In 1924 a French physicist and nobleman, Prince Louis de Broglie (pronounced
“de broy”;), made a remarkable proposal about the nature of matter. His
reasoning, freely paraphrased, went like this: Nature loves symmetry. Light is
dualistic in nature, behaving in some situations like waves and in others like par-
ticles. 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 broy”;), made a remarkable proposal about the nature of matter. His
reasoning, freely paraphrased, went like this: Nature loves symmetry. Light is
dualistic in nature, behaving in some situations like waves and in others like par-
ticles. 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’s proposal was a bold one, made at a time when there was no direct
experimental evidence that particles have wave characteristics. But within a few
years of de Broglie’s publication of his ideas, they were resoundingly verified by
a diffraction experiment with electrons. This experiment was analogous, in which 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
wave nature of x rays.
In 1927 the American physicists Clinton Davisson and Lester Germer, working
at the Bell Telephone Laboratories, were studying the surface of a piece of nickel
by directing a beam of electrons at the surface and observing how many electrons
bounced off at various angles. Figure shows an experimental setup like theirs.
Like many ordinary metals, the sample was polycrystalline: It consisted of many
randomly oriented microscopic crystals bonded together. As a result, the electron
beam reflected diffusely, like light bouncing off a rough surface,
with a smooth distribution of intensity as a function of the angle theta
experimental evidence that particles have wave characteristics. But within a few
years of de Broglie’s publication of his ideas, they were resoundingly verified by
a diffraction experiment with electrons. This experiment was analogous, in which 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
wave nature of x rays.
In 1927 the American physicists Clinton Davisson and Lester Germer, working
at the Bell Telephone Laboratories, were studying the surface of a piece of nickel
by directing a beam of electrons at the surface and observing how many electrons
bounced off at various angles. Figure shows an experimental setup like theirs.
Like many ordinary metals, the sample was polycrystalline: It consisted of many
randomly oriented microscopic crystals bonded together. As a result, the electron
beam reflected diffusely, like light bouncing off a rough surface,
with a smooth distribution of intensity as a function of the angle theta
During the experiment an accident occurred that permitted air to enter the vac-
uum chamber, and an oxide film formed on the metal surface. To remove this
film, Davisson and Germer baked the sample in a high-temperature oven, almost
hot enough to melt it. Unknown to them, this had the effect of creating large
regions within the nickel with crystal planes that were continuous over the width
of the electron beam. From the perspective of the electrons, the sample looked
like a single crystal of nickel.
When the observations were repeated with this sample, the results were quite
different. Now strong maxima in the intensity of the reflected electron beam
occurred at specific angles , in contrast to the smooth variation of
intensity with angle that Davisson and Germer had observed before the accident.
The angular positions of the maxima depended on the accelerating voltage
used to produce the electron beam. Davisson and Germer were familiar with
de Broglie’s hypothesis, and they noticed the similarity of this behavior to x-ray
diffraction. This was not the effect 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 from
Eqn above. If an electron is accelerated from rest at point a to point b through a
potential increase, the work done on the
electron equals its kinetic energy K. Using for a non-
relativistic particle, we have
uum chamber, and an oxide film formed on the metal surface. To remove this
film, Davisson and Germer baked the sample in a high-temperature oven, almost
hot enough to melt it. Unknown to them, this had the effect of creating large
regions within the nickel with crystal planes that were continuous over the width
of the electron beam. From the perspective of the electrons, the sample looked
like a single crystal of nickel.
When the observations were repeated with this sample, the results were quite
different. Now strong maxima in the intensity of the reflected electron beam
occurred at specific angles , in contrast to the smooth variation of
intensity with angle that Davisson and Germer had observed before the accident.
The angular positions of the maxima depended on the accelerating voltage
used to produce the electron beam. Davisson and Germer were familiar with
de Broglie’s hypothesis, and they noticed the similarity of this behavior to x-ray
diffraction. This was not the effect 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 from
Eqn above. If an electron is accelerated from rest at point a to point b through a
potential increase, the work done on the
electron equals its kinetic energy K. Using for a non-
relativistic particle, we have
The greater the accelerating voltage , the shorter the wavelength of the electron.
To predict the angles at which strong reflection occurs, note that the electrons
were scattered primarily by the planes of atoms near the surface of the crystal.
Atoms in a surface plane are arranged in rows, with a distance d that can be
measured by x-ray diffraction techniques. These rows act like a reflecting diffrac-
tion grating; the angles at which strong reflection occurs are the same as for a
grating with center-to-center distance d between its slits
Davisson and Germer found that the angles predicted by this equation, using the
de Broglie wavelength, agreed with the observed values. Thus the accidental discovery of electron diffraction was the first direct evidence confirming de Broglie’s hypothesis.
In 1928, just a year after the Davisson–Germer discovery, the English physicist
G. P. Thomson carried out electron-diffraction experiments using a thin, polycrys-
talline, metallic foil as a target. Debye and Sherrer had used a similar technique
several years earlier to study x-ray diffraction from polycrystalline specimens. In
these experiments the beam passes through the target rather than being reflected
from it. Because of the random orientations of the individual microscopic crystals
in the foil, the diffraction pattern consists of intensity maxima forming rings around
the direction of the incident beam. Thomson’s results again confirmed the
de Broglie relationship. Figure 39.4 shows both x-ray and electron diffraction patterns for a polycrystalline aluminum foil. (G. P. Thomson was the son of J. J.
Thomson, who 31 years earlier discovered the electron. Davisson and the younger
Thomson shared the 1937 Nobel Prize in physics for their discoveries.)
Additional diffraction experiments were soon carried out in many laboratories
using not only electrons but also various ions and low-energy neutrons. All of
these are in agreement with de Broglie’s bold predictions. Thus the wave nature of
particles, so strange in 1924, became firmly established in the years that followed.
To predict the angles at which strong reflection occurs, note that the electrons
were scattered primarily by the planes of atoms near the surface of the crystal.
Atoms in a surface plane are arranged in rows, with a distance d that can be
measured by x-ray diffraction techniques. These rows act like a reflecting diffrac-
tion grating; the angles at which strong reflection occurs are the same as for a
grating with center-to-center distance d between its slits
Davisson and Germer found that the angles predicted by this equation, using the
de Broglie wavelength, agreed with the observed values. Thus the accidental discovery of electron diffraction was the first direct evidence confirming de Broglie’s hypothesis.
In 1928, just a year after the Davisson–Germer discovery, the English physicist
G. P. Thomson carried out electron-diffraction experiments using a thin, polycrys-
talline, metallic foil as a target. Debye and Sherrer had used a similar technique
several years earlier to study x-ray diffraction from polycrystalline specimens. In
these experiments the beam passes through the target rather than being reflected
from it. Because of the random orientations of the individual microscopic crystals
in the foil, the diffraction pattern consists of intensity maxima forming rings around
the direction of the incident beam. Thomson’s results again confirmed the
de Broglie relationship. Figure 39.4 shows both x-ray and electron diffraction patterns for a polycrystalline aluminum foil. (G. P. Thomson was the son of J. J.
Thomson, who 31 years earlier discovered the electron. Davisson and the younger
Thomson shared the 1937 Nobel Prize in physics for their discoveries.)
Additional diffraction experiments were soon carried out in many laboratories
using not only electrons but also various ions and low-energy neutrons. All of
these are in agreement with de Broglie’s bold predictions. Thus the wave nature of
particles, so strange in 1924, became firmly established in the years that followed.