A black body radiated maximum energy around a particular wavelength at a given temperature. If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength `n` time the original wavelength `(n lt 1)` then power radiate by it will increases by a factor of:

Options

A. `1/n^(2)`
B. `n^(2)`
C. `1/n^(4)`
D. `n^(4)`

Answer

C

Explanation

`lambda_(0)T_(0)=b`
`P = CT_(0)^(4)`
`nlambda_(0)*(T_0)/(n)=b`
or, `lambda_(1)T_(1)=b`
so, `T_(1)=T_(0)//n`
`P=CT_(1)^(4) = C(T_(0)//n)^(4) = P//n^(4)`.