Davisson-Germer experiment

C.J Davisson and L.H Germer proved the wave nature of the electrons through their experiment. Their experiment of electron diffraction arrangement confirms the wave nature of a beam of electrons and the de Broglie relation of wavelength. 

Later, in 1988, the wave nature of a beam of electrons was again verified according to a double-slit experiment. The David-Germer experiment proved quantum mechanics ultimately.

The atomic models proposed by the scientists earlier could define only the nature of the particle of the electrons, but they could not define the properties of the nature of waves. Clinton Joseph Davisson and Lester Halbert Germer in 1927 accomplished an experiment, which is very popular and is called Davisson-Germer’s experiment. This experiment defines the wave nature of electrons via electron diffraction. Let us learn the observations and conclusions given by Davisson and Germer in their experiment. This is the first successful experiment to prove the validity of the de Broglie Hypothesis.

Setup of Davisson-Germer experiment

The Davisson-Germer experiment is embedded within a vacuum chamber, which results in the deflection of electrons and scattering by the medium are being ignored. The following are the major parts of the experimental setup:

ⅰ) Electron gun: An electron gun consisting of filament made up of tungsten, which on heating emits a large number of electrons by a process called thermionic emission. So, we conclude that  an electron gun emits electrons when it gets heated to a specific temperature.

ⅱ) Electrostatic particle accelerator: As a large number of electrons are emitted from the electron gun, so to accelerate these electrons at a specified potential, two charges are employed that are opposite to each other (positive and negative plate).

ⅲ) Collimator: The accelerator is adjusted within the cylinder in such a way that it restricts the path for electrons to run along its axis. The aim of the collimator is to make a slight and straight beam of electrons for acceleration.

ⅳ) Target: The motive of the target is to find a nickel crystal, and the electron beam is thrown generally on the nickel crystal, the position of which is in such a way that it will revolve around a fixed axis.

ⅴ) Detector: A detector is accommodated so that it collects dispersed electrons from the nickel crystal. The detector may be moved in a semicircular arc.

Working

A fine beam of electrons is made to fall on the nickel crystal, and the upcoming electrons are then attacked by the atoms of the nickel crystal in different directions. By rotating the electron detector on a circular scale, the intensity of the scattered beam is measured at different latitude angles ∅.

Then, the polar graphs plotted between the intensity of the scattered electrons and the latitude angle for different accelerating voltages varying from 44 to 68 volts. The graphs obtained show that there is a sharp bump  if the accelerating voltage is 54V &∅= 50°.

The appearance of this sharp bump in an appropriate direction is mainly due to the constructive interference of electrons, which are scattered from the nickel crystal. This initiates the wave nature of the electrons.

From simple geometry, and for∅ = 50°,

θ+ ∅ + θ = 180° (here  is scattering angle )

2 θ+ ∅= 180°

2θ = ( 180° – ∅)

2θ =  180° – 50° 

2θ = 130°

θ = 65°

Also, for nickel crystal, the interatomic separation, d = 0.91°A.

According to Bragg’s law, and for first order diffraction maxima, (n = 1)

2d Sinθ = nλ 

2d Sin = 1 λ 

2  0.91 Sin 65° = λ

λ = 1.65°A

According to the de Broglie Hypothesis, the wavelength of a wave corresponding with the electron is given by:

λ = h/√2mev

(or)

λ = 12.27/√V 

λ = 12.27/√54 

λ = 1.66°A

This clearly shows that there is a close agreement between the estimated value and the experimental value, which further shows the existence of De-Broglie waves for the electrons in motion.

De Broglie Equation

In later years, de Broglie established the wave nature of matter. The waves linked with the moving material particles are known as matter waves or de Broglie waves. 

The de Broglie wavelength is equal to λ = h/p. 

λ in the equation denoted the wave nature, and p denoted particle nature. Therefore, this equation solved both the nature of radiation and matter.

The wavelength calculated by the de Broglie hypothesis equation is not dependent on the charge and nature of the material. de Broglie’s experiment is the basis of all theories and modern quantum mechanics. The wave nature of electrons is utilized in the design of electron microscopes. 

Derivation of de Broglie Equation

hf = mc²

As we know that f = c/ ƛ

It shows that hc/ ƛ = mc² or ƛ = h/mc

If c = v; then ƛ = h/mv

We also know that the momentum of a particle is given by P= mv.

Therefore, ƛ = h/P.

Correlation of Davisson-Germer experiment and de Broglie relation

From de Broglie,

λ = h /p

λ = (1.227/√54) = 0.167nm                     

Conclusion

The Davisson-Germer experiment is the first successful experiment to demonstrate the validity of the de Broglie hypothesis.

The electrons coming from the filament F of an electron gun are accelerated by a potential difference varying between 40 to 68 volts and are made to fall on a nickel chloride crystal. The electrons behave like waves and are thus diffracted in certain preferred directions. The diffracted electrons are received by an electron collector. It is found that for an accelerating potential of 54 volts, the diffraction is a must and occurs at an angle of 50°. It shows that waves are associated with electrons, which give rise to constructive interference and travel along a definite path.