29.6 The Wave Nature of Matter De Broglie Wavelength In 1923 a French physics graduate student named Prince Louis-Victor de Broglie (1892–1987) made a radical proposal based on the hope that nature is symmetric. If EM radiation has both particle and wave properties, then nature would be symmetric if matter also had both particle and wave properties. If what we once thought of as an unequivocal wave (EM radiation) is also a particle, then what we think of as an unequivocal particle (matter) may also be a wave. De Broglie's suggestion, made as part of his doctoral thesis, was so radical that it was greeted with some skepticism. A copy of his thesis was sent to Einstein, who said it was not only probably correct, but that it might be of fundamental importance. With the support of Einstein and a few other prominent physicists, de Broglie was awarded his doctorate. De Broglie took both relativity and quantum mechanics into account to develop the proposal that all particles have a wavelength, given by a =(matter and photons), (29.34) where h is Planck's constant and p is momentum. This is defined to be the de Broglie wavelength. (Note that we already have this for photons, from the equation p = hl2.) The hallmark of a wave is interference. If matter is a wave, then it must exhibit constructive and destructive interference. Why isn't this ordinarily observed? The answer is that in order to see significant This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 Chapter 29 | Introduction to Quantum Physics 1161 interference effects, a wave must interact with an object about the same size as its wavelength. Since h is very small, a is also small, especially for macroscopic objects. A 3-kg bowling ball moving at 10 m/s, for example, has 1 = hlp = (6.63×10-34 J-s) /[(3 kg)(10 m/s)] = 2x10-35 (29.35) m.

29.6 The Wave Nature of Matter De Broglie Wavelength In 1923 a French physics graduate student named Prince Louis-Victor de Broglie (1892–1987) made a radical proposal based on the hope that nature is symmetric. If EM radiation has both particle and wave properties, then nature would be symmetric if matter also had both particle and wave properties. If what we once thought of as an unequivocal wave (EM radiation) is also a particle, then what we think of as an unequivocal particle (matter) may also be a wave. De Broglie's suggestion, made as part of his doctoral thesis, was so radical that it was greeted with some skepticism. A copy of his thesis was sent to Einstein, who said it was not only probably correct, but that it might be of fundamental importance. With the support of Einstein and a few other prominent physicists, de Broglie was awarded his doctorate. De Broglie took both relativity and quantum mechanics into account to develop the proposal that all particles have a wavelength, given by a =(matter and photons), (29.34) where h is Planck's constant and p is momentum. This is defined to be the de Broglie wavelength. (Note that we already have this for photons, from the equation p = hl2.) The hallmark of a wave is interference. If matter is a wave, then it must exhibit constructive and destructive interference. Why isn't this ordinarily observed? The answer is that in order to see significant This OpenStax book is available for free at http://cnx.org/content/col11406/1.9 Chapter 29 | Introduction to Quantum Physics 1161 interference effects, a wave must interact with an object about the same size as its wavelength. Since h is very small, a is also small, especially for macroscopic objects. A 3-kg bowling ball moving at 10 m/s, for example, has 1 = hlp = (6.63×10-34 J-s) /[(3 kg)(10 m/s)] = 2x10-35 (29.35) m.

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The Wave Nature of Matter
• Describe the Davisson-Germer experiment, and explain how it provides evidence for the wave nature of electrons.

29.6 The Wave Nature of Matter
De Broglie Wavelength
In 1923 a French physics graduate student named Prince Louis-Victor de Broglie (1892–1987) made a radical proposal based on
the hope that nature is symmetric. If EM radiation has both particle and wave properties, then nature would be symmetric if
matter also had both particle and wave properties. If what we once thought of as an unequivocal wave (EM radiation) is also a
particle, then what we think of as an unequivocal particle (matter) may also be a wave. De Broglie's suggestion, made as part of
his doctoral thesis, was so radical that it was greeted with some skepticism. A copy of his thesis was sent to Einstein, who said it
was not only probably correct, but that it might be of fundamental importance. With the support of Einstein and a few other
prominent physicists, de Broglie was awarded his doctorate.
De Broglie took both relativity and quantum mechanics into account to develop the proposal that all particles have a wavelength,
given by
a =(matter and photons),
(29.34)
where h is Planck's constant and p is momentum. This is defined to be the de Broglie wavelength. (Note that we already
have this for photons, from the equation p = hl2.) The hallmark of a wave is interference. If matter is a wave, then it must
exhibit constructive and destructive interference. Why isn't this ordinarily observed? The answer is that in order to see significant
This OpenStax book is available for free at http://cnx.org/content/col11406/1.9
Chapter 29 | Introduction to Quantum Physics
1161
interference effects, a wave must interact with an object about the same size as its wavelength. Since h is very small, a is also
small, especially for macroscopic objects. A 3-kg bowling ball moving at 10 m/s, for example, has
1 = hlp = (6.63×10-34 J-s) /[(3 kg)(10 m/s)] = 2x10-35
(29.35)
m.

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