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 black body, wavelength for maximum intensity:
`lamdaprop(1)/(T)` and `P propT^4 implies Pprop(1)/(lamda^4)`
`P' =16P :. P' T' =32PT`