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Electron Diffraction
In 1927, George Paget Thomson discovered that if a beam of electrons
is made to pass through a thin metal film then the regular atomic array in the metal acts as a
sort of diffraction grating, so that when a photographic film, placed behind the metal, is developed an
interference pattern is discernible. This implies that electrons have wavelike
properties. Moreover, the electron wavelength,
, or, alternatively, the wavenumber,
, can be deduced from the spacing
of the maxima in the interference pattern. (See Chapter 11.)
Thomson found that the momentum,
, of an electron is related to its wavenumber,
, according to the
following
simple relation:

(1082) 
(Gasiorowicz 1996).
The associated wavelength,
, is known as the de Broglie wavelength, because this relation was first hypothesized by Louis de Broglie in 1926.
In the following, we shall assume that Equation (1082) is a general result that applies to all particles, not just electrons.
It turns out that waveparticle duality only manifests itself on lengthscales less than,
or of order, the de Broglie wavelength (Dirac 1982). Under normal circumstances, this wavelength is fairly small. For instance,
the de Broglie wavelength of an electron is

(1083) 
where the electron energy is conveniently measured in units of electronvolts (eV).
(An electron accelerated from rest through a potential difference of
V
acquires an energy of
eV, and so on. Electrons in atoms typically have energies in the range
to
eV.) Moreover, the de Broglie wavelength
of a proton is

(1084) 
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Previous: Photoelectric Effect
Richard Fitzpatrick
20130408