The power radiated by a black body is `P` and it radiates maximum energy around the wavelength `lambda_(0)` If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength `3lambda_(0)//4` the power radiated by it will increase by a factor of .

Options

A. `(4)/(3)`
B. `(16)/(9)`
C. `(64)/(27)`
D. `(256)/(81)`

Answer

D

Explanation

(4) `lambda_(0) T_(1) = (3 lambda_(0))/(4) T_(2)`
`(T_(2))/(T_(1)) = (4)/(3)`
`(u_(2))/(u_(1)) = ((T_(2))/(T_(1)))^(4) = ((4)/(3))^(4) = (256)/(81)`