Power radiated by a black body is `P_0` and the wavelength corresponding to maximum energy is around `lamda_0`, On changing the temperature of the black body, it was observed that the power radiated becames `(256)/(81)P_0`. The shift in wavelength corresponding to the maximum energy will be

Options

A. `(+lambda_(0))/(4)`
B. `(+lambda_(2))/(2)`
C. `-(lambda_(0))/(4)`
D. `-(lambda_(0))/(2)`

Explanation

According to wien's law, `lambda_(0)T_(0)=lambdaT`
According to stefan's law, `(P_(0))/(P)=[(T_(0))/(T)]^(4)`
Now, `(P)/(P_(0))=(256)/(81)=[(4)/(3)]^(4)`
`therefore (T_(0))/(T)=(3)/(4)=(lambda)/(lambda_(0))`,
or `lambda=(3)/(4)lambda_(0)`
wavelength shift `Deltalambda=lambda-lambda_(0)=(3)/(4)lambda_(0)-lambda_(0)`
`=-(lambda_(0))/(4)`