Question

The energy spectrum of a blackbody 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 blackbody will now increase by a factor:

• A. $\frac{256}{81}$
• B. $\frac{16}{9}$
• C. $\frac{4}{3}$
• D. None

Answer 1

The correct option is A

$\frac{256}{81}$

According to Wien's law wavelength corresponding to maximum energy decreases. When the temperature of blackbody increases i.e.,

${\lambda }_{m}T=constant\Rightarrow \frac{T_2}{T_1}=\frac{{\lambda }_1}{{\lambda }_2}=\frac{{\lambda }_0}{\frac{3{\lambda }_0}{4}}=\frac{4}{3}$

Now according to Stefan's law

$\frac{E_2}{E_1}={\left(\frac{T_2}{T_1}\right)}^4={\left(\frac{4}{3}\right)}^4=\frac{256}{81}$.