A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength at which the radiation has maximum intensity is `lamda_0`, If at another temperature `T'` the power radiated is `P'` and wavelength at maximum intensity is `(lamda_0)/(2)` then

Options

A. `P'T' = 32PT`
B. `P'T = 16PT`
C. `P'T' = 8PT`
D. `P'T' = 4PT`

Answer

A

Explanation

For balck body
`lambda_(0)T = (lambda_(0))/(2)T' implies T^(1) = 2T`
`(P)/(P') = (sigmaAT^(4))/(sigmaAT'^(4)) = (1)/(16) implies P'T' = (16P)(2T) = 32PT`