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, $P_0=C{T}_0^4,$ 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, $P=C{T}^4=C{T}_0^4{\left(\frac{4}{3}\right)}^4$
$P=\frac{256}{81}{P}_0$