80 / 123
Electrons as waves
De Broglie had been thinking that Bohr’s quantized electron orbits had characteristics
similar to those of waves. For example, as
Figures 13a
and
13b
show, only multiples of
half-wavelengths are possible on a plucked harp string because the string is fixed at
both ends. Similarly, de Broglie saw that only whole numbers of wavelengths are
allowed in a circular orbit of fixed radius, as shown in
Figure 13c
.
De Broglie also reflected on the fact that light—at one time thought to be strictly a wave
phenomenon—has both wave and particle characteristics. These thoughts led de Broglie
to pose a new question: If waves can have particlelike behavior, could the opposite also
be true? That is, can particles of matter, including electrons, behave like waves?
De Broglie knew that if an electron has wavelike motion and is restricted to circular orbits
of fixed radius, only certain wavelengths, frequencies, and energies are possible. Develop-
ing his idea, de Broglie derived the following equation, called the
de Broglie equation.
The de Broglie equation predicts that all moving particles have wave characteristics. Note
that the equation includes Planck’s constant. Planck’s constant is an exceedingly small
number, 6.626
×
10
-
34
J
⋅
s, which helps explain why it is difficult or impossible to observe
the wave characteristics of objects at the scale of everyday experience. For example, an
automobile moving at 25 m/s and having a mass of 910 kg has a wavelength of 2.9
×
10
-
38
m,
far too small to be seen or detected. By comparison, an electron moving at the same speed
has the easily measured wavelength of 2.9
×
10
-
5
m. Subsequent experiments have
proven that electrons and other moving particles do indeed have wave characteristics.
The Heisenberg uncertainty principle
Step by step, scientists such as Rutherford, Bohr, and de Broglie had been unraveling the
mysteries of the atom. However, a conclusion reached by the German theoretical physicist
Werner Heisenberg (1901–1976) proved to have profound implications for atomic models.
Heisenberg showed that it is impossible to take any measurement of an object without
disturbing the object. Imagine trying to locate a hovering, helium-filled balloon in a
darkened room. If you wave your hand about, you can locate the balloon’s position
when you touch it. However, when you touch the balloon, you transfer energy to it and
change its position. You could also detect the balloon’s position by turning on a
flashlight. Using this method, photons of light reflected from the balloon would reach
your eyes and reveal the balloon’s location. Because the balloon is a macroscopic object,
the effect of the rebounding photons on its position is very small and not observable.
Get It?
Identify
which variables in the de Broglie equation represent wavelike properties.
Particle Electromagnetic-Wave Relationship
λ =
h
___
m
ν
λ
represents wavelength.
h
is Planck’s constant.
m
represents mass of the particle.
ν
represents velocity.
The wavelength of a particle is the ratio of Planck’s constant and the product of the
particle’s mass and its velocity.
120
Module 4 • Electrons in Atoms