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Cosmic Radiation and Elementary Particles 289

10.4. Waves and particles

It is daily experience that moving bodies have a kinetic energy which involves a mass and
a velocity. Less familiar is the concept of Planck (1900) in which light moves in wave
packets of energy:

E = hu (I0.I)

Here ~, is the frequency of light with wavelength h

c = u~, (10.2)

and h the Planck constant, 6.63 • 10 -34 J s.
Einstein in the theory of the photoelectric effect, and Compton in the theory of the
scattering of photons (Ch. 6), showed that photons have not only a discrete energy, but also
a discrete momentum (cf. w

Pv = Ev /c (10.3)

Photons seem to collide with other particles as if they have a real mass and velocity as in
the classical mechanical expression for momentum: p = mv (4.3). If we put v = c and
equate with (10.3) we obtain a relativistic mass of the photon as

m v = E v/c 2 (10.4)

This is the mass-energy relation of Einstein, eqn. (4.23).
There are many examples of mass properties of photons. To the two mentioned above we
may add the solar pressure (i.e. photons from the sun which push atoms away from the sun
and into space), which has played a significant part in the formation of our planetary
system, and measurements showing that photons are attracted by large masses through the
gravitational force. Thus we see the evidence for the statement in the beginning that all
elementary particles must have relativistic mass, even if the rest mass is zero.
It is reasonable to assume, as de Broglie did in 1924, that since photons can behave as
moving particles moving particles may show wave properties. From the previous equation,
we can devise that the wavelength of such matter waves is
h = h/mv (10.5)

This relation is of importance in explaimng nuclear reactions, and has led to practical
consequences in the use of electron diffraction and in the development of electron
microscopy.
The wave and particle properties of matter complement each other (the complementarity
principle; N. Bohr, 1928). Throughout this book we use models based on wave properties
and sometimes on particle properties, depending on which more directly explain the
particular phenomenon under discussion.