Atom - the smallest amount of matter which retains chemical properties of a given chemical element.

Each atom is built from a nucleus containing >99.9% mass of the whole atom, and electrons orbiting around it. Nucleus contains protons which have positive electric charge, and neutrons without a charge. Electrons are negatively charged, so that the electric charge can be precisely and completely balanced for the whole atom. The number of protons identifies the element and is known as the atomic number.¹⁾

Atom of helium: blue - spherical orbitals of electrons (size around 100 pm), red - protons, grey - neutrons (size of nucleus is around 0.001 pm) ²⁾³⁾

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All atoms of the same chemical element possess the same chemical properties, which are dictated mostly by the configuration of electrons. There are around 120 known elements, with only around first 100 forming stable nuclides or isotopes.

Atoms of different elements can combine by chemical bonding in order to form molecules of various chemical substances.

Depending on the energy present in the system, the atoms can assemble in several ways, known as states of matter: solid, liquid, gas or plasma (nuclei and electrons separated by high energy). There are also other states occurring at extreme energies or conditions.

The atoms are too small to be visualised by ordinary light. Very high resolution techniques such as electron microscopy are required, using electrons as the image-probing medium. The images of gold (Au) atoms shown below were created using such techniques.

An atom is composed of a relatively very small nucleus at its centre, and electrons orbiting around it.

Because of the range of dimensions involved it is not possible to represent an atom on a two-dimensional picture to scale, because the size of the nucleus is around 100 000 times smaller than the outer radius of the whole atom. For an element with atomic mass A, the radius r_N of its nucleus can be roughly approximated as:⁷⁾ $r_N = 1.2 · A^{1/3}$ (fm).

The electrons do not move on fixed orbits but on three-dimensional orbitals, which represent spatial probability of distribution. The location of a single electron cannot be known precisely because of the uncertainty principle.

From a classical physics viewpoint, a negative electron (point charge) orbiting around positive nucleus would be centripetally accelerated and thus energy should be radiated out. If the law of energy conservation is to be fulfilled then the electron would become less and less energetic and it would eventually spiral towards the nucleus. Therefore classical physics is insufficient to explain the atomic and sub-atomic phenomena - instead the quantum physics has to be employed to describe many of the effects, which are still not completely understood despite tremendous amount of international research devoted to this subject.

More than 99.9% of the mass of each atom is contained in the nucleus, which is composed of protons and neutrons. All the electric positive charge of an atom resides in the nucleus, and the electric charge is compensated out by the negative charges of the orbiting electrons, so that an atom can be electrically (electrostatically) neutral. Therefore, if an atom loses some electrons in effect it becomes positively charged (by the absense of the compensating negative charge).

Despite the electrostatic repulsive force between protons, the nucleus is held together by the strong force which is stronger at shorter distance than the electrostatic repulsion.⁸⁾

A nucleus has some magnetic moment, but its value is typically so small that it does not contribute significantly to the magnetic properties of magnetic materials.⁹⁾

Solid matter consists of atoms with some ordering; an atom has electrons and a nucleus, which further comprises neutrons (grey) and protons (red), which themselves are built from quarks (red, green, blue) and gluons (yellow wavy lines)¹⁰⁾¹¹⁾

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Protons and neutrons both reside in the nucleus and for this reason they are called nucleons, and they are also classified as hadrons, being subject to the strong force.¹²⁾ Experiments with collisions of sub-atomic particles indicate that that nucleons can be further split into quarks: proton comprising two “up” quarks (u), and one “down” quark (d), whereas neutron is built from one “up” and two “down” quarks. Quarks are held together by gluons which are the carriers of the strong force. Gluons are to the strong force what photons are to the electromagnetic force.¹³⁾

Quarks can have fractional elementary electric charge but they only occur with combination of other quarks to form hadrons.¹⁴⁾ Therefore, from electromagnetics viewpoint, in ordinary matter, the minimum amount of charge is the elementary electric charge (as quantised in protons and electrons).

Other fundamental sub-atomic particles (electron neutrino, muon neutrino, muon, tau) are also mostly irrelevant from the viewpoint of macroscopic electromagnetism.

A proton possess positive electric charge (elementary charge), with a value of 1.602 × 10⁻¹⁹ C. It has also a rest mass of 1.6726 × 10⁻²⁷ kg, which is very close to that of electrically neutral neutrons, with a mass of 1.6749 × 10⁻²⁷ kg.^15)16)17)

An isolated neutron is an unstable and can decay (characteristic lifetime of around 15 minutes)¹⁸⁾ to become a proton, by emitting an electron and an electron neutrino. However, when bound in the atomic nucleus, in the presence of other protons and neutrons it can remain stable for infinitely long time.¹⁹⁾

An atom of a given chemical element has a fixed number of protons in the nucleus, but the number of neutrons can differ. Atoms with different number of neutrons are called isotopes. The chemical properties of isotopes are similar but they differ in mass, and therefore can be detected by means of mass spectroscopy.²⁰⁾

Atomic species with various configurations of protons and neutrons are called nuclides. Nuclides can have various numbers of protons and neutrons, and hence may or may not represent the same chemical element.

Chart of stable and radioactive nuclides: Z - number of protons (atomic number), N - number of neutrons^{21) by Ben RG, Public domain}

Unstable nuclides (radionuclides) decay by emission of subatomic particles or electromagnetic radiation, or by spontaneous fission.

This process can produce other isotopes or other elements. For example, uranium ²³⁸₉₂U decays with a very long half-life of 4.5 billion years, by alpha radiation to thorium ²³⁴₉₀Th. Then thorium-234 decays with half-life of just 24 days, by emitting beta radiation and becoming protactinium ²³⁴₉₁Pa. A whole chain of further “transmutations” occurs, with half-life values ranging quite randomly from 4.5 billion years to 160 μs, ending with a stable isotope of lead ²⁰⁶₈₀Pb.²²⁾

Lorentz force acting on: α (positive), β (negative) and γ (electromagnetic radiation)²³⁾

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Alpha radiation (α) involves emitting an alpha particle (two protons and two neutrons), which reduces the mass number by 4 and atomic number by 2. Alpha particles are positively charged but also quite massive. They are easily stopped by matter (e.g. a sheet of paper), but are highly ionising. In the presence of magnetic field their trajectory is bent according to the Lorentz force.

Beta radiation (β^-) causes a neutron to become a proton, by emitting an electron (and an electron neutrino). This does not change the mass number, but increases the atomic number by 1. Electrons have negative charge and are significantly lighter than alpha particles, and therefore their trajectories are bent with a proportionally smaller radius in magnetic field, and in the opposite direction to the alpha rays.

There is also another kind of beta radiation (β⁺), in which a positron (positively charged electron) is emitted, turning a proton into a neutron. The β^- is more probable for nuclides with the number of neutrons exceeding the value for the stable isotopes and the β⁺ for nuclides with fewer neutrons - so that the decay is towards a stable nuclide.

Gamma radiation does not change atomic or mass number of an atom, but it reduces the energy stored in the nucleus. Gamma radiation is just an electromagnetic wave, but with frequency even higher than that of hard X-rays. Their trajectory is not affected by the Lorentz force.²⁴⁾

A plutonium-238 pellet assembled in a high-strength graphite impact shell for Multi-Mission Radioisotope Thermoelectric Generator ^{Idaho National Laboratory, CC-BY-2.0}

Radioactive decay, spontaneous or induced nuclear activity can generate significant amount of heat. These processes can be utilised for generation of useful energy.

Cherenkov radiation in an open nuclear reactor ^{United States Nuclear Regulatory Commission, Public domain}

For example, long-range spacecraft are powered by devices such as Multi-Mission Radioisotope Thermoelectric Generator (MMRTG), which uses a plutonium-238 pellet. The radioactivity can generate hundreds of watts of power, which is extracted by thermocouples to provide electrical current as a power supply. The heat is also used to warm up the inside of the spacecraft. Such generators can perform reliably for several years.²⁵⁾

Heat generated in nuclear processes is also used in power plants. Water is heated to create steam which mechanically drives a turbine connected to an electromagnetic generator (similarly as in conventional power plants).

In dense materials light travels slower than in vacuum, e.g. in water the speed is around 25% slower. Highly energetic particles (typically electrons, β radiation) ejected in the nuclear processes can travel faster than light in water and as a result generate Cherenkov radiation, which is in some sense analogous to the sonic shock wave generated by a body travelling faster than sound in air.

Electrons are subatomic particles which hold negative electric charge (elementary charge), with a value of -1.602 × 10⁻¹⁹ C, and a rest mass of 9.109 × 10⁻³¹ kg. Electron's electric charge has precisely the same absolute value (but opposite sign) as proton's, but the rest mass is around 1836 times smaller.²⁶⁾

Electrons orbit the nucleus in an atom, and for an electrically neutral atom the number of orbiting electrons is the same as the number of protons in the nucleus (atomic number).

The configuration of electrons in an atom can be described by a combination of several quantum numbers, dictating the solutions of the Schrödinger equation which describes the configuration and energy levels of electrons:²⁷⁾

• principal - defines the shells
• azimuthal (angular, orbital) - the subshells
• magnetic - orientation of orbitals
• spin - orientation of the spin of an electron (spin up, spin down).

In atoms, the electrons are bound to the nucleus by electromagnetic (electrostatic) force. They occupy energy “levels” called orbitals. The lowest energy orbital (1s) has a spherical form, and the complexity of the shape generally increases with the amount of energy. The shapes of orbitals within a given sub-shell complement each other so that they also add up to essentially a spherical distribution.

The orbitals are organised in subshells and shells. Subshells can hold several orbitals, each with two electrons, as dictated by the combination of the quantum numbers.

Pauli exclusion principle requires that no two electrons can have the same set of quantum numbers, and as a consequence a pair of electrons can share the same orbitals only if their spins have opposite signs, and therefore their magnetic spin contributions are cancelled out if both electrons are present.

Diagram of electron structure in an atom: shells, subshells and orbitals, with example of subshell diagram for iron

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The simplest orbital (electron in hydrogen atom) has a spherical symmetry. Higher-order orbitals exhibit increasing complexity, as dictated by the given combination of quantum numbers and result of the Schroedinger equation.²⁸⁾

Complexity of orbitals increases for higher order orbitals (just some typical examples are shown here for illustration)²⁹⁾

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Electrons in atoms are held by a certain amount of binding energy, depending primarily on the atomic number. The lowest level of energy is called ground state, and the electrons can be excited into higher levels by delivering energy, for example by irradiating the atom with photons, or otherwise by increasing the energy in the system.

If the binding energy is exceeded an electron can be released from an atom. For example, electrons in metal can be “boiled off” by applying heat and accelerating away by applying electric field (i.e. negative charge to the hot electrode with electrons and positive charge to some other electrode nearby).

Excitation with heat was widely used in vacuum tubes such as cathode ray tube in old TVs and analogue oscilloscopes.

Excitation with with photons is the basis for operation of photovoltaic panels, in which photons with higher energy (visible and ultraviolet light, but not infrared which too small energy) knock out electrons which are collected by the electrodes and create enough potential difference so that the generated voltage can be used to supply electrical power.

An atom without one or more electrons becomes in effect a positively charged ion (cation). An additional electron makes the atom negatively charged (anion). Such charged ions, nuclei or electrons interact electrostatically.

Free electrons are by definition electrically charged “ions” (anion).

Electron is excited to a higher energy state (higher subshell or shell) by absorbing a photon, and photon is released when electron drops to a lower energy level

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Electromagnetic radiation (photons) is generated whenever an electric charge is accelerated or decelerated. Charges moving at constant speed have both electric and magnetic field associated with them (velocity field), but the energy is not radiated out.

Charged particles (ions and electrons) can be accelerated in electric field, in vacuum tubes or particle accelerators. Very high velocities of the particles can be achieved (comparable with the speed of light), but many stages of acceleration are required.

On the other hand, it is relatively much easier to employ deceleration of particles - if the beam of electrons is made to hit some matter. This phenomenon is employed in vacuum tubes for generation of X-rays. Electrons are accelerated by very high voltage (typically between 20-150 kV) and directed to hit a metal target. The travelling electrons can collide with the ground state electrons in the matter and pass the energy so that they can be knocked to a higher energy level. These electrons can then return to their lower energy state by radiating out the energy in the form of X-ray photons.

Various metals can generate different X-ray signatures, which can be also used for X-ray spectroscopy.

Ordinary matter dominates in our part of the universe. However, a different kind of matter can also exist, which has some “opposite” properties, so it is called antimatter.

One of the main differences is the opposite sign of electric charge of antiprotons which are negatively charged, and positrons (anti-electrons) which are positively charged, but otherwise possess the same mass and other properties as their “ordinary” equivalents. For instance, anti-neutrons are also electrically neutral, but they possess opposite spin. When antimatter comes in contact with matter they annihilate each other, radiating gamma rays and other elementary particles.³⁰⁾

Sub-atomic antimatter particles can be generated in radioactive processes. For example, an ordinary proton can become an ordinary neutron by emitting a positron.³¹⁾ It should be noted that in that kind of process the balance of electric charges in the universe remains unchanged (conservation of charge), as it is when a positive and negative particle annihilate.³²⁾

For practical purposes, a “material” is a large collection of atoms. Many various properties can be identified, depending on the particular application or branch of science under consideration.

Chemical properties of elements are dictated mostly by the electromagnetic interactions between atoms.³³⁾

Atoms can form multi-atom molecules of chemical compounds by forming bonds. All chemical bonds are electromagnetic in nature, and they arise because of the activity of the electrons on the outermost shells.³⁴⁾

Atomic subshells have a preference to be fully occupied, and an atom with fully occupied outer shell is inert chemically (He, Ne, Ar, etc.) On the other hand, if an atom has just a single electron in the outermost shell then it is very reactive chemically (H, Li, Na, etc.) Some atoms are reactive enough that in the absence of other types of atoms they can form bonds between themselves. For example, in common air, both oxygen and nitrogen occur predominantly in diatomic configuration: O₂ and N₂.³⁵⁾³⁶⁾

Depending on the exact details of energetic conditions the bonds can be broadly classified as covalent or ionic.³⁷⁾

In the same energetic state (no ionisation), all atoms of the same chemical element (and of the same isotope) have the same electron configuration, and therefore the same chemical activity.

All materials respond to magnetic field to some extend, including vacuum (which is a reference point for the magnetic constant)³⁸⁾, but some with stronger interaction than others. The response is dictated by the configuration of magnetic moments of the electrons in the atoms, arising from both the spin magnetic moment and orbital magnetic moment, and the interactions between them (spin-orbit coupling). However, in most substances, the electron magnetic spin moments have the dominant contribution.³⁹⁾

There are three main types of magnetic responses, or types of magnetism:

• Diamagnetism - all electrons are paired in all orbitals. As a result there is no net spin moment. Application of magnetic field to such materials introduces changes to the shape of orbitals, similar to a current induced in a loop, in the direction opposing the applied field. Thus diamagnets have permeability lower than vacuum (or slightly negative susceptibility) and are repelled from magnetic field. However, this effect is so small that in everyday applications they are simply classified as non-magnetic materials.
• Paramagnetism - some atoms have at least one unpaired electron, and its spin can respond to the applied field. The more the spin can be oriented with the field the larger the permeability. Paramagnets are attracted to magnetic field, but the effect is also very weak (permeability slightly greater than unity, or susceptibility greater than zero). Paramagnets are also treated as “non-magnetic” from a technological viewpoint.
• Ordered magnetism - the atoms have unpaired electrons and they are positioned such that they can interact with each other, which leads to spontaneous magnetisation, high permeability and strong magnetic forces (magnetic materials). Depending on the type of ordering there can be:
  • ferromagnetism
  • ferrimagnetism
  • antiferromagnetism (magnetically ordered, but non-magnetic, similar to paramagnets)⁴⁰⁾
  • and several others.

All highly magnetic materials (exhibiting ordered magnetism) become paramagnetic at sufficiently high temperatures (above Curie temperature), because the thermal agitation of atoms can overcome the magnetic ordering of electron spins. Conversely, paramagnets increase their permeability with lowering temperature, such that some become ferromagnetic.⁴¹⁾

Periodic table of elements, with magnetic properties⁴²⁾ (at very low temperatures, and also high pressure, many elements become superconducting and hence strongly diamagnetic)

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By convention, direction of electric current is opposite to the movement of electrons

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Electricity is related to the presence (electrostatics) and movement (electric current) of electric charges. The properties of electricity have been harnessed for generation, storage, transmission, and utilisation of energy, on a local and global scale.

Electric energy is based on the flow of electric charges, which is equivalent to electric current. In ordinary metal conductors the electrons are free to move, and even small electric field (voltage) applied across a conductor can results in a significant current flow.⁴³⁾

In liquids and gasses the electric field can separate electrons from atoms, thus forming positively charged ions (cations), which can also move. Such positive charges move in the same direction as the assumed convention of electric current (from plus to minus). However, metals in a liquid form remain relatively good conductors, for example mercury, which is liquid at room temperature. In such metals the electrons are the main carrier of electric current.

Depending on the mobility of electrons and the associated resistivity, materials can be broadly classified into four groups, significant from engineering viewpoint: insulators, semiconductors, conductors and superconductors.⁴⁴⁾

There are many materials and substances which can have resistivity values in-between these ranges, for various reasons (temperature, moisture content, etc.) In general, higher temperature adds energy to the system and increases quantity or mobility of electrons in insulators and semiconductors.

On the other hand, in metals increased thermal agitation of the atoms scatters the movement of electrons and increases electrical resistance.

In superconductors, lattice vibrations due to thermal agitation are involved in conduction, and for some materials at low temperatures the current can flow with zero resistance (no loss). Superconductive current flow is sustained by electrons in pairs (Cooper pairs). The exact physics of all the superconducting phenomena, especially in type II superconductors is still incomplete.⁴⁶⁾

Resistivity of materials at room temperature spans over more than 30 orders of magnitude (superconductors have zero resistivity and cannot be represented on a logarithmic scale, but they would lie to the left of conductors)

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There are three basic (and several special) states of matter: gas, liquid, solid state. They all have very different mechanical properties, based on the spacing and forces acting between the atoms.⁴⁷⁾

In gases the atoms are agitated sufficiently so that they are separated from each other and can move freely. Gases can be easily compressed in volume. The atoms move chaotically and bounce against each other, through electrostatic repulsion.

In liquids the thermal agitation is comparatively lower than in gases, and gases can be liquefied by lowering the temperature, or liquids can be evaporated. Electromagnetic forces between the atoms are so strong that liquids are typically not compressible in volume. This property is used in hydraulic actuators for generation of large forces (e.g. in hydraulic presses).

Atoms can also coalesce into a state with fixed positions in the given volume - forming a solid. Many materials crystallise so that atoms form a well-defined spatial structure, repeated over large number of atoms. Some metals can be cooled fast enough that the atoms do not have time to form crystals and structures similar to glass is formed. Atoms are “frozen” in random positions (amorphous metal). Mechanical properties of solids are dictated not only by the types of atoms, but also by their spatial arrangement, which can be affected by processes such as: mechanical (rolling), thermal (annealing), and so on.⁴⁸⁾

• Nucleus
• Electron
• Proton
• Neutron
• Electric charge