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.
Hint.
Answer.
Solution.
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*}
Hint.
Answer.
Solution.
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?
Hint.
Answer.
Solution.
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.
