Explain the method of the Davisson and Germer experiment and its results.

(N/A) In the Davisson and Germer experiment,a detector is moved along a circular scale to measure the intensity of scattered electrons at different positions.
The angle between the incident beam and the scattered beam is called the angle of scattering $(\theta)$.
The intensity of the scattered electron beam is measured for different accelerating voltages $(V)$ and different scattering angles $(\theta)$.
The experiment was performed by varying the accelerating voltage from $44 \ V$ to $68 \ V$.
It was observed that a strong peak appeared in the intensity $(I)$ of the scattered electrons at an accelerating voltage of $54 \ V$ and a scattering angle of $\theta = 50^{\circ}$. This indicates that the number of scattered electrons is maximum at this point.
Let stationary electrons be accelerated by a potential $V$. Their kinetic energy is given by:
$K = eV$
$\therefore \frac{1}{2}mv^2 = eV$
$\therefore \frac{1}{2} \frac{m^2v^2}{m} = eV$
$\therefore \frac{p^2}{2m} = eV$ (where $p = mv$ is momentum)
$\therefore p = \sqrt{2meV}$
The wavelength of the matter wave (de Broglie wavelength) is:
$\lambda = \frac{h}{p} = \frac{h}{\sqrt{2meV}}$
Substituting the values of Planck's constant $(h)$,mass $(m)$,and charge $(e)$,we get:
$\lambda = \frac{1.227}{\sqrt{V}} \text{ nm}$