Everything about De Broglie Wavelength totally explained
In
physics, the
de Broglie hypothesis (pronounced /brœj/, as French breuil, close to "broy") is the statement that all
matter (any object) has a
wave-like nature (
wave-particle duality). The
de Broglie relations show that the
wavelength is
inversely proportional to the
momentum of a particle and that the
frequency is directly proportional to the particle's
kinetic energy. The hypothesis was advanced by
Louis de Broglie in
1924 in his PhD thesis; he was awarded the
Nobel Prize for Physics in
1929 for this work, which made him the first person to receive a Nobel Prize on a PhD thesis.
Historical context
After strides made by
Max Planck (1858-1947) and
Albert Einstein (1879-1955) in understanding the behavior of electrons and what would be known as quantum physics,
Niels Bohr (1885-1962) began (among other things) trying to explain how electrons behave. He came up with new fundamental ideas about electrons and mathematically derived the
Rydberg equation, an equation that was discovered only through trial and error. This equation explains the
energies of the
light emitted when hydrogen gas is compressed and electrified (similar to neon signs, but with hydrogen in this case). Unfortunately, his model only worked for the hydrogen-atom-configuration, but his ideas were so revolutionary that they broke up the classical view of electrons' behavior and paved the way for fresh new ideas in what would become quantum physics and quantum mechanics.
Louis de Broglie (1892-1987) tried to expand on Bohr's ideas, and he pushed for their application beyond hydrogen. In fact he looked for an equation which could explain the wavelength characteristics of all matter. His equation was experimentally confirmed in 1927 when physicists Lester Germer and Clinton Davisson fired electrons at a crystalline nickel target and the resulting diffraction pattern was found to match the predicted values. . Nevertheless, his hypothesis would hold true for both electrons and for everyday objects. In de Broglie's equation an electron's wavelength will be a function of
Planck's constant (
where
is the frequency and
is the total energy. The two equations are often written as
»
where
is momentum,
is the reduced
Planck's constant (also known as
Dirac's constant, pronounced "h-bar"),
is the
wavenumber, and
is the
angular frequency.
See the article on
group velocity for detail on the argument and derivation of the de Broglie relations.
Experimental confirmation
Elementary particles
In 1927 at Bell Labs,
Clinton Davisson and
Lester Germer fired slow-moving
electrons at a
crystalline nickel target. The angular dependence of the reflected electron intensity was measured, and was determined to have the same
diffraction pattern as those predicted by
Bragg for
X-Rays. Before the acceptance of the de Broglie hypothesis, diffraction was a property that was thought to be only exhibited by waves. Therefore, the presence of any
diffraction effects by matter demonstrated the wave-like nature of matter. When the de Broglie wavelength was inserted into the
Bragg condition, the observed diffraction pattern was predicted, thereby experimentally confirming the de Broglie hypothesis for electrons.
This was a pivotal result in the development of
quantum mechanics. Just as
Arthur Compton demonstrated the particle nature of light, the
Davisson-Germer experiment showed the wave-nature of matter, and completed the theory of wave-particle duality. For
physicists this idea was important because it means that not only can any particle exhibit wave characteristics, but that one can use
wave equations to describe phenomena in matter if one uses the de Broglie wavelength.
Since the original Davisson-Germer experiment for electrons, the
de Broglie hypothesis has been confirmed for other
elementary particles.
Neutral atoms
Experiments with
Fresnel diffraction
and
specular reflection
of neutral atoms
confirm the application of the De Broglie hypothesis to atoms, for example the existence of
atomic waves which undergo
diffraction,
interference and allow
quantum reflection by the tails of the attractive potential
.
This effect has been used to demonstrate atomic
holography
, and it may allow the construction of an atom probe imaging system with nanometer resolution .
The description of these phenomena is based on the wave properties of neutral atoms, confirming the
de Broglie hypothesis.
Waves of molecules
Recent experiments even confirm the relations for molecules and even
macromolecules, which are normally considered too large to undergo quantum mechanical effects. In
1999, a research team in
Vienna demonstrated diffraction for molecules as large as
fullerenes.
In general, the
De Broglie hypothesis is expected to apply to any well isolated object.
Spatial Zeno effect
The De Broglie hypothesis leads to the spatial version of the
Zeno effect. If an object (particle) is observed with frequency
in a half-space (say,
), then this observation prevents the particle, which stays in the half-space
from entry into this half-space
. Such an "observation" can be realized with a set of rapidly moving absorbing ridges, filling one half-space. In the system of coordinates related to
the ridges, this phenomenon appears as a
specular reflection of a particle from a
ridged mirror, assuming the grazing incidence (small values of the
grazing angle).
Such a ridged mirror is universal; while we consider the idealised "absorption" of the de Broglie wave at the ridges, the reflectivity is determined by wavenumber
and doesn't depend on other properties of a particle.
Further Information
Get more info on 'De Broglie Wavelength'.
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