. 9
C. 10
D. 12

Answer

B

Explanation

Using Wien's law, we have
`lamda_(A)T_(A)=lamda_(B)T_(B)" "thereforeT_(A)/T_(B)=lamda_(B)/lamda_(A)=(1500nm)/(500nm)=3`
By Stefan's law, rate of radiation of total energy `EpropAT^(4)`
`thereforeE_(1)/E_(2)=(4piR_(A)^(2))/(4piR_(B)^(2))xx(T_(A)/T_(B))^(2)=(R_(A)/R_(B))^(2)xx(T_(A)/T_(B))^(2)`
`=(6/18)^(2)xx3^(4)=(1/3)^(2)xx3^(4)=9`