Davisson-Germer Experiment

In this problem, we will consider the experiment that was first performed in 1927 by C. Davisson and L. Germer. This experiment has convincingly demonstrated the wave nature of electrons.

(a)

An ``electron gun'' is a device in which electrons are created and accelerated by an electric field. The electrons are emitted by the source with very small (essentially zero) velocities. The potential difference between the source and the point where the electrons exit the gun is 750 V. Find the momentum of electrons as they exit the gun. An electron has a mass $m=9.1\cdot 10^{-31}$ kg and electric charge $e=-1.6\cdot 10^{-19}$ C.

(b)

According to de Broglie hypothesis, what is the wavelength of the electrons exiting the gun?

(c)

A beam of electrons from the gun is directed at the surface of a nickel crystal. Electron velocities are perpendicular to the surface. The crystal is an array of equally spaced Ni atoms, with two neighboring atoms separated by $d=0.1$ nm. Electrons hitting the atoms are reflected. Davisson and Germer studied how many electrons bounce off at different angles. Sketch the flux of electrons as a function of the angle $\theta$. Find the values of $\theta$ at which the electron flux is maximal.

HINT: The crystal acts like a ``reflection grating'' which was studied in problem set # 9, problem 2.

Figure 1: Davisson-Germer experiment.