Quantum
Theory

I INTRODUCTION

Quantum Theory, in physics, description of
the particles that make up matter and how they interact with each other and
with energy. Quantum theory explains in principle
how to calculate what will happen in any experiment involving physical or
biological systems, and how to understand how our world works. The name
“quantum theory” comes from the fact that the theory describes the matter and
energy in the universe in terms of single indivisible units called *quanta*
(singular *quantum*). Quantum theory is different from classical physics.
Classical physics is an approximation of the set of rules and equations in
quantum theory. Classical physics accurately describes the behavior
of matter and energy in the everyday universe. For example, classical physics
explains the motion of a car accelerating or of a ball flying through the air.
Quantum theory, on the other hand, can accurately describe the behavior of the universe on a much smaller scale, that of
atoms and smaller particles. The rules of classical physics do not explain the behavior of matter and energy on this small scale. Quantum
theory is more general than classical physics, and in principle, it could be
used to predict the behavior of any physical,
chemical, or biological system. However, explaining the behavior
of the everyday world with quantum theory is too complicated to be practical.

Quantum theory not only specifies new rules for
describing the universe but also introduces new ways of thinking about matter
and energy. The tiny particles that quantum theory describes do not have
defined locations, speeds, and paths like objects described by classical
physics. Instead, quantum theory describes positions and other properties of
particles in terms of the chances that the property will have a certain value.
For example, it allows scientists to calculate how likely it is that a particle
will be in a certain position at a certain time.

Quantum description of particles allows scientists to
understand how particles combine to form atoms. Quantum description of atoms
helps scientists understand the chemical and physical properties of molecules,
atoms, and subatomic particles. Quantum theory enabled scientists to understand
the conditions of the early universe, how the Sun shines, and how atoms and
molecules determine the characteristics of the material that they make up.
Without quantum theory, scientists could not have developed nuclear energy or
the electric circuits that provide the basis for computers.

Quantum theory describes all of the fundamental
forces—except gravitation—that physicists have found in nature. The forces that
quantum theory describes are the electrical, the magnetic, the weak, and the
strong. Physicists often refer to these forces as interactions, because the
forces control the way particles interact with each other. Interactions also
affect spontaneous changes in isolated particles.

II WAVES AND PARTICLES

One of the striking differences between
quantum theory and classical physics is that quantum theory describes energy
and matter both as waves and as particles. The type of energy physicists study
most often with quantum theory is light. Classical physics considers light to
be only a wave, and it treats matter strictly as particles. Quantum theory acknowledges
that both light and matter can behave like waves and like particles.

It is important to understand how scientists
describe the properties of waves in order to understand how waves fit into
quantum theory. A familiar type of wave occurs when a rope is tied to a solid
object and someone moves the free end up and down. Waves travel along the rope.
The highest points on the rope are called the crests of the waves. The lowest
points are called troughs. One full wave consists of a crest and trough. The distance
from crest to crest or from trough to trough—or from any point on one wave to
the identical point on the next wave—is called the wavelength. The frequency of
the waves is the number of waves per second that pass by a given point along
the rope.

If waves traveling down
the rope hit the stationary end and bounce back, like water waves bouncing
against a wall, two waves on the rope may meet each other, hitting the same
place on the rope at the same time. These two waves will interfere, or combine
(*see *Interference). If the two waves exactly line up—that is, if the
crests and troughs of the waves line up—the waves interfere constructively.
This means that the trough of the combined wave is deeper and the crest is
higher than those of the waves before they combined. If the two waves are
offset by exactly half of a wavelength, the trough of one wave lines up with
the crest of the other. This alignment creates destructive interference—the two
waves cancel each other out and a momentary flat spot appears on the rope. *See
also *Wave Motion.

A Light as a Wave and as a Particle

Like classical physics, quantum theory sometimes
describes light as a wave, because light behaves like a wave in many
situations. Light is not a vibration of a solid substance, such as a rope.
Instead, a light wave is made up of a vibration in the intensity of the
electric and magnetic fields that surround any electrically charged object.

Like the waves moving along a rope, light waves
travel and carry energy. The amount of energy depends on the frequency of the
light waves: the higher the frequency, the higher the energy. The frequency of
a light wave is also related to the color of the
light. For example, blue light has a higher frequency than that of red light.
Therefore, a beam of blue light has more energy than an equally intense beam of
red light has.

Unlike classical physics, quantum theory also describes
light as a particle. Scientists revealed this aspect of light behavior in several experiments performed during the early
20th century. In one experiment, physicists discovered an interaction between
light and particles in a metal. They called this interaction the photoelectric
effect. In the photoelectric effect, a beam of light shining on a piece of
metal makes the metal emit electrons. The light adds energy to the metal’s
electrons, giving them enough energy to break free from the metal. If light was
made strictly of waves, each electron in the metal could absorb many continuous
waves of light and gain more and more energy. Increasing the intensity of the
light, or adding more light waves, would add more energy to the emitted
electrons. Shining a more and more intense beam of light on the metal would
make the metal emit electrons with more and more energy.

Scientists found, however, that shining a more intense
beam of light on the metal just made the metal emit more electrons. Each of
these electrons had the same energy as that of electrons emitted with low
intensity light. The electrons could not be interacting with waves, because
adding more waves did not add more energy to the electrons. Instead, each
electron had to be interacting with just a small piece of the light beam. These
pieces were like little packets of light energy, or particles of light. The
size, or energy, of each packet depended only on the frequency, or color, of the light—not on the intensity of the light. A
more intense beam of light just had more packets of light energy, but each
packet contained the same amount of energy. Individual electrons could absorb
one packet of light energy and break free from the metal. Increasing the
intensity of the light added more packets of energy to the beam and enabled a
greater number of electrons to break free—but each of these emitted electrons
had the same amount of energy. Scientists could only change the energy of the
emitted electrons by changing the frequency, or color,
of the beam. Changing from red light to blue light, for example, increased the
energy of each packet of light. In this case, each emitted electron absorbed a
bigger packet of light energy and had more energy after it broke free of the
metal. Using these results, physicists developed a model of light as a
particle, and they called these light particles photons.

In 1922 American physicist Arthur Compton
discovered another interaction, now called the Compton effect,
that reveals the particle nature of light. In the Compton effect,
light collides with an electron. The collision knocks the electron off course
and changes the frequency, and therefore energy, of the light. The light
affects the electron in the same way a particle with momentum would: It bumps
the electron and changes the electron’s path. The light is also affected by the
collision as though it were a particle, in that its energy and momentum
changes.

Momentum is a quantity that can be defined for all
particles. For light particles, or photons, momentum depends on the frequency,
or color, of the photon, which in turn depends on the
photon’s energy. The energy of a photon is equal to a constant number, called
Planck’s constant, times the frequency of the photon. Planck’s constant is
named for German physicist Max Planck, who first proposed the relationship
between energy and frequency. The accepted value of Planck’s constant is 6.626
× 10^{-34} joule-second. This number is very small—written out, it is a
decimal point followed by 33 zeroes, followed by the digits 6626. The energy of
a single photon is therefore very small.

The dual nature of light seems puzzling
because we have no everyday experience with wave-particle duality. Waves are
everyday phenomena; we are all familiar with waves on a body of water or on a
vibrating rope. Particles, too, are everyday objects—baseballs, cars,
buildings, and even people can be thought of as particles. But to our senses,
there are no everyday objects that are both waves and particles. Scientists
increasingly find that the rules that apply to the world we see are only
approximations of the rules that govern the unseen world of light and subatomic
particles.

B Matter as Waves and Particles

In 1923 French physicist Louis de Broglie suggested that all particles—not just photons—have
both wave and particle properties. He calculated that every particle has a
wavelength (represented by λ, the Greek letter *lambda*) equal to
Planck’s constant (h) divided by the momentum (p) of the particle: λ =
h/p. Electrons, atoms, and all other particles have de Broglie
wavelengths. The momentum of an object depends on its speed and mass, so the
faster and heavier an object is, the larger its momentum (p) will be. Because
Planck’s constant (h) is an extremely tiny number, the de Broglie
wavelength (h/p) of any visible object is exceedingly small. In fact, the de Broglie wavelength of anything much larger than an atom is
smaller than the size of one of its atoms. For example, the de Broglie wavelength of a baseball moving at 150 km/h (90
mph) is 1.1 × 10^{-34} m (3.6 × 10^{-34} ft). The diameter of a
hydrogen atom (the simplest and smallest atom) is about 5 × 10^{-11} m
(about 2 × 10^{-10} ft), more than 100 billion trillion times larger
than the de Broglie wavelength of the baseball. The
de Broglie wavelengths of everyday objects are so
tiny that the wave nature of these objects does not affect their visible behavior, so their wave-particle duality is undetectable to
us.

De Broglie wavelengths become
important when the mass, and therefore momentum, of particles is very small.
Particles the size of atoms and electrons have demonstrable wavelike
properties. One of the most dramatic and interesting demonstrations of the wave
behavior of electrons comes from the double-slit
experiment. This experiment consists of a barrier set between a source of
electrons and an electron detector. The barrier contains two slits, each about
the width of the de Broglie wavelength of an
electron. On this small scale, the wave nature of electrons becomes evident, as
described in the following paragraphs.

Scientists can determine whether the electrons are
behaving like waves or like particles by comparing the results of double-slit
experiments with those of similar experiments performed with visible waves and
particles. To establish how visible waves behave in a double-slit apparatus,
physicists can replace the electron source with a device that creates waves in
a tank of water. The slits in the barrier are about as wide as the wavelength
of the water waves. In this experiment, the waves spread out spherically from
the source until they hit the barrier. The waves pass through the slits and
spread out again, producing two new wave fronts with centers
as far apart as the slits are. These two new sets of waves interfere with each
other as they travel toward the detector at the far end of the tank.

The waves interfere constructively in some places
(adding together) and destructively in others (canceling
each other out). The most intense waves—that is, those formed by the most
constructive interference—hit the detector at the spot opposite the midpoint
between the two slits. These strong waves form a peak of intensity on the
detector. On either side of this peak, the waves destructively interfere and
cancel each other out, creating a low point in intensity. Further out from
these low points, the waves are weaker, but they constructively interfere again
and create two more peaks of intensity, smaller than the large peak in the
middle. The intensity then drops again as the waves
destructively interfere. The intensity of the waves forms a symmetrical
pattern on the detector, with a large peak directly across from the midpoint
between the slits and alternating low points and smaller and smaller peaks on
either side.

To see how particles behave in the double-slit
experiment, physicists replace the water with marbles. The barrier slits are
about the width of a marble, as the point of this experiment is to allow
particles (in this case, marbles) to pass through the barrier. The marbles are
put in motion and pass through the barrier, striking the detector at the far
end of the apparatus. The results show that the marbles do not interfere with
each other or with themselves like waves do. Instead, the marbles strike the
detector most frequently in the two points directly opposite each slit.

When physicists perform the double-slit experiment with
electrons, the detection pattern matches that produced by the waves, not the
marbles. These results show that electrons do have wave properties. However, if
scientists run the experiment using a barrier whose slits are much wider than
the de Broglie wavelength of the electrons, the
pattern resembles the one produced by the marbles. This shows that tiny
particles such as electrons behave as waves in some circumstances and as
particles in others.

C Uncertainty Principle

Before the development of quantum theory, physicists
assumed that, with perfect equipment in perfect conditions, measuring any
physical quantity as accurately as desired was
possible. Quantum mechanical equations show that accurate measurement of both
the position and the momentum of a particle at the same time is
impossible. This rule is called Heisenberg’s uncertainty principle after German
physicist Werner Heisenberg, who derived it from other rules of quantum theory.
The uncertainty principle means that as physicists measure a particle’s
position with more and more accuracy, the momentum of the particle becomes less
and less precise, or more and more uncertain, and vice versa.

Heisenberg formally stated his principle by describing
the relationship between the uncertainty in the measurement of a particle’s
position and the uncertainty in the measurement of its momentum. Heisenberg
said that the uncertainty in position (represented by Δx)
times the uncertainty in momentum (represented by Δp;)
must be greater than a constant number equal to Planck’s constant (h) divided
by 4 ( is a constant approximately equal to 3.14).
Mathematically, the uncertainty principle can be written as Δx
Δp > h / 4.
This relationship means that as a scientist measures a particle’s position more
and more accurately—so the uncertainty in its position becomes very small—the
uncertainty in its momentum must become large to compensate and make this expression
true. Likewise, if the uncertainty in momentum, Δp, becomes small, Δx
must become large to make the expression true.

One way to understand the uncertainty principle is
to consider the dual wave-particle nature of light and matter. Physicists can
measure the position and momentum of an atom by bouncing light off of the atom.
If they treat the light as a wave, they have to consider a property of waves
called diffraction when measuring the atom’s position. Diffraction occurs when
waves encounter an object—the waves bend around the object instead of traveling in a straight line. If the length of the waves is
much shorter than the size of the object, the bending of the waves just at the
edges of the object is not a problem. Most of the waves bounce back and give an
accurate measurement of the object’s position. If the length of the waves is
close to the size of the object, however, most of the waves diffract, making
the measurement of the object’s position fuzzy. Physicists must bounce shorter
and shorter waves off an atom to measure its position more accurately. Using
shorter wavelengths of light, however, increases the uncertainty in the
measurement of the atom’s momentum.

Light carries energy and momentum, because of its
particle nature (described in the Compton effect).
Photons that strike the atom being measured will change the atom’s energy and
momentum. The fact that measuring an object also affects the object is an
important principle in quantum theory. Normally the affect is so small it does
not matter, but on the small scale of atoms, it becomes important. The bump to
the atom increases the uncertainty in the measurement of the atom’s momentum.
Light with more energy and momentum will knock the atom harder and create more
uncertainty. The momentum of light is equal to Plank’s constant divided by the
light’s wavelength, or p = h/λ. Physicists can increase the wavelength to
decrease the light’s momentum and measure the atom’s momentum more accurately.
Because of diffraction, however, increasing the light’s wavelength increases
the uncertainty in the measurement of the atom’s position. Physicists most
often use the uncertainty principle that describes the relationship between
position and momentum, but a similar and important uncertainty relationship
also exists between the measurement of energy and the measurement of time.

III PROBABILITY AND WAVE FUNCTIONS

Quantum theory gives exact answers to many
questions, but it can only give probabilities for some values. A probability is
the likelihood of an answer being a certain value. Probability is often
represented by a graph, with the highest point on the graph representing the
most likely value and the lowest representing the least likely value. For
example, the graph that shows the likelihood of finding the electron of a
hydrogen atom at a certain distance from the nucleus looks like the following:

The nucleus of the atom is at the left of the
graph. The probability of finding the electron very near the nucleus is very
low. The probability reaches a definite peak, marking the spot at which the
electron is most likely to be.

Scientists use a mathematical expression called a
wave function to describe the characteristics of a particle that are related to
time and space—such as position and velocity. The wave function helps determine
the probability of these aspects being certain values. The wave function of a
particle is not the same as the wave suggested by wave-particle duality. A wave
function is strictly a mathematical way of expressing the characteristics of a
particle. Physicists usually represent these types of wave functions with the
Greek letter *psi**,* Ψ. The wave
function of the electron in a hydrogen atom is:

The symbol and the letter *e*
in this equation represent constant numbers derived from mathematics. The
letter *a* is also a constant number called the
Bohr radius for the hydrogen atom. The square of a wave function, or a wave
function multiplied by itself, is equal to the
probability density of the particle that the wave function describes. The
probability density of a particle gives the likelihood of finding the particle
at a certain point.

The wave function described above does not depend
on time. An isolated hydrogen atom does not change over time, so leaving time
out of the atom’s wave function is acceptable. For particles in systems that
change over time, physicists use wave functions that depend on time. This lets
them calculate how the system and the particle’s properties change over time.
Physicists represent a time-dependent wave function with Ψ(t),
where t represents time.

The wave function for a single atom can only reveal
the probability that an atom will have a certain set of characteristics at a
certain time. Physicists call the set of characteristics describing an atom the
state of the atom. The wave function cannot describe the actual state of the
atom, just the probability that the atom will be in a certain state.

The wave functions of individual particles can be
added together to create a wave function for a system, so quantum theory allows
physicists to examine many particles at once. The rules of probability state
that probabilities and actual values match better and better as the number of
particles (or dice thrown, or coins tossed, whatever the probability refers to)
increases. Therefore, if physicists consider a large group of atoms, the wave
function for the group of atoms provides information that is more definite and
useful than that provided by the wave function of a single atom.

An example of a wave function for a
single atom is one that describes an atom that has absorbed some energy. The
energy has boosted the atom’s electrons to a higher energy level, and the atom
is said to be in an excited state. It can return to its normal ground state (or
lowest energy state) by emitting energy in the form of a photon. Scientists
call the wave function of the initial exited state Ψ_{i}
(with “i” indicating it is the initial state) and the
wave function of the final ground state Ψ_{f}
(with “f” representing the final state). To describe the atom’s state over
time, they multiply Ψ_{i} by some
function, a(t), that decreases with time, because the
chances of the atom being in this excited state decrease with time. They
multiply Ψ_{f} by some function, b(t), that increases with time, because the chances of the
atom being in this state increase with time. The physicist completing the
calculation chooses a(t) and b(t) based on the
characteristics of the system. The complete wave equation for the transition is
the following:

Ψ = a(t) Ψ_{i} + b(t) Ψ_{f}.

At any time, the rules of probability state
that the probability of finding a single atom in either state is found by
multiplying the coefficient of its wave function (a(t)
or b(t)) by itself. For one atom, this does not give a very satisfactory answer.
Even though the physicist knows the probability of finding the atom in one
state or the other, whether or not reality will match probability is still far
from certain. This idea is similar to rolling a pair of dice. There is a 1 in 6
chance that the roll will add up to seven, which is the most likely sum. Each
roll is random, however, and not connected to the rolls before it. It would not
be surprising if ten rolls of the dice failed to yield a sum of seven. However,
the actual number of times that seven appears matches probability better as the
number of rolls increases. For one million or one billion rolls of the dice,
one of every six rolls would almost certainly add up to seven.

Similarly, for a large number of atoms, the
probabilities become approximate percentages of atoms in each state, and these
percentages become more accurate as the number of atoms observed increases. For
example, if the square of a(t) at a certain time is
0.2, then in a very large sample of atoms, 20 percent (0.2) of the atoms will
be in the initial state and 80 percent (0.8) will be in the final state.

One of the most puzzling results of quantum
mechanics is the effect of measurement on a quantum system. Before a scientist
measures the characteristics of a particle, its characteristics do not have
definite values. Instead, they are described by a wave function, which gives
the characteristics only as fuzzy probabilities. In effect, the particle does
not exist in an exact location until a scientist measures its position. Measuring
the particle fixes its characteristics at specific values, effectively
“collapsing” the particle’s wave function. The particle’s position is no longer
fuzzy, so the wave function that describes it has one high, sharp peak of
probability. If the position of a particle has just been measured, the graph of
its probability density looks like the following:

In the 1930s physicists proposed an imaginary
experiment to demonstrate how measurement causes complications in quantum
mechanics. They imagined a system that contained two particles with opposite
values of *spin*, a property of particles that is analogous to angular
momentum. The physicists can know that the two particles have opposite spins by
setting the total spin of the system to be zero. They can measure the total
spin without directly measuring the spin of either particle. Because they have
not yet measured the spin of either particle, the spins do not actually have
defined values. They exist only as fuzzy probabilities. The spins only take on
definite values when the scientists measure them.

In this hypothetical experiment the scientists do
not measure the spin of each particle right away. They send the two particles,
called an entangled pair, off in opposite directions until they are far apart
from each other. The scientists then measure the spin of one of the particles,
fixing its value. Instantaneously, the spin of the other particle becomes known
and fixed. It is no longer a fuzzy probability but must be the opposite of the
other particle, so that their spins will add to zero. It is as though the first
particle communicated with the second. This apparent instantaneous passing of
information from one particle to the other would violate the rule that nothing,
not even information, can travel faster than the speed of light. The two
particles do not, however, communicate with each other. Physicists can
instantaneously know the spin of the second particle because they set the total
spin of the system to be zero at the beginning of the experiment. In 1997
Austrian researchers performed an experiment similar to the hypothetical
experiment of the 1930s, confirming the effect of measurement on a quantum
system.

IV THE QUANTUM ATOM

The first great achievement of quantum theory was
to explain how atoms work. Physicists found explaining the structure of the
atom with classical physics to be impossible. Atoms consist of negatively
charged electrons bound to a positively charged nucleus. The nucleus of an atom
contains positively charged particles called protons and may contain neutral
particles called neutrons. Protons and neutrons are about the same size but are
much larger and heavier than electrons are. Classical physics describes a
hydrogen atom as an electron orbiting a proton, much as the Moon orbits Earth.
By the rules of classical physics, the electron has a property called inertia
that makes it want to continue traveling in a
straight line. The attractive electrical force of the positively charged proton
overcomes this inertia and bends the electron’s path into a circle, making it
stay in a closed orbit. The classical theory of electromagnetism says that
charged particles (such as electrons) radiate energy when they bend their
paths. If classical physics applied to the atom, the electron would radiate
away all of its energy. It would slow down and its orbit would collapse into
the proton within a fraction of a second. However, physicists know that atoms
can be stable for centuries or longer.

Quantum theory gives a model of the atom that
explains its stability. It still treats atoms as electrons surrounding a
nucleus, but the electrons do not orbit the nucleus like moons orbiting
planets. Quantum mechanics gives the location of an electron as a probability
instead of pinpointing it at a certain position. Even though the position of an
electron is uncertain, quantum theory prohibits the electron from being at some
places. The easiest way to describe the differences between the allowed and
prohibited positions of electrons in an atom is to think of the electron as a
wave. The wave-particle duality of quantum theory allows electrons to be
described as waves, using the electron’s de Broglie
wavelength.

If the electron is described as a continuous
wave, its motion may be described as that of a standing wave. Standing waves
occur when a continuous wave occupies one of a set of certain distances. These
distances enable the wave to interfere with itself in such a way that the wave
appears to remain stationary. Plucking the string of a musical instrument sets
up a standing wave in the string that makes the string resonate and produce
sound. The length of the string, or the distance the wave on the string
occupies, is equal to a whole or half number of wavelengths. At these
distances, the wave bounces back at either end and constructively interferes
with itself, which strengthens the wave. Similarly, an electron wave occupies a
distance around the nucleus of an atom, or a circumference, that enables it to
travel a whole or half number of wavelengths before looping back on itself. The
electron wave therefore constructively interferes with itself and remains
stable:

An electron wave cannot occupy a distance that is
not equal to a whole or half number of wavelengths. In a distance such as this,
the wave would interfere with itself in a complicated way, and would become
unstable:

An electron has a certain amount of energy
when its wave occupies one of the allowed circumferences around the nucleus of
an atom. This energy depends on the number of wavelengths in the circumference,
and it is called the electron’s energy level. Because only certain
circumferences, and therefore energy levels, are allowed, physicists say that
the energy levels are quantized. This quantization means that the energies of
the levels can only take on certain values.

The regions of space in which electrons are
most likely to be found are called orbitals. Orbitals look like fuzzy, three-dimensional shapes. More
than one orbital, meaning more than one shape, may
exist at certain energy levels. Electron orbitals are
also quantized, meaning that only certain shapes are allowed in each energy
level. The quantization of electron orbitals and
energy levels in atoms explains the stability of atoms. An electron in an
energy level that allows only one wavelength is at the lowest possible energy
level. An atom with all of its electrons in their lowest possible energy levels
is said to be in its ground state. Unless it is affected by external forces, an
atom will stay in its ground state forever.

The quantum theory explanation of the atom led to a
deeper understanding of the periodic table of the chemical elements. The
periodic table of elements is a chart of the known elements. Scientists
originally arranged the elements in this table in order of increasing atomic
number (which is equal to the number of protons in the nuclei of each element’s
atoms) and according to the chemical behavior of the
elements. They grouped elements that behave in a similar way together in
columns. Scientists found that elements that behave similarly occur in a
periodic fashion according to their atomic number. For example, a family of
elements called the noble gases all share similar chemical properties. The
noble gases include neon, xenon, and argon. They do not react easily with other
elements and are almost never found in chemical compounds. The atomic numbers
of the noble gases increase from one element to the next in a periodic way.
They belong to the same column at the far right edge of the periodic table.

Quantum theory showed that an element’s chemical
properties have little to do with the nucleus of the element’s atoms, but
instead depend on the number and arrangement of the electrons in each atom. An
atom has the same number of electrons as protons, making the atom electrically
neutral. The arrangement of electrons in an atom depends on two important parts
of quantum theory. The first is the quantization of electron energy, which
limits the regions of space that electrons can occupy. The second part is a
rule called the Pauli exclusion
principle, first proposed by Austrian-born Swiss physicist Wolfgang Pauli.

The Pauli exclusion principle
states that no electron can have exactly the same characteristics as those of
another electron. These characteristics include orbital, direction of rotation
(called spin), and direction of orbit. Each energy level in an atom has a set
number of ways these characteristics can combine. The number of combinations
determines how many electrons can occupy an energy level before the electrons
have to start filling up the next level.

An atom is the most stable when it has
the least amount of energy, so its lowest energy levels fill with electrons
first. Each energy level must be filled before electrons begin filling up the
next level. These rules, and the rules of quantum theory, determine how many
electrons an atom has in each energy level, and in particular, how many it has
in its outermost level. Using the quantum mechanical model of the atom,
physicists found that all the elements in the same column of the periodic table
also have the same number of electrons in the outer energy level of their
atoms. Quantum theory shows that the number of electrons in an atom’s outer level
determines the atom’s chemical properties, or how it will react with other
atoms.

The number of electrons in an atom’s outer energy
level is important because atoms are most stable when their outermost energy
level is filled, which is the case for atoms of the noble gases. Atoms imitate
the noble gases by donating electrons to, taking electrons from, or sharing
electrons with other atoms. If an atom’s outer energy level is only partially
filled, it will bond easily with atoms that can help it fill its outer level.
Atoms that are missing the same number of electrons from their outer energy
level will react similarly to fill their outer energy level.

Quantum theory also explains why different atoms
emit and absorb different wavelengths of light. An atom stores energy in its
electrons. An atom with all of its electrons at their lowest possible energy
levels has its lowest possible energy and is said to be in its ground state.
One of the ways atoms can gain more energy is to absorb light in the form of photons,
or particles of light. When a photon hits an atom, one of the atom’s electrons
absorbs the photon. The photon’s energy makes the electron jump from its
original energy level up to a higher energy level. This jump leaves an empty
space in the original inner energy level, making the atom less stable. The atom
is now in an excited state, but it cannot store the new energy indefinitely,
because atoms always seek their most stable state. When the
atom releases the energy, the electron drops back down to its original energy
level. As it does, the electron releases a photon.

Quantum theory defines the possible energy levels of an
atom, so it defines the particular jumps that an electron can make between
energy levels. The difference between the old and new energy levels of the
electron is equal to the amount of energy the atom stores. Because the energy
levels are quantized, atoms can only absorb and store photons with certain
amounts of energy. The photon’s energy is related to its frequency, or color. As the frequency of photons increases, their energy
increases. Atoms can only absorb certain amounts of energy, so only certain
frequencies of light can excite atoms. Likewise, atoms only emit certain
frequencies of light when they drop to their ground state. The different
frequencies available to different atoms help astronomers,
for example, determine the chemical makeup of a star by observing which
wavelengths are especially weak or strong in the star’s light. *See also *Spectroscopy.

V DEVELOPMENT OF QUANTUM THEORY

The development of quantum theory began with German
physicist Max Planck’s proposal in 1900 that matter can emit or absorb energy
only in small, discrete packets, called quanta. This idea introduced the
particle nature of light. In 1905 German-born American physicist Albert
Einstein used Planck’s work to explain the photoelectric effect, in which light
hitting a metal makes the metal emit electrons. British physicist Ernest
Rutherford proved that atoms consisted of electrons bound to a nucleus in 1911.
In 1913 Danish physicist Niels Bohr proposed that
classical mechanics could not explain the structure of the atom and developed a
model of the atom with electrons in fixed orbits. Bohr’s model of the atom
proved difficult to apply to all but the simplest atoms.

In 1923 French physicist Louis de Broglie suggested that matter could be described as a wave,
just as light could be described as a particle. The wave model of the electron
allowed Austrian physicist Erwin Schrödinger to develop a mathematical method
of determining the probability that an electron will be at a particular place
at a certain time. Schrödinger published his theory of wave mechanics in 1926.
Around the same time, German physicist Werner Heisenberg developed a way of
calculating the characteristics of electrons that was quite different from
Schrödinger’s method but yielded the same results. Heisenberg’s method was
called matrix mechanics.

In 1925 Austrian-born Swiss physicist Wolfgang Pauli developed the Pauli exclusion principle, which allowed physicists to calculate
the structure of the quantum atom for the first time. In 1926 Heisenberg and
two of his colleagues, German physicists Max Born and Ernst Pascual
Jordan, published a theory that combined the principles of quantum theory with
the classical theory of light (called electrodynamics). Heisenberg made another
important contribution to quantum theory in 1927 when he introduced the Heisenberg
uncertainty principle.

Since these first breakthroughs in quantum
mechanical research, physicists have focused on testing and refining quantum
theory, further connecting the theory to other theories, and finding new
applications. In 1928 British physicist Paul Dirac
refined the theory that combined quantum theory with electrodynamics. He
developed a model of the electron that was consistent with both quantum theory
and Einstein’s special theory of relativity, and in doing so he created a
theory that came to be known as quantum electrodynamics, or QED. In the early
1950s Japanese physicist Tomonaga Shin’ichirō
and American physicists Richard Feynman and Julian Schwinger
each independently improved the scientific community’s understanding of QED and
made it an experimentally testable theory that successfully predicted or
explained the results of many experiments.

VI CURRENT RESEARCH AND APPLICATIONS

At the turn of the 21st century,
physicists were still finding new problems to study with quantum theory and new
applications for quantum theory. This research will probably continue for many
decades. Quantum theory is technically a fully formulated theory—any questions
about the physical world can be calculated using quantum mechanics, but some
are too complicated to solve in practice. The attempt to find
quantum explanations of gravitation and to find a unified description of all
the forces in nature are promising and active areas of research.
Researchers try to find out why* *quantum theory explains the way nature
works—they may never find an answer, but the effort to do so is underway.
Physicists also study the complicated area of overlap between classical physics
and quantum mechanics and work on the applications of quantum mechanics.

Studying the intersection of quantum theory and
classical physics requires developing a theory that can predict how quantum
systems will behave as they get larger or as the number of particles involved
approaches the size of problems described by classical physics. The mathematics
involved is extremely difficult, but physicists continue to advance in their
research. The constantly increasing power of computers should continue to help
scientists with these calculations.

New research in quantum theory also promises new
applications and improvements to known applications. One of the most
potentially powerful applications is quantum computing. In quantum computing,
scientists make use of the behavior of subatomic
particles to perform calculations. Making calculations on the atomic level, a
quantum computer could theoretically investigate all the possible answers to a
query at the same time and make many calculations in parallel. This ability
would make quantum computers thousands or even millions of time faster than
current computers. Advancements in quantum theory also hold promise for the
fields of optics, chemistry, and atomic theory.

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