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Charge number
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Charge number (denoted z) is a quantized and dimensionless quantity derived from electric charge, with the quantum of electric charge being the elementary charge (e, constant). The charge number equals the electric charge (q, in coulombs) divided by the elementary charge: z = q/e. Atomic numbers (Z) are a special case of charge numbers, referring to the charge number of an atomic nucleus, as opposed to the net charge of an atom or ion. The charge numbers for ions (and also subatomic particles) are written in superscript, e.g., Na+ is a sodium ion with charge number positive one (an electric charge of one elementary charge). All particles of ordinary matter have integer-value charge numbers, with the exception of quarks, which cannot exist in isolation under ordinary circumstances (the strong force keeps them bound into hadrons of integer charge numbers).
Charge numbers in chemistry
[edit]Charge number or valence[1] of an ion is the coefficient that, when multiplied by the elementary charge, gives the ion's charge.[2]
For example, the charge on a chloride ion, , is , where e is the elementary charge. This means that the charge number for the ion is .
is used as the symbol for the charge number. In that case, the charge of an ion could be written as .
The charge number in chemistry normally relates to an electric charge. This is a property of specific subatomic atoms. These elements define the electromagnetic contact between the two elements.
A chemical charge can be found by using the periodic table. An element's placement on the periodic table indicates whether its chemical charge is negative or positive. Looking at the table, one can see that the positive charges are on the left side of the table and the negative charges are on the right side of the table. Charges that are positive are called cations. Charges that are negative are called anions. Elements in the same group have the same charge. A group in the periodic table is a term used to represent the vertical columns.
The noble gases of the periodic table do not have a charge because they are nonreactive. Noble gases are considered stable since they contain the desired eight electrons. The other atoms or ions have charges because they are very reactive and want to react with another atom or ion to become stable. When elements are bonded, they can either be bonded by ionic bonding or covalent bonding. When elements bond between positive and negative charged atoms, their charges will be switched and carried down on the other element to combine them equally. This is shown below. Using the chart provided, if ammonium with a plus 1 charge is combined with an acetate ion with a negative 1 charge, the charges will be cancelled out, shown in the figure below.
![{\displaystyle {\mathrm {NH} {\vphantom {A}}_{\smash[{t}]{4}}{\vphantom {A}}^{+}{}+{}\mathrm {C} {\vphantom {A}}_{\smash[{t}]{2}}\mathrm {H} {\vphantom {A}}_{\smash[{t}]{3}}\mathrm {O} {\vphantom {A}}_{\smash[{t}]{2}}{\vphantom {A}}^{-}{}\mathrel {\longrightarrow } {}\mathrm {NC} {\vphantom {A}}_{\smash[{t}]{2}}\mathrm {H} {\vphantom {A}}_{\smash[{t}]{7}}\mathrm {O} {\vphantom {A}}_{\smash[{t}]{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bb5d9216de512446be05526649efa076793cf78)
Another example below.
![{\displaystyle {2\,\mathrm {NH} {\vphantom {A}}_{\smash[{t}]{4}}{\vphantom {A}}^{+}{}+{}\mathrm {CO} {\vphantom {A}}_{\smash[{t}]{3}}{\vphantom {A}}^{2-}{}\mathrel {\longrightarrow } {}(\mathrm {NH} {\vphantom {A}}_{\smash[{t}]{4}}){\vphantom {A}}_{\smash[{t}]{2}}\mathrm {CO} {\vphantom {A}}_{\smash[{t}]{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1379d80c29e33ae9839e1a5f725f9a357850aa4)
both and are salts.
![{\displaystyle {\mathrm {NC} {\vphantom {A}}_{\smash[{t}]{2}}\mathrm {H} {\vphantom {A}}_{\smash[{t}]{7}}\mathrm {O} {\vphantom {A}}_{\smash[{t}]{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ab5b1568a43a4ab750edad412307feaa4080b00)
![{\displaystyle {(\mathrm {NH} {\vphantom {A}}_{\smash[{t}]{4}}){\vphantom {A}}_{\smash[{t}]{2}}\mathrm {CO} {\vphantom {A}}_{\smash[{t}]{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/20655b6413f360696359c9ce96222c92f2dbd8eb)
Charge numbers also help to determine other aspects of chemistry. One example is that someone can use the charge of an ion to find the oxidation number of a monatomic ion. For example, the oxidation number of is +1. This helps when trying to solve oxidation questions.
A charge number also can help when drawing Lewis dot structures. For example, if the structure is an ion, the charge will be included outside of the Lewis dot structure.
Since there is a negative charge on the outside of the Lewis dot structure, one electron needs to be added to the structure. If the charge was positive, an electron would be lost and taken away.
Charge numbers in nuclear and hadron physics
[edit]For an atomic nucleus, which can be regarded as an ion having stripped off all electrons, the charge number is identical with the atomic number Z, which corresponds to the number of protons in ordinary atomic nuclei.
Unlike in chemistry, subatomic particles with electric charges of two elementary charges (e.g. some delta baryons) are indicated with a superscript "++" or "−−". In chemistry, the same charge numbers are usually indicated as superscript "+2" or "−2".
Charge numbers in elementary-particle physics
[edit]In particle physics, the charge number is a (derived) flavor quantum number. For color-charged particles like quarks and hypothetical leptoquarks, the charge number is a multiple of 1/3.
See also
[edit]References
[edit]- ^ Dynamic Systems in Neuroscience by Izhikevich
- ^ IUPAC, Compendium of Chemical Terminology, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "charge number, z". doi:10.1351/goldbook.C00993
Charge number
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Definition and Basics
Core Definition
The charge number, denoted as , is a dimensionless quantity defined as the ratio of the electric charge of a particle to the elementary charge , expressed as .[1] The elementary charge is the fundamental unit of electric charge, with an exact value of coulombs.[6] This definition normalizes the charge to a unitless measure, representing the effective number of elementary charges carried by the particle, and is applicable across various physical contexts from atomic ions to subatomic particles. The charge number differs from the electric charge itself, which is a physical quantity with dimensions of current times time (coulombs) and governs the magnitude of electromagnetic forces via Coulomb's law. In contrast, serves as a normalized, context-agnostic descriptor that simplifies the analysis of charge-related phenomena without reference to absolute units. The foundational experimental confirmation of charge quantization and the value of originated from Robert Millikan's oil-drop experiments conducted between 1909 and 1913. The terminology of "charge number" was established in IUPAC's Quantities, Units and Symbols in Physical Chemistry (Green Book, 2nd edition, 1993), with refinements in subsequent updates around 2006.[2]Notation and Units
The charge number, denoted by the symbol , represents the ratio of a particle's electric charge to the elementary charge , such that . In chemical contexts, particularly for ions, is an integer indicating the magnitude and sign of the charge, with the ionic formula using a right superscript where the number precedes the sign, as in or .[7] Particle physics data groups often list the charge as a numerical multiple of , sometimes using for the value in those units. The charge number is a dimensionless quantity, as it normalizes the physical charge to the fundamental unit C. Although is measured in coulombs (C), carries no units and is expressed solely as a signed number.[8] By convention, is positive for particles with positive charge, such as protons () and cations, and negative for those with negative charge, such as electrons () and anions. In practice, the charge number is determined experimentally through the charge-to-mass ratio. In particle accelerators, particles are deflected in magnetic fields via the Lorentz force , allowing (and thus ) to be inferred from the trajectory radius compared to known references. In electrochemical cells, for ions is derived from Faraday's first law of electrolysis, where the mass deposited is (with the molar mass, the total charge, and the Faraday constant), solved for using measured quantities.Chemical Context
Ions and Charge Numbers
In chemical systems, the charge number of an ion represents the net electric charge divided by the elementary charge , yielding an integer that quantifies the excess or deficit of electrons relative to a neutral atom.[1] This value arises from the gain or loss of valence electrons to achieve more stable electron configurations, such as noble gas octets. For monatomic ions, the sodium cation exhibits upon losing one valence electron, while the chloride anion has after gaining one. Periodic trends in ion formation reflect the electronegativity and metallic character across the table. Metals on the left side predominantly lose electrons to form cations with positive charge numbers, typically to , as seen in alkali metals like lithium () and alkaline earth metals like magnesium ().[9] Nonmetals on the right side gain electrons to form anions with negative charge numbers, generally to , exemplified by halogens like fluorine () and oxygen ().[9] Noble gases in group 18 maintain due to their stable octet configuration, rarely forming ions under standard conditions. Polyatomic ions consist of two or more atoms covalently bonded with an overall charge number resulting from unequal electron sharing or transfer. The ammonium ion , formed by nitrogen and four hydrogens, carries from the net loss of one electron equivalent. Similarly, the sulfate ion has , arising from the central sulfur and four oxygens sharing electrons unevenly to yield a two-unit electron excess. For simple monatomic ions, the charge number directly equals the oxidation number of the element, reflecting its hypothetical charge in an ionic model. In more complex species like coordination compounds, however, oxidation numbers assigned to central atoms may not match the overall ionic charge due to ligand interactions.[10]Role in Chemical Bonding and Reactions
In ionic bonding, the charge number governs the electrostatic attraction between oppositely charged ions, forming stable crystal lattices in compounds like salts. The lattice energy , which quantifies the bond strength, is proportional to the product of the ions' charge numbers divided by their separation distance, , where and are the charges and is the internuclear distance. For sodium chloride, Na⁺ () transfers an electron to Cl⁻ (), yielding a lattice energy of approximately -788 kJ/mol due to the term and pm.[11] Higher values, as in MgO (, lattice energy approximately -3795 kJ/mol), increase lattice energy magnitude, enhancing compound stability.[11] Charge numbers are essential for balancing chemical equations involving ions, ensuring conservation of both mass and charge in stoichiometric reactions. In ionic equations, the sum of charges must equal zero on both reactant and product sides; for example, the neutralization NH₄⁺ () + CH₃COO⁻ () → NH₄CH₃COO (neutral, ) balances as +1 and -1 on the left yield 0 overall.[12] Net ionic equations, such as Ag⁺ () + Cl⁻ () → AgCl (s), omit spectator ions while preserving charge equality (+1 -1 = 0).[12] This principle extends to precipitation and acid-base reactions, where mismatched charges would violate electroneutrality.[12] Lewis dot structures illustrate charge numbers by depicting valence electron transfers that achieve stable configurations, often the octet rule for main-group elements. In ionic compounds, these structures show metal atoms losing electrons to form cations with positive , while nonmetals gain electrons for negative , resulting in ions mimicking noble gas electron counts for stability.[13] For NaCl, Na donates its valence electron (dot) to Cl, forming Na⁺ (, octet in inner shell) and Cl⁻ (, octet completed), with the arrow indicating transfer toward charge-neutral valence shells.[13] Such representations highlight how ions stabilize through electrostatic pairing rather than shared electrons.[13] In electrochemistry, the charge number dictates the quantity of material transformed per unit charge via Faraday's first law, where mass deposited , with as the Faraday constant (96,500 C/mol) and as molar mass, implying one Faraday liberates one equivalent (1/|z| moles) of ion.[14] For Ag⁺ (), 96,500 C deposits 108 g Ag, but for Cu²⁺ (), the same charge deposits 63.5/2 g.[14] For polyprotic acids, varies with pH due to stepwise deprotonation; the average charge , where are pH-dependent ionization fractions and is the fully protonated charge, influences speciation and buffering capacity.[15] In sulfuric acid (H₂SO₄), shifts from 0 to -1 to -2 across pH ranges, altering reactivity.[15]Nuclear and Hadron Physics
Atomic Number Z
The atomic number , also referred to as the proton number, defines the number of protons within the nucleus of an atom and corresponds directly to the nuclear charge number when expressed in units of the elementary charge . This integer value uniquely identifies the chemical element, as it determines the number of electrons in a neutral atom and thus its chemical properties; for instance, hydrogen possesses with a single proton, while carbon has with six protons.[16] In nuclear structure, remains fixed for all isotopes of a given element, whereas the neutron number can vary, resulting in different mass numbers . For example, the three stable isotopes of oxygen all have , but differ in (8, 9, or 10 neutrons), yielding or . This variation in allows for isotopic diversity without altering the elemental identity defined by .[17] The magnitude of plays a critical role in nuclear stability by governing the electrostatic Coulomb repulsion among protons, which scales with and becomes a dominant destabilizing force in heavier nuclei, ultimately limiting the size of stable configurations. Nuclei with specific "magic" values of , such as 2, 8, 20, 28, 50, or 82, exhibit enhanced stability due to the completion of proton shells in the nuclear shell model, analogous to filled electron shells in atomic structure; these configurations minimize energy and resist fission or decay.[18] Historically, the concept of the atomic nucleus—and by extension as its charge—emerged from Ernest Rutherford's 1911 analysis of alpha particle scattering by thin metal foils, which revealed a tiny, dense, positively charged core deflecting particles at large angles, implying concentrated positive charge rather than a diffuse distribution. This discovery was refined in 1913 by Henry Moseley, who used X-ray spectroscopy to establish that the square root of the frequency of emitted characteristic X-rays is linearly proportional to (specifically, , where is a screening constant), providing a precise empirical measure of atomic numbers and resolving ambiguities in the periodic table ordering.[19][20]Charges of Hadrons and Nuclei
Hadrons, as composite particles bound by the strong force, exhibit integer charge numbers that reflect their quark content in bound states. Baryons, consisting of three quarks, include the proton with a charge number and the neutron with . Mesons, made of a quark-antiquark pair, feature charged pions such as with and with . These charges are fundamental properties verified through scattering experiments and decay analyses. Higher-mass hadrons, like the delta resonances, demonstrate multiple charge states within isospin multiplets. The baryon, for instance, carries , while other members of the family have . These particles are short-lived excitations observed in pion-nucleon collisions, with their charges conserved in production and decay processes. In particle physics tables, such multi-charge notations use superscripts like for and for , facilitating clear representation of isospin symmetry. In nuclear reactions, the total charge number is strictly conserved, ensuring balance between initial and final states. For example, in fusion processes like the proton-proton chain in stars, the combined of reactants equals that of products, maintaining overall neutrality when considering emitted particles. In fission, such as the spontaneous splitting of uranium-235, the sum of for fragments and any prompt neutrons equals the parent's . Alpha decay exemplifies this: a nucleus emits an alpha particle (, ), reducing the daughter nucleus's by 2 while conserving total . Beta decay alters individual nuclear charges without violating total conservation. In beta-minus decay, a neutron transforms into a proton, increasing by 1 and emitting an electron () and antineutrino (), so the total remains unchanged. Conversely, beta-plus decay decreases by 1, producing a positron () and neutrino. These processes, mediated by the weak interaction, are crucial for stellar nucleosynthesis and radioactive dating. Excited nuclei maintain a total charge number , equivalent to the ground-state atomic number, despite rearrangements in nucleon configurations. In the nuclear shell model, protons occupy discrete energy levels analogous to atomic orbitals, distributing the charge across shells while preserving the overall . This model explains stability near magic numbers (e.g., ), where filled proton shells minimize excitation energies, but the total charge remains fixed. Recent experiments as of August 2025 have identified additional magic numbers in exotic nuclei, such as in silicon-22.[21][22] Isobars, nuclei sharing the same mass number but differing in , illustrate variations in charge for fixed nucleon count. Representative examples include with (6 protons, 8 neutrons) and with (7 protons, 7 neutrons), where is unstable and decays to via beta-minus emission. Such pairs highlight charge differences driving beta stability and are key in understanding nuclear mass parabolas.Elementary Particle Physics
Charges of Leptons and Bosons
Leptons in the Standard Model are spin-1/2 fermions organized into three generations, each consisting of a charged lepton and a neutral neutrino. The charged leptons—the electron (), muon (), and tau ()—possess an electric charge of in units of the elementary charge , while their antiparticles (, , ) have . All three generations exhibit identical charge assignments, reflecting the generational symmetry in electroweak interactions. Neutrinos (, , ) and antineutrinos are electrically neutral with charge $0$, a property essential for their role in weak processes without altering electric charge. The following table summarizes the electric charges of leptons:| Particle | Symbol | Charge () |
|---|---|---|
| Electron | ||
| Positron | ||
| Muon | ||
| Antimuon | ||
| Tau | ||
| Antitau | ||
| Electron neutrino | $0$ | |
| Electron antineutrino | $0$ | |
| Muon neutrino | $0$ | |
| Muon antineutrino | $0$ | |
| Tau neutrino | $0$ | |
| Tau antineutrino | $0$ |
| Particle | Symbol | Charge () | Role |
|---|---|---|---|
| Photon | $0$ | Electromagnetism | |
| Boson | Weak charged current | ||
| Boson | Weak charged current | ||
| Boson | $0$ | Weak neutral current | |
| Gluon | $0$ | Strong force |