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

Options

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

Answer

C

Explanation

From Stefan - Boltzmann.s law,
`P=sigmaAT^(4)" "[becausee=1]`
`:.PpropT^(4)" "[becausesigma" and A equal"]`
Now, from Wein.s displacement law,
`Tprop(1)/(lamda_(m))`
`:.Pprop(1)/(lamda_(m)^(4))`
`:.(P_(2))/(P_(1))=((lamdam_(1))/(lamdam_(2)))^(4)=((lamda_(0))/(3/4lamda_(0)))^(4)`
`:.(nP)/(P)=((4)/(3))^(4)=(256)/(81)`
`:.n=(256)/(81)`