Electrons and Atoms

Type of physical science: Atomic physics

Field of study: Nonrelativistic quantum mechanics

Electrons are the smallest elementary particles to possess a rest mass. They also carry a negative electrical charge. Although they account for less than one two-thousandth of the mass of normal atoms, they occupy almost all of their volume. The behavior of electrons in atoms determines their chemical and electrical properties.

Overview

All ordinary matter is composed of atoms, which are in turn composed of only three kinds of elementary particles: protons, neutrons, and electrons. While protons and neutrons have almost the same mass, electrons are much smaller, with a rest mass about 1/1,840 of that of a proton or neutron. Electrons and protons carry electrical charges of equal size but opposite sign, with the electrons having negative charge and the protons having positive charge. The protons and neutrons are held together in the tiny nucleus of the atom by very strong, but very short-range nuclear forces. The electrons are bound to the nucleus by the much weaker, but long-range electrical forces. The sharing or exchange of electrons by atoms is responsible for their chemical and electrical properties.

Because atoms and the particles that compose them are so small, special units have been defined to express their mass, size, and charge. The atomic mass unit is defined to be one-twelfth of the mass of a carbon atom, which contains six protons and six neutrons in its nucleus. There are 600 billion trillion atomic mass units in 1 gram. The angstrom is 1/100,000 of a meter. Atoms range in diameter from 1 to a few angstroms. The elementary charge is the charge on a single proton, usually denoted by the symbol e. The charge of the electron is then written as -e. An electric current in a circuit of 1 ampere involves the flow of about 6.241509 quintillion elementary charges past any point in that circuit per second. The energies associated with electron motion in atoms are conveniently measured in electronvolts. The energy released as light or heat by each electron passing through the filament of a flashlight powered by a 6-volt battery is 6 electronvolts.

Electrons can be effectively studied by themselves only in a vacuum, for they will otherwise become attached to many different types of gas molecules. Free electrons can be produced by placing a metallic point in a strong electric field, a process known as field emission; by heating a metal surface, called thermionic emission; and by the illumination of a metal source by light of an appropriate wavelength, known as photoemission or the photoelectric effect.

Electrons are also produced by a variety of nuclear processes. Electrons produced in radioactive decay are traditionally referred to as β particles.

Electrons are so small that their behavior is generally not describable by classical mechanics. Instead, quantum mechanics must be used. For electrons moving at speeds smaller than the speed of light, nonrelativist quantum mechanics may be used. In this case, the behavior of electrons is described by a wave function, a solution of the Schrödinger wave equation, which describes the probability of an electron being found at different points in space. For electrons moving at higher speeds, the Dirac equation of relativistic quantum mechanics must be employed.

The interaction of electrons and light reveals not only the quantum mechanical nature of the electrons but also the quantized nature of light energy. In its interaction with electrons, light of a given frequency behaves as if composed of many packets or quanta of energy. These packets are usually called photons. Each photon carries an amount of light energy proportional to the frequency of the light, with the ratio of energy to frequency known as Planck's constant. One of the most characteristically quantum mechanical processes involving electrons and photons is Compton scattering, in effect a collision between an electron and a photon, in which the electron gains or loses energy, and the photon undergoes a corresponding change in frequency.

In addition to mass and charge, electrons have a magnetic moment and appear to carry angular momentum, behaving in some respects as if they are spinning balls with charged surfaces. In this model, the motion of the surface charge consists of an electric current and creates a magnetic field in the manner of an electromagnet. Although physicists speak of electron spin, the model of the electron as a spinning sphere must not be taken too seriously. Unlike the classical case, only one value of angular momentum is allowed, equal to one half of Planck's constant, divided by 2pi. In an external magnetic field, electrons are found to align themselves with their magnetic moments either parallel or antiparallel to the field. Further, there are both theoretical and experimental reasons to believe that electrons are best described as point particles that have no detectable radius.

Although electrons are particles of matter, they display some wave characteristics. The wavelength associated with an electron is inversely proportional to its speed. The electron microscope takes advantage of this wavelength, which can easily be made much smaller than that of visible light, to magnify images of objects too small to be seen with an optical microscope. The wavelike character of electrons is also in evidence when a beam of electrons is scattered by a crystal, leaving a characteristic diffraction pattern.

The diameter of the atomic nucleus is about 1/100,000 of an angstrom. Therefore, almost all the volume of the atom is empty space, through which the electrons move in their motion around the nucleus. The patterns of electron motion allowed by quantum mechanics can be grouped within energy levels, or shells, traditionally described by the letters K, L, M, N, and so on, each of which is composed of a set number of sublevels or orbitals and can be occupied by no more than two electrons, in keeping with the Pauli exclusion principle. The interactions of atoms with light and electrons is governed by the transitions between energy levels that are possible in the atom.

Atoms absorb light at frequencies such that the energy of the absorbed photons corresponds to the energy required to promote an electron to a higher energy level. The absorption occurs at discrete frequencies only, until a limit is reached corresponding to the ionization potential of the atom, above which light of any frequency can be absorbed. The ionization potential is the least amount of energy that must be provided to an atom to allow one of the electrons to escape completely from the atom. Atoms that have been excited by the absorption of light or some other process can relax to their ground state through the emission of light of an appropriate frequency. Far less frequent than the absorption of whole photons is the Raman effect, in which an atom undergoes a transition from one discrete energy level to another, but only a portion of the photon energy is absorbed.

Atoms also become excited through collisions with other atoms or electrons. Passing a stream of electrons through a gas at low pressure results in the emission of light as in a fluorescent light or neon sign. X-rays are produced when an inner-shell electron is removed from an atom and the vacancy is subsequently filled by an outer-shell electron. Sometimes the production of an inner-shell vacancy is followed by an Auger effect, in which the energy released by an electron filling the inner-shell vacancy is transferred directly to another electron, which is then ejected from the atom. The emission of X-rays tends to be favored in the heavier atoms, and the Auger effect in lighter ones.

From the standpoint of particle physics, electrons belong to the group of particles called leptons, which experience the weak nuclear force but not the strong nuclear force. This group includes three charged particles, three uncharged particles, and their six antiparticles. The charged particles are the electron, the muon, and the tau, all of which have the charge -e and a rest mass. The antiparticle of the electron is often called the positron. The uncharged particles are the electron neutrino, the muon neutrino, and the τ neutrino. Neutrinos have no rest mass and travel at the speed of light, but unlike light do not interact with particles by the electromagnetic force. Since neutrinos interact with other matter only by the weak force, they are very difficult to detect.

A number of nuclear processes involve electrons. According to the shell model of nuclear structure, protons and neutrons within the nucleus occupy separate sets of energy levels.

In an isotope with many more neutrons than protons, a lower-energy nuclear state can be reached when a neutron decays to form a proton, an electron, and an electron antineutrino. This process is called β decay, since an electron, or β particle, is produced. An isotope with too small a ratio of neutrons to protons can attain a lower-energy state by the reverse process, in which a proton captures one of the orbital electrons and a neutrino is released. This process is called Kcapture, since it is usually a K shell electron that is involved. In internal conversion, the energy of a γ-ray photon produced by a nuclear process is transferred to an orbital electron, which then leaves the atom at high speed.

Positrons are produced in a number of radioactive decays and in cosmic-ray events.

Positron emission has the same overall effect on a nucleus as K-capture, in that a proton is converted into a neutron. If allowed to approach each other, a positron and an electron will eventually annihilate each other with the conversion of their rest mass into energy in the form of γ rays, according to the Albert Einstein formula E = mc². In turn, γ rays of sufficient energy can give rise to an electron-positron pair when they collide with a nucleus. Positrons, however formed, have a relatively short life expectancy in the vicinity of ordinary matter, resulting from the abundance of ordinary electrons. Prior to their mutual annihilation, however, an electron and a positron can form a short-lived atom called positronium, which resembles hydrogen in its characteristics but with much smaller mass.

Applications

The relative ease with which electrons can be produced and manipulated in a vacuum has led to the development of numerous useful devices. In the cathode-ray tube, used in oscilloscopes and television sets, a thin beam of electrons is formed and given sufficient kinetic energy to cause the emission of light when they strike a suitably coated screen. The trajectory of the beam is controlled by the voltages applied to pairs of parallel plates through which the beam passes. In the vacuum tubes that formed the basis of electronic technology prior to the introduction of semiconductor devices, electrons are released by thermionic emission at the heated cathode and attracted to the positively charged anode, the current being regulated by the voltage applied to one or more metallic grids placed between the two electrodes. In the transistors, semiconductor diodes and integrated circuits that have replaced vacuum tubes, the characteristics of electron flow through regions of semiconductors with different chemical compositions are exploited to achieve the same effects.

In an X-ray tube, a beam of electrons is accelerated to an energy sufficient to knock core electrons out of the atoms in a metal target. Outer-shell electrons emit electromagnetic radiation in the X-ray region as they fill the vacant energy level. In the Geiger-Muller tube, used to detect ionizing radiation, a large electric field is established across the region of gas at low pressure. When an electron is ejected from a gas atom by incoming radiation, it is accelerated until it has enough energy to ionize other gas molecules, which in turn ionize others until a substantial current is flowing. In photomultiplier tubes, used to detect low levels of light or even individual photons, an electron ejected from a metal plate is accelerated so that it strikes a second metal plate with sufficient impact to eject additional electrons that are, in turn, accelerated toward a third plate, and so on, until a significant current is produced.

Electron accelerators are used to produce beams of electrons traveling with velocities very close to the speed of light and with energies high enough to give rise to the creation of additional particles in collisions. The principal types of large electron accelerators are the synchrotron and the linear accelerator. In synchrotrons, the particles being accelerated pass repeatedly through a series of accelerating voltages, the particle path being bent into a rough circle through the action of magnets. Since all charged particles emit electromagnetic radiation when they are deflected from straight line motion, and since the amount of energy loss is greater for low mass particles, only linear electron accelerators are effective in producing electrons with energies in the billions of electronvolts. The radiation in electron synchrotrons is, however, a useful by-product, in that these machines can be adapted to produce intense beams of ultraviolet light or X-rays with well-defined wavelengths for research purposes.

Since electrons are charged particles of very low mass, they interact strongly with matter in the solid or liquid state and do not penetrate very deeply. This property provides the basis for a number of experimental techniques used to study the surface properties of solids and the structure of absorbed layers. Lower energy electron diffraction is used to determine the systematic arrangement of atoms at the surface of a crystal. In photoelectron spectroscopy, X-rays or ultraviolet light is used to eject electrons from the surface layers of a material. In Auger spectroscopy, electron bombardment is used to eject core electrons from a sample, and the Auger electrons produced as the core levels are refilled are analyzed. While photoelectron spectroscopy and Auger spectroscopy provide a direct measurement of inner-shell energy levels, the chemical bonding in which the outer-shell electrons of an atom are involved is reflected in small shifts in the inner-shell energy levels, which are measured by these electron spectroscopies.

Context

The hypothesis that all matter is composed of atoms dates back to the ancient Greeks, notably the philosophers Leucippus and Democritus, who lived in the fifth century B.C. The scientific study of atoms and their properties dates only to the seventeenth century. Robert Boyle, an English physicist of that period, was perhaps the first individual to employ the atomic hypothesis in the interpretation of experiments. By the late nineteenth century, belief in atoms was so strongly established in some quarters that it was difficult to accept the fact that atoms themselves could be broken into smaller particles.

The discovery of the electron is generally attributed to the English physicist, Sir Joseph John Thomson, who was the first to demonstrate that the mysterious cathode rays that appeared to emanate from the negative electrode in primitive vacuum tubes were in fact material particles.

Thomson also devised a means to determine the ratio of the electron's charge to its mass by comparing the effects of imposed electric and magnetic fields on the path of a beam of electrons in a cathode-ray tube. The American physicist Robert Andrews Millikan was the first to measure the charge on the electron in the famous Millikan oil drop experiment, in which he measured the electrical force necessary to balance the weight of microscopic droplets of oil, each of which possessed a very small number of extra electrons, produced by friction when the drop emerged from a tiny nozzle.

The discovery of the electron, along with the discovery of the nucleus in 1911 by the New Zealand physicist Ernest Rutherford, then working in Canada, presented a serious problem for theoretical physicists, as no arrangement of charged particles obeying classical mechanics was known to be stable. The resolution of this problem was first suggested by Danish physicist Niels Bohr in 1913, who proposed that the electron orbits in an atom had to obey an additional quantum condition involving Planck's constant. Bohr's proposal worked perfectly for the hydrogen atom, which has only one electron, providing an explanation for the spectrum of the atom in complete agreement with experiment. Nevertheless, Bohr's proposal did not work for many electron atoms. A full solution of the problem came with the discovery of the Schrodinger equation by the Austrian physicist Erwin Schrodinger in 1925 and the equivalent theory by the German physicist, Werner Heisenberg at about the same time, followed within a few years by the discovery of a wave equation compatible with the theory of relativity by the British physicist Paul Adrien Maurice Dirac.

Since 1925, the equations of quantum mechanics have been used successfully to explain the spectra of atoms and molecules, the nature of chemical bonding, and the structure of solids. This has particularly been the case since the development of digital computers in the years following World War II, and accurate numerical solutions of the Schrodinger equation become possible for many systems. Quantum mechanics appears to provide a complete explanation of the electric properties of solids, including the behavior of semiconductors and superconductors. The scattering of electrons by atoms, molecules, and solids is also described accurately by the quantum theory, which is now used extensively in the interpretation of all experiments conducted with electron beams.

Further developments in the study of electrons continued throughout the remainder of the twentieth and into the twenty-first centuries. For example, in 2023, three researchers (Pierre Agostini, Ferenc Krausz and Anne L’Huillier) won the Nobel Prize in physics for developing a new technique, which used short pulses of light, to record electron movement and energy changes. This breakthrough gave researchers new tools to study electrons in greater detail despite the extremely high speed (43 miles per second) at which electrons move.

Principal terms

ATOM: the smallest unit of a chemical element, composed of a tiny but massive central nucleus surrounded by a characteristic number of electrons

CATHODE-RAY TUBE: an evacuated tube in which an electron beam is formed and accelerated to a speed sufficient to cause the emission of light when the beam strikes a phosphorescent screen

ELECTRON: a negatively charged subatomic particle, with rest mass about 1/1,840 of that of a proton

IONIZATION POTENTIAL: the minimum energy, usually expressed in electronvolts, required to remove an electron from an atom and to produce a positively charged atom (cation)

NUCLEUS: the very small and dense central portion of the atom, composed of protons and neutrons bound together by strong but short-range nuclear forces

PAULI EXCLUSION PRINCIPLE: a principle of quantum mechanics that prevents more than two electrons from occupying the same atomic orbital

SPECTRUM: the set of characteristic wavelengths of light emitted or absorbed by an atom

SPIN: a quantum mechanical property of electrons, protons, and other subatomic particles, which is sometimes described by analogy to the rotation of the particle around its axis

Bibliography

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“The Nobel Prize in Physics 2023.” The Nobel Prize, Nobel Prize Outreach AB, 2024, www.nobelprize.org/prizes/physics/2023/popular-information/. Accessed 16 Oct. 2024.