The power radiated by a black body is P and it radiates maximum energy at wavelength, `lambda_(0)`. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength `(3)/(4)lambda_(0)`, the power radiated by it becomes nP. The value of n is

Options

A. `256/81 `
B. `4/3 `
C. `3/4 `
D. `81/256`

Answer

A

Explanation

Wien.s law can be written as follows:
`lamda_(max)` T = constant
T is absolute temperature of body and max is the wavelength of energy which is radiated maximum by the body.
So ` lamda_(max_1) T_1 = lamda_(max_2) T_2`
` rArr lamda_0 = (3 lamda_0)/(4) T.`
` rArr T. = 4/3 T`
Power radiated by the black body is proportional to the fourth power of the absolute temperature of the body.
` P_2/P_1 = ( (T.)/(T) )^4 = (4/3)^4 = 256/81 `
So, `(nP)/(P) = 256/81`
`n = 256/81`