Question

The power radiated by a black-body is $P_{0}$ and it radiates maximum energy around the wavelength $\lambda _{0}.$ If the temperature of the black-body is now changed so that it radiates maximum energy around a wavelength $3 \lambda _{0}/4$ , then the power radiated by it will be

• A. $\frac{4}{3}P_{0}$
• B. $\frac{16}{9}P_{0}$
• C. $\frac{64}{27}P_{0}$
• D. $\frac{256}{81}P_{0}$

Answer 1

Answer: (D)

Let $T_{0}$ be the initial temperature of the black body
$\therefore \, \lambda _{0}T_{0}=b \, $ (Wien's law)
Power radiated, $P_{0}=CT_{0}^{4}, \, $ where, $C$ is constant.
If $T$ is new temperature of black body, then
$\frac{3 \lambda _{0}}{4}T=b=\lambda _{0}T_{0} $ or $ T=\frac{4}{3} \, T_{0}$
Power radiated, $P=CT^{4}=CT_{0}^{4}\left(\frac{4}{3}\right)^{4}$
$P=\frac{256}{81}P_{0}$