Question

Describe Davisson and Germer's experiment to demonstrate the wave nature of electrons.Draw a labelled diagram of apparatus used.

Answer 1

Davisson and Germer Experiment: In 1927 Davisson and Germer performed a diffraction experiment with electron beam in analogy with X-ray diffraction to observe the wave nature of matter.
Apparatus: It consists of three parts
(i) Electron Gun: It given a fine beam of electrons, de Broglie used electron beam of energy 54eV. de Broglie wavelength associated with this beam
$$\lambda=\dfrac{h}{\sqrt{2mE_K}}$$
Here m=mass of electron =$$9.1\times10^{-31}kg$$
E-K=Kinetic energy of electron =$$54eV$$
$$=54\times1.6\times10^{-19}joule =86.4\times10^{-19}joule$$
$$\therefore \lambda=\dfrac{6.6\times10^{-24}}{\sqrt{2\times9.1\times10^{-31}\times86.4\times10^{-19}}}$$
$$=1.66\times10^{-10}m=1.66A^\circ$$
(i) Nickel Crystal: The electron beam was directed on nickel crystal against its (iii) face.
The smallest separation between nickel atoms is $$0.914A^\circ$$. Nickel crystal behaves as diffraction grating.

(ii) Electron Detector: It measures the intensity of electron beam diffracted from nickel crystal. It may be an ionisation chamber fitted with a sensitive galvanometer. The energy of electron beam, the angle of incidence of beam on nickel crystal and the position of detector can all be varied.

Method: The crystal is rotated in small steps to change the angle ($$\alpha$$ say) between incidence and scattered directions and the corresponding intensity (I) of scattered beam is measured. The variation of the intensity (I) of the scattered electrons with the angle of scattering $$\alpha$$ is obtained for different accelerating voltages.
The experiment was performed by varying the accelerating voltage from 44V to 68V. It was noticed that a strong peak appeared in the intensity (I) of the scattered electron for an accelerating voltage of 54V at a scattering angle $$\alpha=50^\circ$$
$$\therefore $$From Bragg's law
$$2dsin=\theta=n\lambda$$
Here n=1,d=0.914 $$A^\circ$$, $$\theta=65 ^\circ$$
The measured wavelength is in close agreement with the estimated de Broglie wavelength.Thus the wave nature of electron is verified. Later on G.P. Thomson demonstrated the wave nature of fast electrons.Due to their work Davission and G.P.Thomson were awarded Nobel prize in 1937.
Later on experiments showed that not only electrons but all material particles in motion(e.g., neutrons, $$\alpha$$ particles,protons etc.) show wave nature.