Power radiated by a black body at temperature `T_(1)` is P and it radiates maximum energy at a wavelength `lambda_(1)`. If the temperature of the black body is changed from `T_(1)` to `T_(2)` , itradiates maximum energy at a wavelength `lambda_(1)//2`.The power radiated at `T_(2)` is

Options

A. ` 2 P`
B. `4 p`
C. `8 P`
D. `16 P`

Answer

D

Explanation

From Weins law , `lambda T` = Constant
`lambda_(1) /lambda_(2) = T_(2)/T_(1) `
` lambda _(1)/((lambda_(1)//2)) = T_(2)/T_(1) implies T_(2) = 2T_(1)`
Power radiated by a blackbody , `E prop T^(4)`
`E_(1)/E_(2) = (T_(1)/T_(2))^(4)`
`implies E_(1)/E_(2) = (T_(1)/(2T_(1)))^(4)`
`implies E_(2) = 16E_(1)`
` therefore P_(2) = 16 P