The Science Book

A PARADIGM SHIFT 229

a French PhD student, Louis de
Broglie, whose suggestion led the
quantum revolution into a dramatic
new phase. Not only did de Broglie
demonstrate with a simple
equation how, in the subatomic
world, particles could equally be
waves, he also showed how any
object, of whatever mass, could
behave as a wave to some extent.
In other words, if light waves had
particle-like properties, then particles
of matter—such as electrons—
must have wavelike properties.
Planck had calculated the
energy of a light photon with the
simple equation E = hv, where E
is the energy of the electromagnetic
quanta, v is the wavelength of
the radiation involved, and h is
a constant, today known as
the Planck constant. De Broglie
showed that a light photon also has
momentum, something normally
only associated with particles
with mass and given by multiplying
the particle’s mass with its speed.
De Broglie showed that a light
photon had a momentum of

h divided by its wavelength.

However, since he was dealing

with particles whose energy and

mass might be affected by motion

at speeds close to that of light, de

Broglie incorporated the Lorentz

factor (p.219) into his equation.

This produced a more sophisticated

version that took into account

the effects of relativity.

De Broglie’s idea was radical

and daring, but it soon had

influential supporters, including

Einstein. The hypothesis was

Two seemingly incompatible

conceptions can each represent

an aspect of the truth.

Louis de Broglie

See also: Thomas Young 110–11 ■ Albert Einstein 214–21 ■ Werner Heisenberg 234–35 ■ Paul Dirac 246–47
Richard Feynman 272–73 ■ Hugh Everett III 284–85

If you fire electrons one-by-one

through two slits onto a screen, they

will build up an interference pattern

on the screen.

This means that they are

behaving like waves.

A wave function provides a way

of calculating the probability of

detecting an electron at a particular

point in space-time.

Particles have

wavelike properties.

also relatively easy to test. By

1927, scientists in two separate

laboratories had conducted

experiments to show that electrons

diffracted and interfered with each

other in exactly the same way as

photons of light. De Broglie’s

hypothesis was proved.

Growing significance

In the meantime, a number of

theoretical physicists were

sufficiently intrigued by de Broglie’s

hypothesis to investigate it further.

In particular, they wanted to know

how the properties of such matter

waves could give rise to the pattern

of specific energy levels among the

electron orbitals of the hydrogen

atom proposed by Bohr’s model of

the atom. De Broglie himself had

suggested that the pattern arose

because the circumference of each

orbital must accommodate a whole

number of wavelengths of the

matter wave. Since the electron’s

energy level depends on its

distance from the atom’s positively

charged nucleus, this meant that ❯❯