Page 21 - Photonics Essentials an introduction with experiments

Electrons and Photons

Electrons and Photons 15

An electron can be characterized by its mass, charge and magnetic
moment, all of which are fixed in magnitude. It is also characterized
by its energy and momentum, which are variable. Although the elec-
tron does not have a well-defined size, it behaves in many respects as
a particle. For example, we could write down expressions for the mo-
mentum and energy of a baseball:
momentum = mv = p

1 (mv) 2 p 2
kinetic energy = mv = = (2.21)
2
2 2m 2m
The same thing is true for electrons. Photons, of course, don’t have
any mass. So this equation does not work for photons.
A graph of the energy of a free electron as a function of its momen-
tum, just like that of a baseball, is a parabola (see Fig. 2.3). Remem-
ber that a 1 eV photon has =1240 nm.
On the other hand, we know from Maxwell’s equations that photons
do have a momentum that is equal to

E hf
p = = (2.22)
c c
But, since c = f ,
h 2
p = = k, where k = (2.23)

So, photons don’t have mass, but they have momentum.

ENERGY

+ MOMENTUM –
Figure 2.3. The kinetic energy of a particle with mass, like that of an electron, is propor-
tional to the square of its momentum.

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