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)`
`n lambda_(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)`