Page 434 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 34

Atomic Physics

MATTERWAVES

Under certain conditions moving bodies exhibit wave properties. The quantity whose variations constitute the
matter waves (or de Broglie waves) of a moving body is known as its wave function ψ (Greek letter psi). The
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likelihood of finding the body at a particular time and place is proportional to the value of ψ at that time and
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place. A large value of ψ signifies a high probability of finding the body; a small value of ψ signifies a low
probability of finding the body.
The matter waves associated with a moving body are in the form of a group of waves that travels with the
same velocity as the body.
The wavelength of the matter waves of a body of mass m and velocity v is
h
de Broglie wavelength = λ =
mv

SOLVED PROBLEM 34.1
Find the de Broglie wavelengths of (a) a 46-g golf ball moving at 30 m/s, and (b) an electron moving at
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10 m/s.
h 6.63 × 10 −34 J·s
(a) λ = = = 4.8 × 10 −34 m
mv (0.046 kg)(30 m/s)
The wavelength of the golf ball is so small compared with its dimensions that we would not expect to find any
wave aspects in its behavior.
(b) The electron mass is 9.1 × 10 −31 kg, so
h 6.63 × 10 −34 J·s −11
λ = = = 7.3 × 10 m
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mv (9.1 × 10 −31 kg)(10 m/s)
The dimensions of atoms are comparable with this figure—the radius of the hydrogen atom, for instance, is
5.3 × 10 −11 m. It is therefore not surprising that the wave character of moving electrons is the key to under-
standing atomic structure and behavior.

SOLVED PROBLEM 34.2
An electron microscope uses a beam of fast electrons that are focused by electric and magnetic fields to
produce an enlarged image of a thin specimen on a screen or photographic plate. Find the resolving power
of an electron microscope which uses 15-keV electrons by assuming that this is equal to the electron
wavelength.
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