In a former post, I described two experiments: the photoelectric effect and the black body radiation. I finish the topic in this post by explaining three more experiments:

### 3) Frank-Hertz experiment

The experiment of Franck and Hertz consisted of bombarding atoms with monoenergetic electrons and measuring the kinetic energy of the scattered electrons. The amount of the energy absorbed in the collision can thus be estimated. Suppose** E_{0}, E_{1}, E_{2}, …** are the sequence of quantized energy levels of the atom and and

**is the kinetic energy of the incident electron. As long as T is below**

*T***, the atoms cannot absorb the energy and all collisions are elastic. As soon as**

*∆=(E*_{1}– E_{0})**, inelastic collisions occur and some atoms go into their first excited states. Similarly, atoms can be excited to second and higher excited states. Thus Frank-Hertz experiment established the quantization of the atomic energy levels.**

*T>(E*_{1}– E_{0})### 4) Davisson-Germer experiment

L. de Broglie, seeking to establish the basis of a unified theory of matter and radiation, postulated that matter, as well as light, exhibited both wave and particle aspects. The first diffraction experiments with matter waves were performed with an electron beam by Davisson and Germer (1927). The incident beam was obtained by accelerating electrons through an electric potential. Knowing the parameters of the crystal lattice, it was possible to deduce an experimental value for the electron wavelength. The result was in agreement with de Broglie relation, ** λ=h/p**, where

**is Planck’s constant and**

*h***is the momentum of electron. Similar experiments were later performed using beams of hydrogen molecule and helium atoms. Hence, it showed the wavelike nature of matter.**

*p*### 5) Compton scattering

Compton observed the scattering of X-rays by free or weakly bounded electrons and found the wavelength of the scattered radiation exceeded that of the incident radiation. The difference, ** ∆λ**, varied as a function of the angle

**between the incident and scattered directions:**

*θ*where ** h** is the Planck’s constant and

**is the rest mass of the electron. Furthermore,**

*m***is independent of the incident wavelength. The Compton effect cannot be explained by any classical theory of light. Hence, it is a confirmation of the photon theory of light.**

*∆λ*