Page 22 - Photonics Essentials an introduction with experiments

Electrons and Photons

16 Introductory Concepts

Electrons have momentum, but can they have a wavelength? Well if
your name were Prince Louis-Victor, Duke de Broglie, and the year
was 1924, maybe such an idea would not seem so strange. If this were
the case, then the energy of an electron would be

1 h 2
E = ·
2m 2
Using this equation, you could actually calculate the wavelength if
you knew the electron energy. Suppose your electron has an energy of
1 eV. This is the energy of an electron that falls through a potential of
1 V.

1 eV = 1.6 × 10 –19 joules
h 6.6 × 10 –34 joule-sec
= = = 12 Å

–19
–31
2 mE 2 · 9 × 1 0 kg · 1 .6 × 1 0 jo u le s
In 1929, de Broglie received the Nobel prize for this revolutionary
idea. His reasoning was different from the simple analysis above, and
involved little math, not to mention Maxwell’s equations. His insight
was based on an analogy with his everyday experience and is present-
ed later on in Section 2.6. Nearly ten years later, in 1937, the Nobel
prize was awarded to Clint Davisson for his observation of electron
diffraction, a property of electrons that can be described only by its
fundamental wave-like nature. His lab partner, Lester Germer, got
left out of the prize list, a mystery to this day.
The work of Davisson and Germer led directly to the invention of
the electron microscope, a widely used instrument in all branches of
materials physics and engineering.

For a 1 eV photon, = 12,400 Å
For a 1 eV electron, = 12 Å

photon
At 1 eV energy (only), = 1000
electron
This ratio depends on the electron energy. But 1 eV is characteristic of
electrons in solids. What does this mean?
Relative to the electron, the photon has mostly energy, but not very
much momentum. We can see this on the diagram of energy and mo-
mentum (Fig. 2.4).
Except for the uninteresting case in which E = 0, the energy mo-
mentum curves for free electrons and photons do not intersect. That
is: there is no point on the curves where the energy and momentum of
an electron are equal to the energy and momentum of a photon. This

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