A black body radiates energy at the rate of `E W//m^(2)` at a high temperature T K. When the temperature is reduced to `(T/2)` K, the radiant energy is

Options

A. `(E)/(2)`
B. 2 E
C. `( E )/(4)`
D. `( E) /(16)`

Answer

D

Explanation

For a black body radiation,
According to stefan's law, `E prop T^(4)`
`E_(1)/E_(2) = (T_(1)/T_(2))^(4)`
`implies E_(1)/E_(2) = (T/(T/2))^(4)`
`implies E_(1) = 16E_(2)`
`therefore E_(2) = E_(1)/(16)`