Answer to Question #124487 in Quantum Mechanics for David

Question

Electrons travelling through matter may be diffracted. Describe and interpret the evidence provided by this observation about the nature of electron. Explain why a person off mass 70kg running at 5ms fails to show diffraction effects when passing through an open door of width 1.0m.

Answer 1

I am providing the exactly same experiments set up from Wikipedia.(https://en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment#:~:text=The%20Davisson%E2%80%93Germer%20experiment%20confirmed,fundamental%20step%20in%20quantum%20theory. )

The experiment consisted of firing an electron beam (from an electron gun, an electrostatic particle accelerator) at a nickel crystal, perpendicular to the surface of the crystal, and measuring how the number of reflected electrons varied as the angle between the detector and the nickel surface varied. The electron gun was a heated tungsten filament that released thermally excited electrons which were then accelerated through an electric potential difference, giving them a certain amount of kinetic energy, towards the nickel crystal. To avoid collisions of the electrons with other atoms on their way towards the surface, the experiment was conducted in a vacuum chamber. To measure the number of electrons that were scattered at different angles, a faraday cup electron detector that could be moved on an arc path about the crystal was used. The detector was designed to accept only elastically scattered electrons.

During the experiment, air accidentally entered the chamber, producing an oxide film on the nickel surface. To remove the oxide, Davisson and Germer heated the specimen in a high temperature oven, not knowing that this caused the formerly polycrystalline structure of the nickel to form large single crystal areas with crystal planes continuous over the width of the electron beam.^[6]

When they started the experiment again and the electrons hit the surface, they were scattered by nickel atoms in crystal planes (so the atoms were regularly spaced) of the crystal. This, in 1925, generated a diffraction pattern with unexpected peaks.

Interpretation:

Therefore, classically we can not describe the above mentioned peaks ,Thus this unexpected peak can be explained only if there is superposition of electron wave and what is exactly De Broglie 's hypothesis expected of matter wave.

Diffraction is a microscopic phenomenon that is, it only happens if the seize of the wave and obstacles are comparable .

Now, in this case mass of man is $m=70\:kg$ and moving with $v=5m/s$ ,thus, momentum is

$$p=mv=350kg\cdot m/s$$

Hence, by De Broglie's hypothesis wave length of the man will be

$$\lambda=\frac{h}{p}=\frac{h}{350}m$$

But,

$$\lambda<<1$$

Hence, wavelength of the man is not comparable with door,Thus no diffraction happens.