How does Davisson and Germer's experiment verify the wave nature of electrons ?

Explanation

Davisson and Germer Experiment
The first experimental proof of the wave nature of particle was proved in 1927 by CJ. Davisson and L.H. Germer.
Principle. Electrons accelerated by a known potential are diffracted from a crystal and their wavelength is measured by optical formula.
Construction. The experimental arrangement used by Davisson and Germer is as shown in the Fig. The electrons from hot tungsten cathode are accelerated by a potential difference V between the cathode C and anode A. This arrangement is called electron gun: A Ni crystal is placed such that the electrons strike on it at art angle `theta`. The detector D can move along an arc scale with its centre O as shown in the figure.
Working. A fine beam of electrons is allowed to strike the Ni target. The intensity of scattered electrons in a given direction is determined by a detector. The intensity of scattered beam is measured at different values of `phi` and a graph is plotted between `phi` and intensity of scattered beam. Such graphs are plotted at different accelerating voltages as shown in the fig. From these graphs we find that the scattered electron beam of 54 V has.diffraction peak at angle `phi = 50^(@)`. This appearance of bump at a particular direction is due to the interference of electrons scattered from different layers of regularly spaced atoms of the crystal. This established wave nature of electrons.

It is found that the maxima in the diffraction pattern occurs, when Bragg.s condition is satisfied.
i.e. `2d sin theta = nlambda.`.............(1)
where d is the distance between atomic planes, `lambda` is the wavelength of the electron and n is the order of spectrum.

From the fig, we have,
`theta + phi + theta = 180^(@)`
`therefore 2theta =180^(@) -phi = 180^(@) - 50^(@)`
`therefore theta = 65^(@)`
For n=1 Eq. (1) becomes
`lambda = 2d sin theta`
For Ni crystal `=d=0.91 Å =0.91 xx 10^(-10)` m
`therefore lambda =2 xx 0.91 xx 10^(-10) xx sin 65^(@)`
`lambda = 1.65 Å`
Also, for 54 V, the de-Broglie wavelength of electron is given by (theoretically)
`lambda = (12.27)/sqrt(54) Å = 1.67 Å`
Thus the two results are in close agreement with each other. So Davisson Germer experiment provides direct Verification of de-Broglie hypothesis of wave nature of moving particles.