Draw a schematic diagram of the experiment used by. Davisson and Germer to establish the wave nature of electrons. Explain briefly how the de-Broglie wave relation experimentally verfied in case of electrons.

Explanation

The wavelength electrons was verified experimentally by Davisson and Germery by using diffraction technique

The experimental arrangement is shown in the figure (a). Davisson and Germer directed an electron beam against a face of a crystal of nickel. The smallest separation between nickel atoms is `d= 0.90Å`. The intensity of the scattered electron was measured as a function of the latitude angle `phi` measured from the axis beam. It was found that the bem has a diffraction peak at `phi=150^(@)`. The corresponding angle `(theta)` of incidence and scattering relative to the Bragg planes is given by `theta +phi+theta=180^(@)`
or `theta=(180^(@)-phi)/(2)=(180^(@)-50^(@))/(2)=65`
According to Bragg's law for first order diffraction maximum, we have
`lambda= 2d sin theta`
`=2xx0.91xxsin 65^(@) =1.65 Å`
Now, according to de-Broglie hypothesis
`lambda=(12.3)/(sqrt(V)Å=(12.3)/(sqrt(54))=1.66Å`
The close agreement between the two values of `lambda` verifies de Broglie relation for electrons.