Quantum theory of the atom

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The simplest atoms to consider are hydrogenic atoms, such as H and He+, because there are no interactions between electrons to complicate the problem. Atom I INTRODUCTION Water MoleculeA water molecule consists of an oxygen atom and two hydrogen atoms, which are attached at an angle of 105°.© Microsoft Corporation. All Rights Reserved. Atom, tiny basic building block of matter. All the material on Earth is composed of various combinations of atoms. Atoms are the smallest particles of a chemical element that still exhibit all the chemical properties unique to that element. A row of 100 million atoms would be only about a centimeter long. See Chemical Element.

Understanding atoms is key to understanding the physical world. More than 100 different elements exist in nature, each with its own unique atomic makeup. The atoms of these elements react with one another and combine in different ways to form a virtually unlimited number of chemical compounds. When two or more atoms combine, they form a molecule. For example, two atoms of the element hydrogen (abbreviated H) combine with one atom of the element oxygen (O) to form a molecule of water (H20).

Since all matter—from its formation in the early universe to present-day biological systems—consists of atoms, understanding their structure and properties plays a vital role in physics, chemistry, and medicine. In fact, knowledge of atoms is essential to the modern scientific understanding of the complex systems that govern the physical and biological worlds. Atoms and the compounds they form play a part in almost all processes that occur on Earth and in space. All organisms rely on a set of chemical compounds and chemical reactions to digest food, transport energy, and reproduce. Stars such as the Sun rely on reactions in atomic nuclei to produce energy. Scientists duplicate these reactions in laboratories on Earth and study them to learn about processes that occur throughout the universe.

Throughout history, people have sought to explain the world in terms of its most basic parts. Ancient Greek philosophers conceived of the idea of the atom, which they defined as the smallest possible piece of a substance. The word atom comes from the Greek word meaning “not divisible.” The ancient Greeks also believed this fundamental particle was indestructible. Scientists have since learned that atoms are not indivisible but made of smaller particles, and atoms of different elements contain different numbers of each type of these smaller particles.


Atoms are made of smaller particles, called electrons, protons, and neutrons. An atom consists of a cloud of electrons surrounding a small, dense nucleus of protons and neutrons. Electrons and protons have a property called electric charge, which affects the way they interact with each other and with other electrically charged particles. Electrons carry a negative electric charge, while protons have a positive electric charge. The negative charge is the opposite of the positive charge, and, like the opposite poles of a magnet, these opposite electric charges attract one another. Conversely, like charges (negative and negative, or positive and positive) repel one another. The attraction between an atom’s electrons and its protons holds the atom together. Normally, an atom is electrically neutral, which means that the negative charge of its electrons is exactly equaled by the positive charge of its protons.

The nucleus contains nearly all of the mass of the atom, but it occupies only a tiny fraction of the space inside the atom. The diameter of a typical nucleus is only about 1 × 10-14 m (4 × 10-13 in), or about 1/100,000 of the diameter of the entire atom. The electron cloud makes up the rest of the atom’s overall size. If an atom were magnified until it was as large as a football stadium, the nucleus would be about the size of a grape.

A Electrons

Electrons are tiny, negatively charged particles that form a cloud around the nucleus of an atom. Each electron carries a single fundamental unit of negative electric charge, or –1.

The electron is one of the lightest particles with a known mass. A droplet of water weighs about a billion, billion, billion times more than an electron. Physicists believe that electrons are one of the fundamental particles of physics, which means they cannot be split into anything smaller. Physicists also believe that electrons do not have any real size, but are instead true points in space—that is, an electron has a radius of zero.

Electrons act differently than everyday objects because electrons can behave as both particles and waves. Actually, all objects have this property, but the wavelike behavior of larger objects, such as sand, marbles, or even people, is too small to measure. In very small particles wave behavior is measurable and important. Electrons travel around the nucleus of an atom, but because they behave like waves, they do not follow a specific path like a planet orbiting the Sun does. Instead they form regions of negative electric charge around the nucleus. These regions are called orbitals, and they correspond to the space in which the electron is most likely to be found. As we will discuss later, orbitals have different sizes and shapes, depending on the energy of the electrons occupying them.

B Protons and Neutrons

Protons carry a positive charge of +1, exactly the opposite electric charge as electrons. The number of protons in the nucleus determines the total quantity of positive charge in the atom. In an electrically neutral atom, the number of the protons and the number of electrons are equal, so that the positive and negative charges balance out to zero. The proton is very small, but it is fairly massive compared to the other particles that make up matter. A proton’s mass is about 1,840 times the mass of an electron.

Neutrons are about the same size as protons but their mass is slightly greater. Without neutrons present, the repulsion among the positively charged protons would cause the nucleus to fly apart. Consider the element helium, which has two protons in its nucleus. If the nucleus did not contain neutrons as well, it would be unstable because of the electrical repulsion between the protons. (The process by which neutrons hold the nucleus together is explained below in the Strong Force section of this article.) A helium nucleus needs either one or two neutrons to be stable. Most atoms are stable and exist for a long period of time, but some atoms are unstable and spontaneously break apart and change, or decay, into other atoms.

Unlike electrons, which are fundamental particles, protons and neutrons are made up of other, smaller particles called quarks. Physicists know of six different quarks. Neutrons and protons are made up of up quarks and down quarks—two of the six different kinds of quarks. The fanciful names of quarks have nothing to do with their properties; the names are simply labels to distinguish one quark from another.

Quarks are unique among all elementary particles in that they have electric charges that are fractions of the fundamental charge. All other particles have electric charges of zero or of whole multiples of the fundamental charge. Up quarks have electric charges of +’. Down quarks have charges of -€. A proton is made up of two up quarks and a down quark, so its electric charge is ’ + ’ - €, for a total charge of +1. A neutron is made up of an up quark and two down quarks, so its electric charge is ’ - € - €, for a net charge of zero. Physicists believe that quarks are true fundamental particles, so they have no internal structure and cannot be split into something smaller.


Atoms have several properties that help distinguish one type of atom from another and determine how atoms change under certain conditions.

A Atomic Number

Each element has a unique number of protons in its atoms. This number is called the atomic number (abbreviated Z). Because atoms are normally electrically neutral, the atomic number also specifies how many electrons an atom will have. The number of electrons, in turn, determines many of the chemical and physical properties of the atom. The lightest atom, hydrogen, has an atomic number equal to one, contains one proton, and (if electrically neutral) one electron. The most massive stable atom found in nature is bismuth (Z = 83). More massive unstable atoms also exist in nature, but they break apart and change into other atoms over time. Scientists have produced even more massive unstable elements in laboratories.

B Mass Number

The total number of protons and neutrons in the nucleus of an atom is the mass number of the atom (abbreviated A). The mass number of an atom is an approximation of the mass of the atom. The electrons contribute very little mass to the atom, so they are not included in the mass number. A stable helium atom can have a mass number equal to three (two protons plus one neutron) or equal to four (two protons plus two neutrons). Bismuth, with 83 protons, requires 126 neutrons for stability, so its mass number is 209 (83 protons plus 126 neutrons).

C Atomic Mass and Weight

Scientists usually measure the mass of an atom in terms of a unit called the atomic mass unit (abbreviated amu). They define an amu as exactly 1/12 the mass of an atom of carbon with six protons and six neutrons. On this scale, the mass of a proton is 1.00728 amu and the mass of a neutron is 1.00866 amu. The mass of an atom measured in amu is nearly equal to its mass number.

Scientists can use a device called a mass spectrometer to measure atomic mass. A mass spectrometer removes one or more electrons from an atom. The electrons are so light that removing them hardly changes the mass of the atom at all. The spectrometer then sends the atom through a magnetic field, a region of space that exerts a force on magnetic or electrically charged particles. Because of the missing electrons, the atom has more protons than electrons and hence a net positive charge. The magnetic field bends the path of the positively charged atom as it moves through the field. The amount of bending depends on the atom’s mass. Lighter atoms will be affected more strongly than heavier atoms. By measuring how much the atom’s path curves, a scientist can determine the atom’s mass.

The atomic mass of an atom, which depends on the number of protons and neutrons present, also relates to the atomic weight of an element. Weight usually refers to the force of gravity on an object, but atomic weight is really just another way to express mass. An element’s atomic weight is given in grams. It represents the mass of one mole (6.02 × 1023 atoms) of that element. Numerically, the atomic weight and the atomic mass of an element are the same, but the first is expressed in grams and the second is in atomic mass units. So, the atomic weight of hydrogen is 1 gram and the atomic mass of hydrogen is 1 amu.

D Isotopes Hydrogen IsotopesThe atomic number of an atom represents the number of protons in its nucleus. This number remains constant for a given element. The number of neutrons may vary, however, creating isotopes that have the same chemical behavior, but different mass. The isotopes of hydrogen are protium (no neutrons), deuterium (one neutron), and tritium (two neutrons). Hydrogen always has one proton in its nucleus. These illustrations are not to scale—the nucleus is approximately 10,000 times smaller than the average orbital radius of the electron, which defines the overall size of the atom.© Microsoft Corporation. All Rights Reserved. Atoms of the same element that differ in mass number are called isotopes. Since all atoms of a given element have the same number of protons in their nucleus, isotopes must have different numbers of neutrons. Helium, for example, has an atomic number of 2 because of the two protons in its nucleus. But helium has two stable isotopes—one with one neutron in the nucleus and a mass number equal to three and another with two neutrons and a mass number equal to four.

Scientists attach the mass number to an element’s name to differentiate between isotopes. Under this convention, helium with a mass number of three is called helium-3, and helium with a mass number of four is called helium-4. Helium in its natural form on Earth is a mixture of these two isotopes. The percentage of each isotope found in nature is called the isotope’s isotopic abundance. The isotopic abundance of helium-3 is very small, only 0.00014 percent, while the abundance of helium-4 is 99.99986 percent. This means that only about one of every 1 million helium atoms is helium-3, and the rest are all helium-4. Bismuth has only one naturally occurring stable isotope, bismuth-209. Bismuth-209’s isotopic abundance is therefore 100 percent. The element with the largest number of stable isotopes found in nature is tin, which has ten stable isotopes.

All elements also have unstable isotopes, which are more susceptible to breaking down, or decaying, than are the other isotopes of an element. When atoms decay, the number of protons in their nucleus changes. Since the number of protons in the nucleus of an atom determines what element that atom belongs to, this decay changes one element into another. Different isotopes decay at different rates. One way to measure the decay rate of an isotope is to find its half-life. An isotope’s half-life is the time that passes until half of a sample of an isotope has decayed.

The various isotopes of a given element have nearly identical chemical properties and many similar physical properties. They differ, of course, in their mass. The mass of a helium-3 atom, for example, is 3.016 amu, while the mass of a helium-4 atom is 4.003 amu.

Usually scientists do not specify the atomic weight of an element in terms of one isotope or another. Instead, they express atomic weight as an average of all of the naturally occurring isotopes of the element, taking into account the isotopic abundance of each. For example, the element copper has two naturally occurring isotopes: copper-63, with a mass of 62.930 amu and an isotopic abundance of 69.2 percent, and copper-65, with a mass of 64.928 amu and an abundance of 30.8 percent. The average mass of naturally occurring copper atoms is equal to the sum of the atomic mass for each isotope multiplied by its isotopic abundance. For copper, it would be (62.930 amu x 0.692) + (64.928 amu x 0.308) = 63.545 amu. The atomic weight of copper is therefore 63.545 g.

E Radioactivity Alpha DecayOne of the ways in which an unstable radioactive atom can decay is by emitting an alpha particle. Alpha particles consist of two protons and two neutrons, and are identical to the nucleus of a helium atom. When an atom’s nucleus emits an alpha particle, the atom transmutes into an atom of a different element.© Microsoft Corporation. All Rights Reserved. About 300 combinations of protons and neutrons in nuclei are stable enough to exist in nature. Scientists can produce another 3,000 nuclei in the laboratory. These nuclei tend to be extremely unstable because they have too many protons or neutrons to stay in one piece for long. Unstable nuclei, whether naturally occurring or created in the laboratory, break apart or change into stable nuclei through a variety of processes known as radioactive decays (see Radioactivity).

Some nuclei with an excess of protons simply eject a proton. A similar process can occur in nuclei with an excess of neutrons. A more common process of decay is for a nucleus to simultaneously eject a cluster of 2 protons and 2 neutrons. This cluster is actually the nucleus of an atom of helium-4, and this decay process is called alpha decay. Before scientists identified the ejected particle as a helium-4 nucleus, they called it an alpha particle. Helium-4 nuclei are still sometimes called alpha particles.

The most common way for a nucleus to get rid of excess protons or neutrons is to convert a proton into a neutron or a neutron into a proton. This process is known as beta decay. The total electric charge before and after the decay must remain the same. Because protons are electrically charged and neutrons are not, the reaction must involve other charged particles. For example, a neutron can decay into a proton, an electron, and another particle called an electron antineutrino. The neutron has no charge, so the charge at the beginning of the reaction is zero. The proton has an electric charge of +1 and the electron has an electric charge of –1. The antineutrino is a tiny particle with no electric charge. The electric charges of the proton and electron cancel each other, leaving a net charge of zero. The electron is the most easily detected product of this type of beta decay, and scientists called these products beta particles before they identified them as electrons.

Beta DecayBeta decay can occur in two ways. As shown on the left, a neutron turns into a proton by emitting an antineutrino and a negatively charged beta particle. As shown on the right, a proton turns into a neutron by emitting a neutrino and a positively charged beta particle. Positive beta particles are called positrons and negative beta particles are called electrons. After the decay, the nucleus of the atom contains either one less or one more proton. Beta decay changes an atom of one element into an atom of a new element.© Microsoft Corporation. All Rights Reserved. Beta decay also results when a proton changes to a neutron. The end result of this decay must have a charge of +1 to balance the charge of the initial proton. The proton changes into a neutron, an anti-electron (also called a positron), and an electron neutrino. A positron is identical to an electron, except the positron has an electric charge of +1. The electron neutrino is a tiny, electrically neutral particle. The difference between the antineutrino in neutron-proton beta decay and the neutrino in proton-neutron beta decay is very subtle—so subtle that scientists have yet to prove that a difference actually exists.

While scientists often create unstable nuclei in the laboratory, several radioactive isotopes also occur naturally. These atoms decay more slowly than most of the radioactive isotopes created in laboratories. If they decayed too rapidly, they wouldn’t stay around long enough for scientists to find them. The heavy radioactive isotopes found on Earth formed in the interiors of stars more than 5 billion years ago. They were part of the cloud of gas and dust that formed our solar system and, as such, are reminders of the origin of Earth and the other planets. In addition, the decay of radioactive material provides much of the energy that heats Earth’s core.

The most common naturally occurring radioactive isotopes are potassium-40 (see Potassium), thorium-232 (see Thorium), and uranium-238 (see Uranium). Atoms of these isotopes last, on average, for billions of years before undergoing alpha or beta decay. The steady decay of these isotopes and other, more stable atoms allows scientists to determine the age of minerals in which these isotopes occur. Scientists begin by estimating the amount of isotope that was present when the mineral formed, then measure how much has decayed. Knowing the rate at which the isotope decays, they can determine how much time has passed. This process, known as radioactive dating (see Dating Methods), allows scientists to measure the age of Earth. The currently accepted value for Earth’s age is about 4.5 billion years. Scientists have also examined rocks from the Moon and other objects in the solar system and have found that they have similar ages.


In physics, a force is a push or pull on an object. There are four fundamental forces, three of which—the electromagnetic force, the strong force, and the weak force—are involved in keeping stable atoms in one piece and determining how unstable atoms will decay. The electromagnetic force keeps electrons attached to their atom. The strong force holds the protons and neutrons together in the nucleus. The weak force governs how atoms decay when they have excess protons or neutrons. The fourth fundamental force, gravity, only becomes apparent with objects much larger than subatomic particles.

A Electromagnetic Force

The most familiar of the forces at work inside the atom is the electromagnetic force. This is the same force that causes people’s hair to stick to a brush or comb when they have a buildup of static electricity. The electromagnetic force causes opposite electric charges to attract each other. Because of this force, the negatively charged electrons in an atom are attracted to the positively charged protons in the atom’s nucleus. This force of attraction binds the electrons to the atom. The electromagnetic force becomes stronger as the distance between charges becomes smaller. This property usually causes oppositely charged particles to come as close to each other as possible. For many years, scientists wondered why electrons didn’t just spiral into the nucleus of an atom, getting as close as possible to the protons. Physicists eventually learned that particles as small as electrons can behave like waves, and this property keeps electrons at set distances from the atom’s nucleus. The wavelike nature of electrons is discussed below in the Quantum Atom section of this article.

The electromagnetic force also causes like charges to repel each other. The negatively charged electrons repel one another and tend to move far apart from each other, but the positively charged nucleus exerts enough electromagnetic force to keep the electrons attached to the atom. Protons in the nucleus also repel one other, but, as described below, the strong force overcomes the electromagnetic force in the nucleus to hold the protons together.

B Strong Force

Protons and neutrons in the nuclei of atoms are held together by the strong force. This force must overcome the electromagnetic force of repulsion the protons in a nucleus exert on one another. The strong force that occurs between protons alone, however, is not enough to hold them together. Other particles that add to the strong force, but not to the electromagnetic force, must be present to make a nucleus stable. The particles that provide this additional force are neutrons. Neutrons add to the strong force of attraction but have no electric charge and so do not increase the electromagnetic repulsion.

B1 Range of the Strong Force

The strong force only operates at very short range—about 2 femtometers (abbreviated fm), or 2 × 10-15 m (8 × 10-14 in). Physicists also use the word fermi (also abbreviated fm) for this unit in honor of Italian-born American physicist Enrico Fermi. The short-range property of the strong force makes it very different from the electromagnetic and gravitational forces. These latter forces become weaker as distance increases, but they continue to affect objects millions of light-years away from each other. Conversely, the strong force has such limited range that not even all protons and neutrons in the same nucleus feel each other’s strong force. Because the diameter of even a small nucleus is about 5 to 6 fm, protons and neutrons on opposite sides of a nucleus only feel the strong force from their nearest neighbors.

The strong force differs from electromagnetic and gravitational forces in another important way—the way it changes with distance. Electromagnetic and gravitational forces of attraction increase as particles move closer to one another, no matter how close the particles get. This increase causes particles to move as close together as possible. The strong force, on the other hand, remains roughly constant as protons and neutrons move closer together than about 2 fm. If the particles are forced much closer together, the attractive nuclear force suddenly turns repulsive. This property causes nuclei to form with the same average spacing—about 2 fm—between the protons and neutrons, no matter how many protons and neutrons there are in the nucleus.

The unique nature of the strong force determines the relative number of protons and neutrons in the nucleus. If a nucleus has too many protons, the strong force cannot overcome the electromagnetic repulsion of the protons. If the nucleus has too many neutrons, the excess strong force tries to crowd the protons and neutrons too close together. Most stable atomic nuclei fall between these extremes. Lighter nuclei, such as carbon-12 and oxygen-16, are made up of 50 percent protons and 50 percent neutrons. More massive nuclei, such as bismuth-209, contain about 40 percent protons and 60 percent neutrons.

B2 Pions

Particle physicists explain the behavior of the strong force by introducing another type of particle, called a pion. Protons and neutrons interact in the nucleus by exchanging pions. Exchanging pions pulls protons and neutrons together. The process is similar to two people having a game of catch with a heavy ball, but with each person attached to the ball by a spring. As one person throws the ball to the other, the spring pulls the thrower toward the ball. If the players exchange the ball rapidly enough, the ball and springs become just a blur to an observer, and it appears as if the two throwers are simply pulled toward one another. This is what occurs in the nuclei of atoms. The protons and neutrons in the nucleus are the people, pions act as the ball, and the strong force acts as the springs holding everything together.

Pions in the nucleus exist only for the briefest instant of time, no more than 1 × 10-23 seconds, but even during their short existence they can provide the attraction that holds the nucleus together. Pions can also exist as independent particles outside of the nucleus of an atom. Scientists have created them by striking high-speed protons against a target. Even though the free pions also live only for a short period of time (about 1 × 10-8 seconds), scientists have been able study their properties.

C Weak Force

The weak force lives up to its name—it is much weaker than the electromagnetic and strong forces. Like the strong force, it only acts over a short distance, about .01 fm. Unlike these other forces, however, the weak force affects all the particles in an atom. The electromagnetic force only affects the electrons and protons, and the strong force only affects the protons and neutrons. When a nucleus has too many protons to hold together or so many neutrons that the strong force squeezes too tightly, the weak force actually changes one type of particle into another. When an atom undergoes one type of decay, for example, the weak force causes a neutron to change into a proton, an electron, and an electron antineutrino. The total electric charge and the total energy of the particles remain the same before and after the change.


Scientists of the early 20th century found they could not explain the behavior of atoms using their current knowledge of matter. They had to develop a new view of matter and energy to accurately describe how atoms behaved. They called this theory quantum theory, or quantum mechanics. Quantum theory describes matter as acting both as a particle and as a wave. In the visible objects encountered in everyday life, the wavelike nature of matter is too small to be apparent. Wavelike nature becomes important, however, in microscopic particles such as electrons. As we have discussed, electrons in atoms behave like waves. They exist as a fuzzy cloud of negative charge around the nucleus, instead of as a particle located at a single point.

A Wave Behavior

In order to understand the quantum model of the atom, we must know some basic facts about waves. Waves are vibrations that repeat regularly over and over again. A familiar example of waves occurs when one end of a rope is tied to a fixed object and someone moves the other end up and down. This action creates waves that travel along the rope. The highest point that the rope reaches is called the crest of the wave. The lowest point is called the trough of the wave. Troughs and crests follow each other in a regular sequence. The distance from one trough to the next trough, or from one crest to the next crest, is called a wavelength. The number of wavelengths that pass a certain point in a given amount of time is called the wave’s frequency.

In physics, the word wave usually means the entire pattern, which may consist of many individual troughs and crests. For example, when the person holding the loose end of the rope moves it up and down very fast, many troughs and crests occupy the rope at once. A physicist would use the word wave to describe the entire set of troughs and crests on the rope.

When two waves meet each other, they merge in a process called interference. Interference creates a new wave pattern. If two waves with the same wavelength and frequency come together, the resulting pattern depends on the relative position of the waves’ crests. If the crests and troughs of the two waves coincide, the waves are said to be in phase. Waves in phase with each other will merge to produce higher crests and lower troughs. Physicists call this type of interference constructive interference.

Sometimes waves with the same wavelength and frequency are out of phase, meaning they meet in such a way that their respective crests and troughs do not coincide. In these cases the waves produce destructive interference. If two identical waves are exactly half a wavelength out of phase, the crests of one wave line up with the troughs of the other. These waves cancel each other out completely, and no wave will appear. If two waves meet that are not exactly in phase and not exactly one-half wavelength out of phase, they will interfere constructively in some places and destructively in others, producing a complicated new wave. See also Wave Motion.

B Electrons as Waves Wave Aspect of ElectronsThis pattern is produced when a narrow beam of electrons passes through a sample of titanium-nickel alloy. The pattern reveals that the electrons move through the sample more like waves than particles. The electrons diffract (bend) around atoms, breaking into many beams and spreading outward. The diffracted beams then interfere with one another, cancelling each other out in some places and reinforcing each other in other places. The bright spots are places where the beams interfered constructively, or reinforced each other. The dark spots are areas in which the beams interfered destructively, or cancelled each other out.Science Source/Photo Researchers, Inc. Electrons behave as both particles and waves in atoms. This characteristic is called wave-particle duality. Wave-particle duality actually affects all particles and collections of particles, including protons, neutrons, and atoms themselves. But in terms of the structure of the atom, the wavelike nature of the electron is the most important.

As waves, electrons have wavelengths and frequencies. The wavelength of an electron depends on the electron’s energy. Since the energy of electrons is kinetic (energy related to motion), an electron’s wavelength depends on how fast it is moving. The more energy an electron has, the shorter its wavelength is. Electron waves can interfere with each other, just as waves along a rope do.

Because of the electron’s wave-particle duality, physicists cannot define an electron’s exact location in an atom. If the electron were just a particle, measuring its location would be relatively simple. As soon as physicists try to measure its location, however, the electron’s wavelike nature becomes apparent, and they cannot pinpoint an exact location. Instead, physicists calculate the probability that the electron is located in a certain place. Adding up all these probabilities, physicists can produce a picture of the electron that resembles a fuzzy cloud around the nucleus. The densest part of this cloud represents the place where the electron is most likely to be located.

C Electron Orbitals and Shells Electron Configuration of NickelElectrons surround the nucleus of an atom in patterns of shells and subshells. In this table showing the electron configuration of a nickel atom, the large numbers (1, 2, 3, 4) indicate shells of electrons (shown as small spheres), the letters (s, p, d) indicate subshells within these shells, and the exponents indicate the number of electrons present in each subshell. Subshells may be further divided into orbitals. Each orbital can contain two electrons, and orbitals are designated in the table by horizontal bars connecting pairs of electrons. The small up and down arrows indicate the direction of each electron’s spin. Electrons that occupy the same orbital always have opposite spins. If all the electrons were stripped away from an atom of nickel (that is, the atom was totally ionized) and electrons were allowed to return one at a time, the electrons would fill up the slots indicated on the chart from left to right, top to bottom. Electrons do not always fill all the subshells of a shell before beginning to fill the next shell. The s subshell of shell 4, for example, actually fills before the d subshell of shell 3 (shown as the lowest row in this chart).© Microsoft Corporation. All Rights Reserved. Physicists call the region of space an electron occupies in an atom the electron’s orbital. Similar orbitals constitute groups called shells. The electrons in the orbitals of a particular shell have similar levels of energy. This energy is in the form of both kinetic energy and potential energy. Lower shells are close to the nucleus and higher shells are farther from the nucleus. Electrons occupying orbitals in higher shells generally have more energy than electrons occupying orbitals in lower shells.

C1 Differences Between Orbitals Atomic Radius Variation in the Periodic TableThe size of the atoms of an element varies in a regular way across the periodic table, increasing down the groups (columns), and decreasing along the periods (rows) from left to right. The size of an atom is largely determined by its electrons. The electrons are arranged in shells surrounding the nucleus of each atom. The top elements of every group have only one or two electron shells. Atoms of elements further down the table have more shells and are therefore larger in size. Moving across a period from left to right, the outermost electron shell fills up but no new shells are added. At the same time, the number of protons in the nucleus of each atom increases. Protons attract electrons. The greater the number of protons present, the stronger the attraction that holds the electrons closer to the nucleus, and the smaller the size of the shells.© Microsoft Corporation. All Rights Reserved. The wavelike nature of electrons sets boundaries for their possible locations and determines what shape their orbital, or cloud of probability, will form. Orbitals differ from each other in size, angular momentum, and magnetic properties. In general, angular momentum is the energy an object contains based on how fast the object is revolving, the object’s mass, and the object’s distance from the axis around which it is revolving. The angular momentum of a whirling ball tied to a string, for example, would be greater if the ball was heavier, the string was longer, or the whirling was faster. In atoms, the angular momentum of an electron orbital depends on the size and shape of the orbital. Orbitals with the same size and shape all have the same angular momentum. Some orbitals, however, can differ in shape but still have the same angular momentum. The magnetic properties of an orbital describe how it would behave in a magnetic field. Magnetic properties also depend on the size and shape of the orbital, as well as on the orbital’s orientation in space.

The orbitals in an atom must occur at certain distances from the nucleus to create a stable atom. At these distances, the orbitals allow the electron wave to complete one or more half-wavelengths (y, 1, 1y, 2, 2y, and so on) as it travels around the nucleus. The electron wave can then double back on itself and constructively interfere with itself in a way that reinforces the wave. Any other distance would cause the electron to interfere with its own wave in an unpredictable and unstable way, creating an unstable atom.

C2 Principal and Secondary Quantum Numbers Quantum Description of ElectronsScientists describe the properties of an electron in an atom with a set of numbers called quantum numbers. Electrons are a type of particle known as a fermion, and according to a rule of physics, no two fermions can be exactly alike. Each electron in an atom therefore has different properties and a different set of quantum numbers. Electrons that share the same principal quantum number form a shell in an atom. This chart shows the first three shells. The two electrons that share the principal quantum number 1 form the first shell. One of these electrons has the quantum numbers 1, s, 0, 1/2, and the other electron has the quantum numbers 1, s, 0, -1/2.© Microsoft Corporation. All Rights Reserved. Physicists call the number of half-wavelengths that an orbital allows the orbital’s principal quantum number (abbreviated n). In general, this number determines the size of the orbital. Larger orbitals allow more half-wavelengths and therefore have higher principal quantum numbers. The orbital that allows one half-wavelength has a principal quantum number of one. Only one orbital allows one half-wavelength. More than one orbital can allow two or more half-wavelengths. These orbitals may have the same principal quantum number, but they differ from each other in their angular momentum and their magnetic properties. The orbitals that allow one wavelength have a principal quantum number of 2 (n = 2), the orbitals that allow one and a half wavelengths have a principal quantum number of 3 (n = 3), and so on. The set of orbitals with the same principal quantum number make up a shell.

Atomic Orbital ShapesAtomic orbitals are mathematical descriptions of where the electrons in an atom (or molecule) are most likely to be found. These descriptions are obtained by solving an equation known as the Schrödinger equation, which expresses our knowledge of the atomic world. As the angular momentum and energy of an electron increases, it tends to reside in differently shaped orbitals. This description has been confirmed by many experiments in chemistry and physics, including an actual picture of a p-orbital made by a scanning tunneling microscope. © Microsoft Corporation. All Rights Reserved. Physicists use a second number to describe the angular momentum of an orbital. This number is called the orbital’s secondary quantum number, or its angular momentum quantum number (abbreviated l). The number of possible values an orbital can have for its angular momentum is one less than the number of half-wavelengths it allows. This means that an orbital with a principal quantum number of n can have n-1 possible values for its secondary quantum number.

Physicists customarily use letters to indicate orbitals with certain secondary quantum numbers. In order of increasing angular momentum, the orbitals with the six lowest secondary quantum numbers are indicated by the letters s, p, d, f, g, and h. The letter s corresponds to the secondary quantum number 0, the letter p corresponds to the secondary quantum number 1, and so on. In general, the angular momentum of an orbital depends on its shape. An s-orbital, with a secondary quantum number of 0, is spherical. A p-orbital, with a secondary quantum number of 1, resembles two hemispheres, facing one another. The possible combinations of principal and secondary quantum numbers for the first five shells are listed below.

C3 Subshells

More than one orbital can allow the same number of half-wavelengths and have the same angular momentum. Physicists call orbitals in a shell that all have the same angular momentum a subshell. They designate a subshell with the subshell’s principal and secondary quantum numbers. For example, the 1s subshell is the group of orbitals in the first shell with an angular momentum described by the letter s. The 2p subshell is the group of orbitals in the second shell with an angular momentum described by the letter p.

Orbitals within a subshell differ from each other in their magnetic properties. The magnetic properties of an orbital depend on its shape and orientation in space. For example, a p-orbital can have three different orientations in space: one situated up and down, one from side to side, and a third from front to back.

C4 Magnetic Quantum Number and Spin

Physicists describe the magnetic properties of an orbital with a third quantum number called the orbital’s magnetic quantum number (abbreviated m). The magnetic quantum number determines how orbitals with the same size and angular momentum are oriented in space. An orbital’s magnetic quantum number can only have whole number values ranging from the value of the orbital’s secondary quantum number down to the negative value of the secondary quantum number. A p-orbital, for example, has a secondary quantum number of 1 (l = 1), so the magnetic quantum number has three possible values: +1, 0, and -1. This means the p-orbital has three possible orientations in space. An s-orbital has a secondary quantum number of 0 (l = 0), so the magnetic quantum number has only one possibility: 0. This orbital is a sphere, and a sphere can only have one orientation in space. For a d-orbital, the secondary quantum number is 2 (l = 2), so the magnetic quantum number has five possible values: -2, -1, 0, +1, and +2. A d-orbital has four possible orientations in space, as well as a fifth orbital that differs in shape from the other four. Together, the principal, secondary, and magnetic quantum numbers specify a particular orbital in an atom.

Electrons are a type of particle known as a fermion. Austrian-American physicist Wolfgang Pauli discovered that no two fermions can have the exact same quantum numbers. This principle is called the Pauli exclusion principle, which states that two or more identical electrons cannot occupy the same orbital in an atom. Scientists know, however, that each orbital can hold two electrons. Electrons have another property, called spin, that differentiates the two electrons in each orbital. An electron’s spin has two possible values: +y (called spin-up) or -y (called spin-down). These two possible values mean that two electrons can occupy the same orbital, as long as their spins are different. Physicists call spin the fourth quantum number of an electron orbital (abbreviated ms). Spin, in addition to the other three quantum numbers, uniquely describes a particular electron’s orbital.

C5 Filling Orbitals

When electrons collect around an atom’s nucleus, they fill up orbitals in a definite pattern. They seek the first available orbital that takes the least amount of energy to occupy. Generally, it takes more energy to occupy orbitals with higher quantum numbers. It takes the same energy to occupy all the orbitals in a subshell. The lowest energy orbital is the one closest to the nucleus. It has a principal quantum number of 1, a secondary quantum number of 0, and a magnetic quantum number of 0. The first two electrons—with opposite spins—occupy this orbital.

If an atom has more than two electrons, the electrons begin filling orbitals in the next subshell with one electron each until all the orbitals in the subshell have one electron. The electrons that are left then go back and fill each orbital in the subshell with a second electron with opposite spin. They follow this order because it takes less energy to add an electron to an empty orbital than to complete a pair of electrons in an orbital. The electrons fill all the subshells in a shell, then go on to the next shell. As the subshells and shells increase, the order of energy for orbitals becomes more complicated. For example, it takes slightly less energy to occupy the s-subshell in the fourth shell than it does to occupy the d-subshell in the third shell. Electrons will therefore fill the orbitals in the 4s subshell before they fill the orbitals in the 3d subshell, even though the 3d subshell is in a lower shell.

D Atomic Properties

The atom’s electron cloud, that is, the arrangement of electrons around an atom, determines most of the atom’s physical and chemical properties. Scientists can therefore predict how atoms will interact with other atoms by studying their electron clouds. The electrons in the outermost shell largely determine the chemical properties of an atom. If this shell is full, meaning all the orbitals in the shell have two electrons, then the atom is stable, and it won’t react readily with other atoms. If the shell is not full, the atom will chemically react with other atoms, exchanging or sharing electrons in order to fill its outer shell. Atoms bond with other atoms to fill their outer shells because it requires less energy to exist in this bonded state. Atoms always seek to exist in the lowest energy state possible.

D1 Valence Shells

Physicists call the outer shell of an atom its valence shell. The valence shell determines the atom’s chemical behavior, or how it reacts with other elements. The fullness of an atom’s valence shell affects how the atom reacts with other atoms. Atoms with valence shells that are completely full are not likely to interact with other atoms. Six gaseous elements—helium, neon, argon, krypton, xenon, and radon—have full valence shells. These six elements are often called the noble gases because they do not normally form compounds with other elements. The noble gases are chemically inert because their atoms are in a state of low energy. A full valence shell, like that of atoms of noble gases, provides the lowest and most stable energy for an atom.

Atoms that do not have a full valence shell try to lower their energy by filling up their valence shell. They can do this in several ways: Two atoms can share electrons to complete the valence shell of both atoms, an atom can shed or take on electrons to create a full valence shell, or a large number of atoms can share a common pool of electrons to complete their valence shells.

D2 Covalent Bonds Covalent BondsIn a covalent bond, the two bonded atoms share electrons. When the atoms involved in the covalent bond are from different elements, one of the atoms will tend to attract the shared electrons more strongly, and the electrons will spend more time near that atom; this is a polar covalent bond. When the atoms connected by a covalent bond are the same, neither atom attracts the shared electrons more strongly than the other; this is a non-polar covalent bond.© Microsoft Corporation. All Rights Reserved. When two atoms share a pair of electrons, they form a covalent bond. When atoms bond covalently, they form molecules. A molecule can be made up of two or more atoms, all joined with covalent bonds. Each atom can share its electrons with one or more other atoms. Some molecules contain chains of thousands of covalently bonded atoms.

Carbon is an important example of an element that readily forms covalent bonds. Carbon has a total of six electrons. Two of the electrons fill up the first orbital, the 1s orbital, which is the only orbital in the first shell. The rest of the electrons partially fill carbon’s valence shell. Two fill up the next orbital, the 2s orbital, which forms the 2s subshell. Carbon’s valence shell still has the 2p subshell, containing three p-orbitals. The two remaining electrons each fill half of the two orbitals in the 2p subshell. The carbon atom thus has two half-full orbitals and one empty orbital in its valence shell. A carbon atom fills its valence shell by sharing electrons with other atoms, creating covalent bonds. The carbon atom can bond with other atoms through any of the three unfilled orbitals in its valence shell. The three available orbitals in carbon’s valence shell enable carbon to bond with other atoms in many different ways. This flexibility allows carbon to form a great variety of molecules, which can have a similarly great variety of geometrical shapes. This diversity of carbon-based molecules is responsible for the importance of carbon in molecules that form the basis for living things (see Organic Chemistry).

D3 Ionic Bonds Ionic Bonding: SaltThe bond (left) between the atoms in ordinary table salt (sodium chloride) is a typical ionic bond. In forming the bond, sodium becomes a cation (a positively charged ion) by “giving up” its valence electron to chlorine, which then becomes an anion (a negatively charged ion). This electron exchange is reflected in the size difference between the atoms before and after bonding. Attracted by electrostatic forces (right), the ions arrange themselves in a crystalline structure in which each is strongly attracted to a set of oppositely charged “nearest neighbors” and, to a lesser extent, all the other oppositely charged ions throughout the entire crystal.© Microsoft Corporation. All Rights Reserved. Atoms can also lose or gain electrons to complete their valence shell. An atom will tend to lose electrons if it has just a few electrons in its valence shell. After losing the electrons, the next lower shell, which is full, becomes its valence shell. An atom will tend to steal electrons away from other atoms if it only needs a few more electrons to complete the shell. Losing or gaining electrons gives an atom a net electric charge because the number of electrons in the atom is no longer the same as the number of protons. Atoms with net electric charge are called ions. Scientists call atoms with a net positive electric charge cations (pronounced CAT-eye-uhns) and atoms with a net negative electric charge anions (pronounced AN-eye-uhns).

The oppositely charged cations and anions are attracted to each other by electromagnetic force and form ionic bonds. When these ions come together, they form crystals. A crystal is a solid material made up of repeating patterns of atoms. Alternating positive and negative ions build up into a solid lattice, or framework. Crystals are also called ionic compounds, or salts.

The element sodium is an example of an atom that has a single electron in its valence shell. It will easily lose this electron and become a cation. Chlorine atoms are just one electron away from completing their valence shell. They will tend to steal an electron away from another atom, forming an anion. When sodium and chlorine atoms come together, the sodium atoms readily give up their outer electron to the chlorine atoms. The oppositely charged ions bond with each other to form the crystal known as sodium chloride, or table salt. See also Chemical Reaction.

D4 Metallic Bonds

Atoms can complete their valence shells in a third way: by bonding together in such a way so that all the atoms in the substance share each other’s outer electrons. This is the way metallic elements bond and fill their valence shells. Metals form crystal lattice structures similar to salts, but the outer electrons in their atoms do not belong to any atom in particular. Instead, the outer electrons belong to all the atoms in the crystal, and they are free to move throughout the crystal. This property makes metals good conductors of electricity.

D5 The Periodic Table Periodic Table of ElementsThe periodic table of elements groups elements in columns and rows by shared chemical properties. Elements appear in sequence according to their atomic number. Clicking on an element in the table provides basic information about the element, including its name, history, electron configuration, and atomic weight. Atomic weights in parentheses indicate the atomic weight of the most stable isotope.© Microsoft Corporation. All Rights Reserved. The organization of the periodic table reflects the way elements fill their orbitals with electrons. Scientists first developed this chart by grouping together elements that behave similarly in order of increasing atomic number. Scientists eventually realized that the chemical and physical behavior of elements was dependant on the electron clouds of the atoms of each element. The periodic table does not have a simple rectangular shape. Each column lists elements that share chemical properties, properties that depend on the arrangement of electrons in the orbitals of atoms. These elements have the same number of electrons in their valence shells. Different numbers of elements have similar valence shells, so the columns of the periodic table differ in height. The noble gases are all located in the rightmost column of the periodic table, labeled column 18 in Encarta’s periodic table. The noble gases all have full valence shells and are extremely stable. The column labeled 11 holds the elements copper, silver, and gold. These elements are metals that have partially filled valence shells and conduct electricity well.

E Electron Energy Levels

Each electron in an atom has a particular energy. This energy depends on the electron’s speed, the presence of other electrons, the electron’s distance from the nucleus, and the positive charge of the nucleus. For atoms with more than one electron, calculating the energy of each electron becomes too complicated to be practical. However, the order and relative energies of electrons follows the order of the electron orbitals, as discussed in the Electron Orbital and Shell section of this article. Physicists call the energy an electron has in a particular orbital the energy state of the electron. For example, the 1s orbital holds the two electrons with the lowest possible energies in an atom. These electrons are in the lowest energy state of any electrons in the atom.

When an atom gains or loses energy, it does so by adding energy to, or removing energy from, its electrons. This change in energy causes the electrons to move from one orbital, or allowed energy state, to another. Under ordinary conditions, all electrons in an atom are in their lowest possible energy states, given that only two electrons can occupy each orbital. Atoms gain energy by absorbing it from light or from a collision with another particle, or they gain it by entering an electric or magnetic field. When an atom absorbs energy, one or more of its electrons moves to a higher, or more energetic, orbital. Usually atoms can only hold energy for a very short amount of time—typically 1 × 10-12 seconds or less. When electrons drop back down to their original energy states, they release their extra energy in the form of a photon (a packet of radiation). Sometimes this radiation is in the form of visible light. The light emitted by a fluorescent lamp is an example of this process.

The outer electrons in an atom are easier to move to higher orbitals than the electrons in lower orbitals. The inner electrons require more energy to move because they are closer to the nucleus and therefore experience a stronger electromagnetic pull toward the nucleus than the outer electrons. When an inner electron absorbs energy and then falls back down, the photon it emits has more energy than the photon an outer electron would emit. The emitted energy relates directly to the wavelength of the photon. Photons with more energy are made of radiation with a shorter wavelength. When inner electrons drop down, they emit high-energy radiation, in the range of an X ray. X rays have much shorter wavelengths than visible light. When outer electrons drop down, they emit light with longer wavelengths, in the range of visible light.


Physicists and chemists first learned about the properties of atoms indirectly, by studying the way that atoms join together in molecules or how atoms and molecules make up solids, liquids, and gases. Modern devices such as electron microscopes, particle traps, spectroscopes, and particle accelerators allow scientists to perform experiments on small groups of atoms and even on individual atoms. Scientists use these experiments to study the properties of atoms more directly.

A Electron Microscopes Atoms Made VisibleIndividual atoms of the element silicon can be seen in this image obtained through the use of a scanning transmission electron microscope. The atoms in each pair are less than a ten-millionth of a millimeter (less than a hundred-millionth of an inch) apart.U.S. Department of Energy, Oak Ridge National Laboratory One of the most direct ways to study an object is to take its photograph. Scientists take photographs of atoms by using an electron microscope. An electron microscope imitates a normal camera, but it uses electrons instead of visible light to form an image. In photography, light reflects off of an object and is recorded on film or some other kind of detector. Taking a photograph of an atom with light is difficult because atoms are so tiny. Light, like all waves, tends to diffract, or bend around objects in its path (see Diffraction). In order to take a sharp photograph of any object, the wavelength of the light that bounces off the object must be much smaller than the size of the object. If the object is about the same size as or smaller than the light’s wavelength, the light will bend around the object and produce a fuzzy image.

Atoms are so small that even the shortest wavelengths of visible light will diffract around them. Therefore, capturing photographic images of atoms requires the use of waves that are shorter than those of visible light. X rays are a type of electromagnetic radiation like visible light, but they have very short wavelengths—much too short to be visible to human eyes. X-ray wavelengths are small enough to prevent the waves from diffracting around atoms. X rays, however, have so much energy that when they bounce off an atom, they knock electrons away from the atom. Scientists, therefore, cannot use X rays to take a picture of an atom without changing the atom. They must use a different method to get an accurate picture.

Electron microscopes provide scientists with an alternate method. Scientists shine electrons, instead of light, on an atom. As discussed in the Electrons as Waves section of this article, electrons have wavelike properties, so they can behave like light waves. The simplest type of electron microscope focuses the electrons reflected off of an object and translates the pattern formed by the reflected electrons into a visible display. Scientists have used this technique to create images of tiny insects and even individual living cells, but they have not been able to use it to make a clear image of objects smaller than about 10 nanometers (abbreviated nm), or 1 × 10-8 m (4 × 10-7 in).

To get to the level of individual atoms, scientists must use a more powerful type of electron microscope called a scanning tunneling microscope (STM). An STM uses a tiny probe, the tip of which can be as small as a single atom, to scan an object. An STM takes advantage of another wavelike property of electrons called tunneling. Tunneling allows electrons emitted from the probe of the microscope to penetrate, or tunnel into, the surface of the object being examined. The rate at which the electrons tunnel from the probe to the surface is related to the distance between the probe and the surface. These moving electrons generate a tiny electric current that the STM measures. The STM constantly adjusts the height of the probe to keep the current constant. By tracking how the height of the probe changes as the probe moves over the surface, scientists can get a detailed map of the surface. The map can be so detailed that individual atoms on the surface are visible.

B Particle Traps

Studying single atoms or small samples of atoms can help scientists understand atomic structure. However, all atoms, even atoms that are part of a solid material, are constantly in motion. This constant motion makes them difficult to examine. To study single atoms, scientists must slow the atoms down and confine them to one place. Scientists can slow and trap atoms using devices called particle traps.

Slowing down atoms is actually the same as cooling them. This is because an atom’s rate of motion is directly related to its temperature. Atoms that are moving very quickly cause a substance to have a high temperature. Atoms moving more slowly create a lower temperature. Scientists therefore build traps that cool atoms down to a very low temperature.

Several different types of particle traps exist. Some traps are designed to slow down ions, while others are designed to slow electrically neutral atoms. Traps for ions often use electric and magnetic fields to influence the movement of the particle, confining it in a small space or slowing it down. Traps for neutral atoms often use lasers, beams of light in which the light waves are uniform and consistent. Light has no mass, but it moves so quickly that it does have momentum. This property allows the light to affect other particles, or “bump” into them. When laser light collides with atoms, the momentum of the light forces the atoms to change speed and direction.

Scientists use trapped and cooled atoms for a variety of experiments, including those that precisely measure the properties of individual atoms and those in which scientists construct extremely accurate atomic clocks. Atomic clocks keep track of time by counting waves of radiation emitted by atoms in traps inside the clock. Because the traps hold the atoms at low temperatures, the mechanisms inside the clock can exercise more control over the atom, reducing the possibility of error. Scientists can also use isolated atoms to measure the force of gravity in an area with extreme accuracy. These measurements are useful in oil exploration, among other things. A deposit of oil or other substance beneath Earth’s surface has a different density than the material surrounding it. The strength of the pull of gravity in an area depends on the density of material in the area, so these changes in density produce changes in the local strength of gravity. Advances in the manipulation of atoms have also raised the possibility of using atoms to etch electronic circuits. This would help make the circuits smaller and thereby allow more circuits to fit in a tinier area.

In 1995 American physicists used particle traps to cool a sample of rubidium atoms to a temperature near absolute zero (-273°C, or –459°F). Absolute zero is the temperature at which all motion stops. When the scientists cooled the rubidium atoms to such a low temperature, the atoms slowed almost to a stop. The scientists knew that the momentum of the atoms, which is related to their speed, was close to zero. At this point, a special rule of quantum physics, called the uncertainty principle, greatly affected the positions of the atoms. This rule states that the momentum and position of a particle both cannot have precise values at the same time. The scientists had a fairly precise value for the atom’s momentum (nearly zero), so the positions of the atoms became very imprecise. The position of each atom could be described as a large, fuzzy cloud of probability. The atoms were very close together in the trap, so the probability clouds of many atoms overlapped one another. It was impossible for the scientists to tell where one atom ended and another began. In effect, the atoms formed one huge particle. This new state of matter is called a Bose-Einstein condensate.

C Spectroscopes Electric Discharge in NitrogenIn this discharge tube filled with nitrogen, an electric current excites the nitrogen atoms. Almost instantaneously, these excited atoms shed their excess energy by emitting light of specific wavelengths. This phenomenon of discrete emission by excited atoms remained unexplained until the advent of quantum mechanics in the early 20th century.Yoav Levy/Phototake NYC Spectroscopy is the study of the radiation, or energy, that atoms, ions, molecules, and atomic nuclei emit. This emitted energy is usually in the form of electromagnetic radiation—vibrating electric and magnetic waves. Electromagnetic waves can have a variety of wavelengths, including those of visible light. X rays, ultraviolet radiation, and infrared radiation are also forms of electromagnetic radiation. Scientists use spectroscopes to measure this emitted radiation.

C1 Characteristic Radiation of Atoms Characteristic SpectraEvery chemical element has a characteristic spectrum, or particular distribution of electromagnetic radiation. Because of these “signature” wavelength patterns, it is possible to identify the constituents of an unknown substance by analyzing its spectrum; this technique is called spectroscopy. Emission spectrums, such as the representative examples shown here, appear as several lines of specific wavelength separated by absolute darkness. The lines are indicative of molecular structure, occurring where atoms make transitions between states of definite energy.© Microsoft Corporation. All Rights Reserved. Atoms emit radiation when their electrons lose energy and drop down to lower orbitals, or energy states, as described in the Electron Energy Levels section above. The difference in energy between the orbitals determines the wavelength of the emitted radiation. This radiation can be in the form of visible light for outer electrons, or it can be radiation of shorter wavelengths, such as X-ray radiation, for inner electrons. Because the energies of the orbitals are strictly defined and differ from element to element, atoms of a particular element can only emit certain wavelengths of radiation. By studying the wavelengths of radiation emitted by a substance, scientists can identify the element or elements comprising the substance. For example, the outer electrons in a sodium atom emit a characteristic yellow light when they return to lower orbitals. This is why street lamps that use sodium vapor have a yellowish glow (See also Sodium-Vapor Lamp).

Chemists often use a procedure called a flame test to identify elements. In a flame test, the chemist burns a sample of the element. The heat excites the outer electrons in the element’s atoms, making the electrons jump to higher energy orbitals. When the electrons drop back down to their original orbitals, they emit light characteristic of that element. This light colors the flame and allows the chemist to identify the element.

Flame TestThe flame test is a simple laboratory procedure that can identify the presence of specific elements in a chemical sample. A small amount of the substance to be tested is placed on the tip of a clean rod, and the rod is inserted in the flame of a Bunsen burner. Different elements give different colors to the flame.© Microsoft Corporation. All Rights Reserved. The inner electrons of atoms also emit radiation that can help scientists identify elements. The energy it takes to boost an inner electron to a higher orbital is directly related to the positive charge of the nucleus and the pull this charge exerts on the electron. When the electron drops back to its original level, it emits the same amount of energy it absorbed, so the emitted energy is also related to the nucleus’s charge. The charge on the nucleus is equal to the atom’s atomic number.

Scientists measure the energy of the emitted radiation by measuring the radiation’s wavelength. The radiation’s energy is directly related to its wavelength, which usually resembles that of an X ray for the inner electrons. By measuring the wavelength of the radiation that an atom’s inner electron emits, scientists can identify the atom by its atomic number. Scientists used this method in the 1910s to identify the atomic number of the elements and to place the elements in their correct order in the periodic table. The method is still used today to identify particularly heavy elements (those with atomic numbers greater than 100) that are produced a few atoms at a time in large accelerators (see Transuranium Elements).

C2 Radiation Released by Radioactivity

Atomic nuclei emit radiation when they undergo radioactive decay, as discussed in the Radioactivity section above. Nuclei usually emit radiation with very short wavelengths (and therefore high energy) when they decay. Often this radiation is in the form of gamma rays, a form of electromagnetic radiation with wavelengths even shorter than X rays. Once again, nuclei of different elements emit radiation of characteristic wavelengths. Scientists can identify nuclei by measuring this radiation. This method is especially useful in neutron activation analysis, a technique scientists use for identifying the presence of tiny amounts of elements. Scientists bombard samples that they wish to identify with neutrons. Some of the neutrons join the nuclei, making them radioactive. When the nuclei decay, they emit radiation that allows the scientists to identify the substance. Environmental scientists use neutron activation analysis in studying air and water pollution. Forensic scientists, who study evidence related to crimes, use this technique to identify gunshot residue and traces of poisons.

D Particle Accelerators Elementary Particle TracksThese tracks were formed by elementary particles in a bubble chamber at the CERN facility located outside of Geneva, Switzerland. By examining these tracks, physicists can determine certain properties of particles that traveled through the bubble chamber. For example, a particle's charge can be determined by noting the type of path the particle followed. The bubble chamber is placed within a magnetic field, which causes a positively charged particle's track to curve in one direction, and a negatively charged particle's track to curve the opposite way; neutral particles, unaffected by the magnetic field, move in a straight line.Patrice Loiez/CERN/Science Source/Photo Researchers, Inc. Particle accelerators are devices that increase the speed of a beam of elementary particles such as protons and electrons. Scientists use the accelerated beam to study collisions between particles. The beam can collide with a target of stationary particles, or it can collide with another accelerated beam of particles moving in the opposite direction. If physicists use the nucleus of an atom as the target, the particles and radiation produced in the collision can help them learn about the nucleus. The faster the particles move, the higher the energy they contain. If collisions occur at very high energy, it is possible to create particles never before detected. In certain circumstances, energy can be converted to matter, resulting in heavier particles after the collision.

Cyclotrons and linear accelerators are two of the most important kinds of particle accelerators. In a cyclotron, a magnetic field holds a beam of charged particles in a circular path. An electric field interacts with the particles’ electric charge to give them a boost of energy and speed each time the beam goes around. In linear accelerators, charged particles move in a straight line. They receive many small boosts of energy from electric fields as they move through the accelerator.

Bombarding nuclei with beams of neutrons forces the nuclei to absorb some of the neutrons and become unstable. The unstable nuclei then decay radioactively. The way atoms decay tells scientists about the original structure of the atom. Scientists can also deduce the size and shape of nuclei from the way particles scatter from nuclei when they collide. Another use of particle accelerators is to create new and exotic isotopes, including atoms of elements with very high atomic numbers that are not found in nature.

At higher energy levels, using particles moving at much higher speeds, scientists can use accelerators to look inside protons and neutrons to examine their internal structure. At these energy levels, accelerators can produce new types of particles. Some of these particles are similar to protons or neutrons but have larger masses and are very unstable. Others have a structure similar to the pion, the particle that is exchanged between the proton and neutron as part of the strong force that binds the nucleus together. By creating new particles and studying their properties, physicists have been able to deduce their common internal structure and to classify them using the theory of quarks. High-energy collisions between one particle and another often produce hundreds of particles. Experimenters have the challenging task of identifying and measuring all of these particles, some of which exist for only the tiniest fraction of a second.


Beginning with Democritus, who lived during the late 5th and early 4th centuries bc, Greek philosophers developed a theory of matter that was not based on experimental evidence, but on their attempts to understand the universe in philosophical terms. According to this theory, all matter was composed of tiny, indivisible particles called atoms (from the Greek word atomos, meaning “indivisible”). If a sample of a pure element was divided into smaller and smaller parts, eventually a point would be reached at which no further cutting would be possible—this was the atom of that element, the smallest possible bit of that element.

According to the ancient Greeks, atoms were all made of the same basic material, but atoms of different elements had different sizes and shapes. The sizes, shapes, and arrangements of a material’s atoms determined the material’s properties. For example, the atoms of a fluid were smooth so that they could easily slide over one another, while the atoms of a solid were rough and jagged so that they could attach to one another. Other than the atoms, matter was empty space. Atoms and empty space were believed to be the ultimate reality.

Although the notion of atoms as tiny bits of elemental matter is consistent with modern atomic theory, the researchers of prior eras did not understand the nature of atoms or their interactions in materials. For centuries scientists did not have the methods or technology to test their theories about the basic structure of matter, so people accepted the ancient Greek view.

A The Birth of the Modern Atomic Theory

The work of British chemist John Dalton at the beginning of the 19th century revealed some of the first clues about the true nature of atoms. Dalton studied how quantities of different elements, such as hydrogen and oxygen, could combine to make other substances, such as water. In his book A New System of Chemical Philosophy (1808), Dalton made two assertions about atoms: (1) atoms of each element are all identical to one another but different from the atoms of all other elements, and (2) atoms of different elements can combine to form more complex substances.

Dalton’s idea that different elements had different atoms was unlike the Greek idea of atoms. The characteristics of Dalton’s atoms determined the chemical and physical properties of a substance, no matter what the substance’s form. For example, carbon atoms can form both hard diamonds and soft graphite. In the Greek theory of atoms, diamond atoms would be very different from graphite atoms. In Dalton’s theory, diamond atoms would be very similar to graphite atoms because both substances are composed of the same chemical element.

While developing his theory of atoms, Dalton observed that two elements can combine in more than one way. For example, modern scientists know that carbon monoxide (CO) and carbon dioxide (CO2) are both compounds of carbon and oxygen. According to Dalton’s experiments, the quantities of an element needed to form different compounds are always whole-number multiples of one another. For example, two times as much oxygen is needed to form a liter of CO2 than is needed to form a liter of CO. Dalton correctly concluded that compounds were created when atoms of pure elements joined together in fixed proportions to form units that scientists today call molecules.

A1 States of Matter

Scientists in the early 19th century struggled in another area of atomic theory. They tried to understand how atoms of a single element could exist in solid, liquid, and gaseous forms. Scientists correctly proposed that atoms in a solid attract each other with enough force to hold the solid together, but they did not understand why the atoms of liquids and gases did not attract each other as strongly. Some scientists theorized that the forces between atoms were attractive at short distances (such as when the atoms were packed very close together to form a solid) and repulsive at larger distances (such as in a gas, where the atoms are on the average relatively far apart).

Scientists had difficulty solving the problem of states of matter because they did not adequately understand the nature of heat. Today scientists recognize that heat is a form of energy, and that different amounts of this energy in a substance lead to different states of matter. In the 19th century, however, people believed that heat was a material substance, called caloric, that could be transferred from one object to another. This explanation of heat was called the caloric theory. Dalton used the caloric theory to propose that each molecule of a gas is surrounded by caloric, which exerts a repulsive force on other molecules. According to Dalton’s theory, as a gas is heated, more caloric is added to the gas, which increases the repulsive force between the molecules. More caloric would also cause the gas to exert a greater pressure on the walls of its container, in accordance with scientists’ experiments.

This early explanation of heat and states of matter broke down when experiments in the middle of the 19th century showed that heat could change into energy of motion. The laws of physics state that the amount of energy in a system cannot increase, so scientists had to accept that heat must be energy, not a substance. This revelation required a new theory of how atoms in different states of matter behave.

A2 Behavior of Gases

In the early 19th century Italian chemist Amedeo Avogadro made an important advance in the understanding of how atoms and molecules in a gas behave. Avogadro began his work from a theory developed by Dalton. Dalton’s theory proposed that a gaseous compound, formed by combining equal numbers of atoms of two elements, should have the same number of molecules as the atoms in one of the original elements. For example, ten atoms of the element hydrogen (H) combine with ten atoms of chlorine (Cl) to form ten gaseous hydrogen chloride (HCl) molecules.

In 1811 Avogadro developed a law of physics that seemed to contradict Dalton’s theory. Avogadro’s law states that equal volumes of different gases contain the same number of particles (atoms or molecules) if both gases are at the same temperature and pressure. In Dalton’s experiment, the volume of the original vessels containing the hydrogen or chlorine gases was the same as the volume of the vessel containing the hydrogen chloride gas. The pressures of the original hydrogen and chlorine gases were equal, but the pressure of the hydrochloric gas was twice as great as either of the original gases. According to Avogadro’s law, this doubled pressure would mean that there were twice as many hydrogen chloride gas particles than there had been chlorine particles prior to their combination.

To reconcile the results of Dalton’s experiment with his new rule, Avogadro was forced to conclude that the original vessels of hydrogen or chlorine contained only half as many particles as Dalton had thought. Dalton, however, knew the total weight of each gas in the vessels, as well as the weight of an individual atom of each gas, so he knew the total number of atoms of each gas that was present in the vessels. Avogadro reconciled the fact that there were twice as many atoms as there were particles in the vessels by proposing that gases such as hydrogen and chlorine are really made up of molecules of hydrogen and chlorine, with two atoms in each molecule. Today scientists write the chemical symbols for hydrogen and chlorine as H2 and Cl2, respectively, indicating that there are two atoms in each molecule. One molecule of hydrogen and one molecule of chlorine combine to form two molecules of hydrogen chlorine (H2 + Cl2 → 2HCl). The sample of hydrogen chloride contains twice the number of particles as either the hydrogen or chlorine because two molecules of hydrogen chloride form when a molecule of hydrogen combines with a molecule of chlorine.

B Electrical Forces in Atoms Evolution of the Model of the AtomAs scientists learned about the structure of the atom through experiments, they modified their models of the atom to fit their data. British physicist Joseph John Thomson understood that atoms contain positive and negative charges, while British physicist Ernest Rutherford discovered that an atom’s positive charge is concentrated in a nucleus. Danish physicist Neils Bohr proposed that electrons orbit only at set distances from the nucleus, and Austrian physicist Erwin Shrödinger discovered that electrons in an atom actually behave more like waves than like particles.© Microsoft Corporation. All Rights Reserved. The work of Dalton and Avogadro led to a consistent view of the quantities of different gases that could be combined to form compounds, but scientists still did not understand the nature of the forces that attracted the atoms to one another in compounds and molecules. Scientists suspected that electrical forces might have something to do with that attraction, but they found it difficult to understand how electrical forces could allow two identical, neutral hydrogen atoms to attract one another to form a hydrogen molecule.

In the 1830s, British physicist Michael Faraday took the first significant step toward appreciating the importance of electrical forces in compounds. Faraday placed two electrodes connected to opposite terminals of a battery into a solution of water containing a dissolved compound. As the electric current flowed through the solution, Faraday observed that one of the elements that comprised the dissolved compound became deposited on one electrode while the other element became deposited on the other electrode. The electric current provided by the electrodes undid the coupling of atoms in the compound. Faraday also observed that the quantity of each element deposited on an electrode was directly proportional to the total quantity of current that flowed through the solution—the stronger the current, the more material became deposited on the electrode. This discovery made it clear that electrical forces must be in some way responsible for the joining of atoms in compounds.

Despite these significant discoveries, most scientists did not immediately accept that atoms as described by Dalton, Faraday, and Avogadro were responsible for the chemical and physical behavior of substances. Before the end of the 19th century, many scientists believed that all chemical and physical properties could be determined by the rules of heat, an understanding of atoms closer to that of the Greek philosophers. The development of the science of thermodynamics (the scientific study of heat) and the recognition that heat was a form of energy eliminated the role of caloric in atomic theory and made atomic theory more acceptable. The new theory of heat, called the kinetic theory, said that the atoms or molecules of a substance move faster, or gain kinetic energy, as heat energy is added to the substance. Nevertheless, a small but powerful group of scientists still did not accept the existence of atoms—they regarded atoms as convenient mathematical devices that explained the chemistry of compounds, not as real entities.

In 1905 French chemist Jean-Baptiste Perrin performed the final experiments that helped prove the atomic theory of matter. Perrin observed the irregular wiggling of pollen grains suspended in a liquid (a phenomenon called Brownian motion) and correctly explained that the wiggling was the result of atoms of the fluid colliding with the pollen grains. This experiment showed that the idea that materials were composed of real atoms in thermal motion was in fact correct.

As scientists began to accept atomic theory, researchers turned their efforts to understanding the electrical properties of the atom. Several scientists, most notably British scientist Sir William Crookes, studied the effects of sending electric current through a gas. The scientists placed a very small amount of gas in a sealed glass tube. The tube had electrodes at either end. When an electric current was applied to the gas, a stream of electrically charged particles flowed from one of the electrodes. This electrode was called the cathode, and the particles were called cathode rays.

At first scientists believed that the rays were composed of charged atoms or molecules, but experiments showed that the cathode rays could penetrate thin sheets of material, which would not be possible for a particle as large as an atom or a molecule. British physicist Sir Joseph John Thomson measured the velocity of the cathode rays and showed that they were much too fast to be atoms or molecules. No known force could accelerate a particle as heavy as an atom or a molecule to such a high speed. Thomson also measured the ratio of the charge of a cathode ray to the mass of the cathode ray. The value he measured was about 1,000 times larger than any previous measurement associated with charged atoms or molecules, indicating that within cathode rays particularly tiny masses carried relatively large amounts of charge. Thomson studied different gases and always found the same value for the charge-to-mass ratio. He concluded that he was observing a new type of particle, which carried a negative electric charge but was about a thousand times less massive than the lightest known atom. He also concluded that these particles were constituents of all atoms. Today scientists know these particles as electrons, and Thomson is credited with their discovery.

C Rutherford’s Nuclear Atom Rutherford ExperimentRutherford studied the structure of the atom by firing a beam of alpha particles at gold atoms. A few alpha particles bounced directly back, indicating that they had struck something massive. Rutherford proposed that most of the mass of atoms was concentrated in their centers. This concentration of mass is now known as the nucleus. Scientists realized that if all atoms contain electrons but are electrically neutral, atoms must also contain an equal quantity of positive charge to balance the electrons’ negative charge. Furthermore, if electrons are indeed much less massive than even the lightest atom, then this positive charge must account for most of the mass of the atom. Thomson proposed a model by which this phenomenon could occur: He suggested that the atom was a sphere of positive charge into which the negative electrons were imbedded, like raisins in a loaf of raisin bread. In 1911 British scientist Ernest Rutherford set out to test Thomson’s proposal by firing a beam of charged particles at atoms.

Rutherford chose alpha particles for his beam. Alpha particles are heavy particles with twice the positive charge of a proton. Alpha particles are now known to be the nuclei of helium atoms, which contain two protons and two neutrons. If Thomson’s model of the atom was correct, Rutherford theorized that the electric charge and the mass of the atoms would be too spread out to significantly deflect the alpha particles. Rutherford was quite surprised to observe something very different. Most of the alpha particles did indeed change their paths by a small angle, and occasionally an alpha particle bounced back in the opposite direction. The alpha particles that bounced back must have struck something at least as heavy as themselves. This led Rutherford to propose a very different model for the atom. Instead of supposing that the positive charge and mass were spread throughout the volume of the atom, he theorized that it was concentrated in the center of the atom. Rutherford called this concentrated region of electric charge the nucleus of the atom.

In the span of 100 years, from Dalton to Rutherford, the basic ideas of atomic structure evolved from very primitive concepts of how atoms combined with one another to an understanding of the constituents of atoms—a positively charged nucleus surrounded by negatively charged electrons. The interactions between the nucleus and the electrons still required study. It was natural for physicists to model the atom, in which tiny electrons orbit a much more massive nucleus, after a familiar structure such as the solar system, in which planets orbit around a much more massive Sun. Rutherford’s model of the atom did indeed resemble a tiny solar system. The only difference between early models of the nuclear atom and the solar system was that atoms were held together by electromagnetic force, while gravitational force holds together the solar system.

D The Bohr Model

Danish physicist Niels Bohr used new knowledge about the radiation emitted from atoms to develop a model of the atom significantly different from Rutherford’s model. Scientists of the 19th century discovered that when an electrical discharge passes through a small quantity of a gas in a glass tube, the atoms in the gas emit light. This radiation occurs only at certain discrete wavelengths, and different elements and compounds emit different wavelengths. Bohr, working in Rutherford’s laboratory, set out to understand the emission of radiation at these wavelengths based on the nuclear model of the atom.

Using Rutherford’s model of the atom as a miniature solar system, Bohr developed a theory by which he could predict the same wavelengths scientists had measured radiating from atoms with a single electron. However, when conceiving this theory, Bohr was forced to make some startling conclusions. He concluded that because atoms emit light only at discrete wavelengths, electrons could only orbit at certain designated radii, and light could be emitted only when an electron jumped from one of these designated orbits to another. Both of these conclusions were in disagreement with classical physics, which imposed no strict rules on the size of orbits. To make his theory work, Bohr had to propose special rules that violated the rules of classical physics. He concluded that, on the atomic scale, certain preferred states of motion were especially stable. In these states of motion an orbiting electron (contrary to the laws of electromagnetism) would not radiate energy.

At the same time that Bohr and Rutherford were developing the nuclear model of the atom, other experiments indicated similar failures of classical physics. These experiments included the emission of radiation from hot, glowing objects (called thermal radiation) and the release of electrons from metal surfaces illuminated with ultraviolet light (the photoelectric effect). Classical physics could not account for these observations, and scientists began to realize that they needed to take a new approach. They called this new approach quantum mechanics (see Quantum Theory), and they developed a mathematical basis for it in the 1920s. The laws of classical physics work perfectly well on the scale of everyday objects, but on the tiny atomic scale, the laws of quantum mechanics apply.

E Quantum Theory of Atoms

The quantum mechanical view of atomic structure maintains some of Rutherford and Bohr’s ideas. The nucleus is still at the center of the atom and provides the electrical attraction that binds the electrons to the atom. Contrary to Bohr’s theory, however, the electrons do not circulate in definite planet-like orbits. The quantum-mechanical approach acknowledges the wavelike character of electrons and provides the framework for viewing the electrons as fuzzy clouds of negative charge. Electrons still have assigned states of motion, but these states of motion do not correspond to fixed orbits. Instead, they tell us something about the geometry of the electron cloud—its size and shape and whether it is spherical or bunched in lobes like a figure eight. Physicists called these states of motion orbitals. Quantum mechanics also provides the mathematical basis for understanding how atoms that join together in molecules share electrons. Nearly 100 years after Faraday’s pioneering experiments, the quantum theory confirmed that it is indeed electrical forces that are responsible for the structure of molecules.

Two of the rules of quantum theory that are most important to explaining the atom are the idea of wave-particle duality and the exclusion principle. French physicist Louis de Broglie first suggested that particles could be described as waves in 1924. In the same decade, Austrian physicist Erwin Schrödinger and German physicist Werner Heisenberg expanded de Broglie’s ideas into formal, mathematical descriptions of quantum mechanics. The exclusion principle was developed by Austrian-born American physicist Wolfgang Pauli in 1925. The Pauli exclusion principle states that no two electrons in an atom can have exactly the same characteristics.

The combination of wave-particle duality and the Pauli exclusion principle sets up the rules for filling electron orbitals in atoms. The way electrons fill up orbitals determines the number of electrons that end up in the atom’s valence shell. This in turn determines an atom’s chemical and physical properties, such as how it reacts with other atoms and how well it conducts electricity. These rules explain why atoms with similar numbers of electrons can have very different properties, and why chemical properties reappear again and again in a regular pattern among the elements.