Q. The power radiated by a black body is $P$, and it radiates maximum energy around the wavelength $\lambda_{0}.$ If the temperature of black body is now changed so that it radiates maximum energy around a wavelength $\lambda_{0}$/4, the power radiated by it will increase by a factor of
A) $\frac{4}{3}$
B) $\frac{16}{9}$
C) $\frac{64}{27}$
D) $\frac{256}{81}$
Explanation
(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, $P = CT^{4} = CT_{0}^{4}\left( \frac{4}{3} \right)^{4}$
$P = P_{0} \times \frac{256}{81}\ or\ \frac{P}{P_{0}} = \frac{256}{81}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.