31.Temperature of an Oven from Blackbody Radiation Data TODO.
An oven is heated to a high temperature and the electromagnetic radiation coming out of the oven through a tiny hole in the oven is analyzed for radiance \(R_T(\lambda)\text{,}\) which is the power content per unit wavelength range per unit cross-section area of the hole. The data obtained at five wavelengths are:
(a) Plot \(R_T\) versus \(\lambda\text{.}\) (b) From the data find the temperature of the oven. (c) Find the total power radiated per unit area of cross-section of the hole.
32.Colision of a Photon with a Free Electron TODO.
A photon of energy \(hf\) collides head-on with a nearly free electron at rest. Let \(E_0\) be the rest energy of an electron. Show that the kinetic energy of the recoiled electron is given by
\begin{equation*}
K = \dfrac{2h^2f^2}{2hf + E_0}.
\end{equation*}
33.Percentage of Energy that Photon can Transfer in Compton Scattering TODO.
(a) Prove that in the Compton scattering, a photon cannot transfer all of its energy to an electron. (b) Is there a maximum percentage of energy that a photon can transfer to an electron at rest? If so, what is it? If not, why not?
34.Formula for Wavelength for Maximum Blackbody Radiation TODO.
(a) Treating \(R_T(\lambda)\) as a function of \(\lambda\text{,}\) prove that the maximum of the radiance occurs at a wavelength \(\lambda_{\textrm{max}}\) whose product with temperature is a constant.
