DAVISSON AND GERMER EXPERIMENT -

It is the basis of electrons shows diffraction effect. In the arrangement, electrons from hot filament F are accelerated by potential difference V between anode A and cathode C. A narrow hole in the anode A renders the electrons into a narrow beam of electrons. These beam of electrons is allowed to fall on the face of nickel crystal.

The electrons are scattered in all directions by the atoms in the nickel crystal. The intensity of the electron beam scattered in a given direction is measured by allowing it to enter an electron collector called Detector D, which is rotated around the crystal through a large scale.

The angle between the incident beam and the scattered beam is known as the scattering angle $\fn_jvn (\Phi)$ and the angle between the scattered beam with the plane of atoms of the crystal is known as the Glancing angle $\fn_jvn (\Theta)$ .

The experiment was performed by varying the accelerating voltage V from 44 Volts to 68 Volts. It was found that when $\fn_jvn \Phi=50^0$ and $\fn_jvn V=50V$ , the intensity of the scattered electrons becomes maximum.

This shows the constructive interference of electrons scattered from different layers of atoms of the nickel crystal. This conforms, the moving electrons are in wave nature.

Let us find the wavelength of the wave associated with the electron.

from fig. $\fn_jvn \Theta+\Phi+\Theta=180^0$

$\fn_jvn \Rightarrow \Theta=\frac{180^0-\Phi}{2}$

$\fn_jvn \Rightarrow \Theta=\frac{180^0-50^0}{2}$

$\fn_jvn \left [ \Theta=65^0 \right ]$

we know that, for diffraction maximum (n=1)

$\fn_jvn \lambda=2d sin\Theta$

Where $\fn_jvn \lambda\rightarrow$ Wavelength

$\fn_jvn d\rightarrow$ Space between the atomic plane $\fn_jvn (0.91A^0\;for\;Ni\;crystal)$

$\fn_jvn \Theta\rightarrow$ Glancing angle

$\fn_jvn i.e \;\;\lambda=2\times0.91\times sin65^0$

$\fn_jvn \left [ \lambda=1.65 A^0 \right ]$

this is found with the above experiment

Now from the De-Broglie hypothesis. The wavelength of an electron is

$\fn_jvn \lambda=\frac{12.27}{\sqrt{V}}A^0$

$\fn_jvn Now\;\;Here\;\;V=54Volt$

$\fn_jvn \therefore \lambda=\frac{12.27}{54}A^0$

$\fn_jvn \left [ \lambda=1.66A^0 \right ]$

This found with theory given by de-Broglie

This gives de Broglie postulation was correct

IMPORTANT LINKS OF DUAL NATURE OF RADIATION AND MATTER
Introduction	Electron Emission
Photoelectric Effect	Experimental Study of Photoelectric Effect
Photoelectric Effect and Wave Theory of Light	Einstein’s Photoelectric Equation: Energy Quantum of Radiation
Particle Nature of Light: The Photon	Wave Nature of Matter
Davisson and Germer Experiment