Page 45 - Electrical Properties of Materials

28 The electron as a wave

So electrons are waves. Are protons waves? Yes, they are; it can be shown
experimentally. Are neutrons waves? Yes, they are; it can be shown experiment-
ally. Are bullets waves? Well, they should be, but there are some experimental
difficulties in proving it. Take a bullet which has a mass of 10 –3 kg and travels
–1
3
at a velocity 10 ms . Then the bullet’s wavelength is 6.6 × 10 –34 m. Thus,
our reflecting agents or slits should be about 10 –34 m apart to observe the
diffraction of bullets, and that would not be easily realizable. Our bullets are
obviously too fast. Perhaps with slower bullets we will get a diffraction pattern
with slits a reasonable distance apart. Taking 10 mm for the distance between
the slits and requiring the same wavelength for the bullets, their velocity comes
–1
to 10 –28 ms ; that is, the bullet would travel 1 m in about 10 21 years. Best
modern estimates give the age of the universe as 10 10 years so this way of
doing the experiment runs again into practical difficulties.
The conclusion from this rather eccentric aside is of some importance. It
seems to suggest that everything, absolutely everything, that we used to regard
as particles may behave like waves if the right conditions are ensured. The
essential difference between electrons and particles encountered in some other
branches of engineering is merely one of size. Admittedly, the factors involved
are rather large. The bullet in our chosen example has a mass 10 27 times the
electron mass, so it is not entirely unreasonable that they behave differently.

2.2 The electron microscope
Particles are waves, waves are particles. This outcome of a few simple experi-
ments mystifies the layman, delights the physicist, and provides the philosopher
with material for a couple of treatises. What about the engineer? The engineer
is supposed to ask the consequential (though grammatically slightly incorrect)
question: what is this good for?
Well, one well-known practical effect of the wave nature of light is that the
resolving power of a microscope is fundamentally limited by the wavelength of
the light. If we want greater resolution, we need a shorter wavelength. Let me
use X-rays then. Yes, but they can not be easily focused. Use electrons then;
they have short enough wavelengths. An electron accelerated to a voltage of
150 V has a wavelength of 0.1 nm. This is already four thousand times shorter
than the wavelength of violet light, and using higher voltages we can get even
shorter wavelengths. Good, but can electrons be focused? Yes, they can. Very
conveniently, just about the same time that Davisson and Germer proved the
wave properties of electrons, Busch discovered that electric and magnetic fields
of the right configuration can bring a diverging electron beam to a focus. So all
we need is a fluorescent screen to make the incident electrons visible, and the
electron microscope is ready.
You know, of course, about the electron microscope, that it has a resolv-
ing power so great that it is possible to see large molecules with it, and using
the latest techniques even individual atoms can be made visible. Our aim is
mainly to emphasize the mental processes that lead from scientific discover-
ies to practical applications. But besides, there is one more interesting aspect
of the electron microscope. It provides perhaps the best example for what is
known as the ‘duality of the electron’. To explain the operation of the elec-
tron microscope, both the ‘wave’ and the ‘particle’ aspects of the electron are