Question

The energy spectrum of a black body exhibits a maximum around a wavelength $\lambda_{0}$. The temperature of the black body is now changed such that the energy is maximum around a wavelength $\frac{3\lambda_{0}}{4}$. The power radiated by the black body will now increase by a factor of

• A. 256/81
• B. 64/27
• C. 16/9
• D. 4/3

Answer 1

Answer: (A)

256/81

Answer 2

According to Wien's law wavelength corresponding to maximum energy decreases. When the temperature of black body increases i.e. $\lambda_{m}T =$ constant ⇒

$\frac{T_{2}}{T_{1}} = \frac{\lambda_{1}}{\lambda_{2}} = \frac{\lambda_{0}}{3\lambda_{0}/4} = \frac{4}{3}$

Now according to Stefan's law

$\frac{E_{2}}{E_{1}} = \left( \frac{T_{2}}{T_{1}} \right)^{4} = \left( \frac{4}{3} \right)^{4} = \frac{256}{81}$.