The Science Book

231

latter pair limited by the value of
the principal number. The fourth
number, with two possible values,
was needed to explain why two
electrons can exist in each subshell
with slightly different energy levels.
Together, the numbers neatly
explained the existence of atomic
orbitals that accept 2, 6, 10, and
14 electrons respectively.
Today, the fourth quantum
number is known as spin; it is
a particle’s intrinsic angular
momentum (which is created by
its rotation as it orbits), and has
positive or negative values that
are either whole- or half-integer
numbers. A few years later, Pauli
would demonstrate that values of
spin split all particles into two
major groups—fermions such as
electrons (with half-integer spins),
which obey a set of rules known as
Fermi–Dirac statistics (pp.246–47),
and bosons such as photons (with
zero or whole-number spin), which
obey different rules known as
Bose–Einstein statistics. Only
fermions obey the exclusion
principle, and this has important
implications for the understanding
of everything from collapsing stars
to the elementary particles that
make up the universe.

Schrödinger’s success
Combined with Pauli’s exclusion
principle, Schrödinger’s wave
equation allowed a new and deeper
understanding of the orbitals,
shells, and subshells within an
atom. Rather than imagining them
as classical orbits—well-defined
paths on which the electrons circle
the nucleus—the wave equation
shows that they are actually clouds
of probability—doughnut-shaped
and lobe-shaped regions in which
a particular electron with certain
quantum numbers is likely to be
found (p.256).

Another major success for

Schrödinger’s approach was

that it offered an explanation for

radioactive alpha decay—in which

a fully formed alpha particle

(consisting of two protons and two

neutrons) escapes from an atomic

nucleus. According to classical

physics, in order to remain intact,

the nucleus had to be surrounded

by a potential well steep enough to

prevent particles escaping from it.

(A potential well is a region in

space where the potential energy

is lower than its surroundings,

meaning that it traps particles.)

If the well was not sufficiently steep,

the nucleus would disintegrate

completely. How, then, could the

intermittent emissions seen in

alpha decay happen while allowing

the remaining nucleus to survive

intact? The wave equations

overcame the problem because

they allowed the energy of the

alpha particle within the nucleus

to vary. Most of the time, its energy

would be low enough to keep it

trapped, but occasionally it would

rise high enough to overcome the ❯❯

A PARADIGM SHIFT

Erwin Schrödinger

Born in Vienna, Austria, in

1887, Erwin Schrödinger

studied physics at the

University of Vienna, attaining

an assistant’s post there

before serving in World War I.

After the war, he moved first

to Germany, and then to

the University of Zurich,

Switzerland, where he did

his most important work,

immersing himself in the

emerging field of quantum

physics. In 1927, he returned

to Germany, and succeeded

Max Planck at the Humboldt

University of Berlin.

Schrödinger was a vocal

opponent of the Nazis, and left

Germany for a post at Oxford

University in 1934. It was

there that he learned he had

been awarded the 1933 Nobel

Prize in Physics, with Paul

Dirac, for the quantum wave

equation. By 1936, he was

back in Austria, but had to flee

again following Germany’s

annexation of the country. He

settled in Ireland for the rest

of his career before retiring to

Austria in the 1950s.

Key works

1920 Color Measurement

1926 Quantization as an

Eigenvalue Problem

Schrödinger’s equation, in its most

general form, shows the development

of a quantum system over time. It

requires the use of complex numbers.

—

∂t

∂

ih⎯ Ψ = Η Ψ