Question

The energy spectrum of a black body exhibits a maximum energy around a wavelength ${\lambda }_0$. The temperature of the black body is now changed such that the energy is maximum around a wavelength $3{\lambda }_0/4$. The power radiated by the black body will now increase by a factor of :

• A. $\frac{256}{81}$
• B. $\frac{64}{27}$
• C. $\frac{16}{9}$
• D. $\frac{4}{3}$

Answer 1

Answer: (A)

$\frac{256}{81}$

From wien's displacement law :$\lambda T=b$
stefan's law $E=\sigma T^4$
ratio $=\frac{E_2}{E_1}=\frac{\sigma {T_2}^4}{\sigma {T_1}^4}=\frac{{T_2}^4}{{T_1}^4}=(\frac{\frac{b}{{\lambda }_2}}{\frac{b}{{\lambda }_1}}{)}^4=(\frac{{\lambda }_1}{{\lambda }_2}{)}^4=(\frac{{\lambda }_o}{\frac{3{\lambda }_o}{4}}{)}^4=(\frac{4}{3}{)}^4=\frac{256}{81}$