Question

The energy spectrum of a black body exhibits a maximum around a wavelength '`lambda`'. The temperature of a black body is now changed such that the energy is maximum around a wavelength 3`lambda`/4. The power radiated by a black body will now increase by a factor of ______.

Options

• `128/27`

• `128/81`

• `256/27`

• `256/81`

Answer 1

The energy spectrum of a black body exhibits a maximum around a wavelength 'λ'. The temperature of a black body is now changed such that the energy is maximum around a wavelength 3λ/4. The power radiated by a black body will now increase by a factor of `underline(256/81)`.

Explanation:

`"E"_1/"E"_2 = lambda^4/((3lambda)/4)^4 = 256/81`