Davisson-Germer Experiment

Prepared by:IVY CLAIRE V. MORDENO

Louis de Broglie (de broy) Made a major advance in the

understanding of atomic structure in 1924

Nature loves symmetry. Light is dualistic in nature, behaving in some situations like waves and in others like particles. If nature is symmetric, this duality should also hold for matter. Electrons and protons, which we usually think of as particles, may in some situations behave like waves

De Broglie Wave De Broglie postulated that a free particle

with rest mass , moving with nonrelativistic speed , should have a wavelength related to its momentum in exactly the same way as for a photon

The de Broglie wavelength of a particle is then

The frequency , according to de Broglie,

is also related to the particle’s energy in the same way as for a photon, namely

The relationships of wavelength to momentum and of frequency to energy, in de Broglie’s Hypothesis, are exactly the same for particles as for photons

de Broglie’s hypothesis, almost immediately received experimental confirmation

The first direct evidence involved a diffraction experiment with electrons that was analogous to the x-ray diffraction experiments

In those experiments, atoms in a crystal act as a three-dimensional diffraction grating for x-rays. An x-ray beam is strongly reflected when it strikes a crystal at an angle that gives constructive interference among the waves scattered from the various atoms in the crystal.

These interference effects demonstrate the nature of x-rays

In 1927, Clinton Davisson and Lester Germer, working at the Bell Telephone Laboratories, were studying the surface of a piece of nickel and observing how many electrons bounced off in various angles.

Davisson-Germer Experiment

An apparatus similar to that used by Davisson and Germer to discover electron diffraction

The specimen was polycrystalline: Like many ordinary metals, it consisted of many microscopic crystals bonded together with random orientations

The experimenters expected that even the smoothest surface attainable would still look rough to an electron and that the electron beam would be diffusely reflected, with a smooth distribution of intensity as a function of the angle θ

During the experiment an accident that permitted air to enter the vacuum chamber, and an oxide film formed on the metal surface.

To remove this beam, Davisson and Germer baked the specimen in a high temperature oven, almost hot enough to melt it

Unknown to them, this had the effect of creating large single-crystal regions with planes that were continuous over the width of the electron beam

When the observations were repeated, the results were quite different

Strong maxima in the intensity of the reflected electron beam occurred at specific angles in contrast to the smooth variation of intensity that had been observed before the accident

The angular positions of the maxima depended on the accelerating voltage Vba used to produce the electron beam

This was not the effect that they had been looking for, but they immediately recognized that the electron beam was being diffracted

They had discovered a very direct experimental confirmation of the wave hypothesis

Davisson and Germer could determine the speeds of the electrons from the accelerating voltage, so they could compute the de Broglie wavelength

=

The electrons were scattered primarily by the planes by atoms at the surface of crystal

Atoms in a surface plane are arranged in rows, with a distance d that can be measured by x-ray diffraction technique

These rows act like a reflecting diffraction grating

The angles of maximum reflection are given by

The de Broglie wavelength of a nonrelativistic particle can be expressed in terms of the particle’s kinetic energy

Consider an electron freely accelerated from rest at point a to point b through a potential difference Vb – Va = Vba

The work done on the electron eVba equals the kinetic energy KE

Using K = we have eVba =

, (de Broglie wavelength of an electron)

References

University Physics 12th Edition