CHAPTER 3
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THE WAVE—LENGTH OF THE ELECTRON
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3—1.
Introduction.—In addition to the properties of inertia
and charge, the electron also has a wave nature. The length of
the wave associated with an electron decreases as the electron
gains speed.
For example, an electron travelling 7.2 X 108 cen''
timeters per second has a wave-lengthof 10—8 centimeters (l angstrom), whereas one which is travelling 1.24 >< 1010 centimeters
per second has a wave-length of only 0.05 angstroms. These
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veloèities may be acquired by accelerating the electron With 150
and 50,000 volts, respectively.
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“The evidence that electrons are waves is similar to
evidencethat light and x—rays are waves.” 1 Certain experiments
are
best explained by considering the electron as a corpuscle,
whereas others require the wave viewpoint. The dualistic character ofthe electron willbe discussed in a later secti0n of this chapter.
For many years the concept of a corpuscular electron was con'
sidered sufcient to explain all observed phenomena. However,
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in 1924, L. de Broglie
2 predicted that an electron should also have
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a wave nature.
In 1927,'Daviss0n and Germer3 discovered this
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property and measured the wave-length of the electr0n. Their
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mental method.
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3—2.
De Broglie’s Equation.——It is possible to state a relation- —
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ship between matter and waves in mathematical form, as was rst
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demonstrated by L. de Broglie in 1924. His work was_soon fol—
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lowed by the “waVe—mechanics” of Schrôdinger, an equivalent of
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thematrix mechanics of Heisenberg, from which many new
coveries in Physics have been made;
sha‘l now reverse the
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process and derive de Brogl—ie’s equation
for the Wave-length of an
electron from the wave-eçùàtiowhichSchrôdinger‘ 5_discovered in
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