The
elementary charge, usually denoted
e, is the
electric chargeElectric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields...
carried by a single
protonThe proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H
+...
, or equivalently, the negative of the electric charge carried by a single
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
. This is a fundamental
physical constantA physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
. To avoid confusion over its sign,
e is sometimes called the "elementary positive charge". It has a measured value of approximately . In
cgsThe centimetre-gram-second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...
, the value is . In the system of
atomic unitsAtomic units form a system of units convenient for atomic physics, electromagnetism, and quantum electrodynamics, especially when the focus is on the properties of electrons. There are two different kinds of atomic units, which one might name Hartree atomic units and Rydberg atomic units, which...
as well as some other systems of
natural unitsIn physics, natural units are physical units of measurement defined in such a way that certain selected universal physical constants are normalized to unity; that is, their numerical value becomes exactly 1.-Introduction:...
,
e functions as the
unitA measurement unit is a scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can be compared to express the ratio of the two quantities as a number....
of electric charge, i.e.
e = 1 in those unit systems.
The magnitude of the elementary charge was first measured in Robert Millikan's famous
oil-drop experimentThe oil-drop experiment was an experiment performed by Robert Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge ....
in 1909.
Charge quantization is the statement that every stable and independent object (meaning an object that can exist independently for a prolonged period of time) has a charge which is an
integerThe integers are natural numbers including 0 and their negatives . They are numbers that can be written without a fractional or decimal component, and fall within the set {.....
multiple of the elementary charge
e: A charge can be exactly 0, or exactly
e, –
e, 2
e, etc., but not, say,
e, or –3.8
e, etc. (This statement must not be interpreted to include
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never found in...
s or
quasiparticleIn physics, quasiparticle refers to a group of discrete phenomena whose behaviour is characterised as that of a single particle in a system, coupled with the effect the former has on the latter. It can be roughly defined as the combination of a particle and its influence on the local environment...
s, since neither quarks nor quasiparticles possess the ability to exist on their own for prolonged periods of time. Quarks have charges that are integer multiples of
e.)
This is the reason for the terminology "elementary charge": it is meant to imply that it is an indivisible unit of charge.
Charges less than an elementary charge
There are two known sorts of exceptions to the indivisibility of the elementary charge:
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never found in...
s and
quasiparticleIn physics, quasiparticle refers to a group of discrete phenomena whose behaviour is characterised as that of a single particle in a system, coupled with the effect the former has on the latter. It can be roughly defined as the combination of a particle and its influence on the local environment...
s.
- Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never found in...
s, first posited in the 1960s, have quantized charge, but the charge is quantized into multiples of e. However, quarks cannot be seen as isolated particles; they only exist in groupings, and stable groupings of quarks (such as a protonThe proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H
+...
, which consists of three quarks) all have charges that are integer multiples of e. For this reason, either e or e can be justifiably considered to be "the quantumIn physics, a quantum is the minimum unit of any physical entity involved in an interaction. An example of an entity that is quantized is the energy transfer of elementary particles of matter and of photons and other bosons...
of charge", depending on the context.
- Quasiparticle
In physics, quasiparticle refers to a group of discrete phenomena whose behaviour is characterised as that of a single particle in a system, coupled with the effect the former has on the latter. It can be roughly defined as the combination of a particle and its influence on the local environment...
s are not particles as such, but rather an emergentIn philosophy, systems theory and science, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems.-Definitions:...
entity in a complex material system that behaves like a particle. In 1982 Robert LaughlinRobert Betts Laughlin is a professor of Physics and Applied Physics at Stanford University. Along with Horst L. Störmer of Columbia University and Daniel C. Tsui of Princeton University, he was awarded the 1998 Nobel Prize in physics for his explanation of the fractional quantum Hall...
explained the fractional quantum Hall effectThe fractional quantum Hall effect is a physical phenomenon in which a certain system behaves as if it were composed of particles with charge smaller than the elementary charge...
by postulating the existence of fractionally-charged quasiparticleIn physics, quasiparticle refers to a group of discrete phenomena whose behaviour is characterised as that of a single particle in a system, coupled with the effect the former has on the latter. It can be roughly defined as the combination of a particle and its influence on the local environment...
s. This theory is now widely accepted, but this is not considered to be a violation of the principle of charge quantization, since quasiparticles are not elementary particles.
What is the quantum of charge?
All known
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s, including quarks, have charges that are integer multiples of
e. Therefore, one can say that the "
quantumIn physics, a quantum is the minimum unit of any physical entity involved in an interaction. An example of an entity that is quantized is the energy transfer of elementary particles of matter and of photons and other bosons...
of charge" is
e. In this case, one says that the "elementary charge" is three times as large as the "quantum of charge".
On the other hand, all
isolatable particles have charges that are integer multiples of
e. (Quarks cannot be isolated, except in combinations like protons that have total charges which are integer multiples of
e.) Therefore, one can say that the "quantum of charge" is
e, with the proviso that quarks are not to be included. In this case, "elementary charge" would be synonymous with the "quantum of charge".
In fact, both terminologies are used. For this reason, phrases like "the quantum of charge" or "the indivisible unit of charge" can be ambiguous, unless further specification is given. On the other hand, the term "elementary charge" is unambiguous: It universally refers to the charge of a proton.
In terms of the Avogadro constant and Faraday constant
If the Avogadro constant
NA and the
Faraday constantIn physics and chemistry, the Faraday constant is the magnitude of electric charge per mole of electrons. While most uses of the Faraday constant, denoted F, have been replaced by the standard SI unit, the coulomb, the Faraday is still widely used in calculations in electrochemistry...
F are independently known, the value of the elementary charge can be deduced, using the formula
(In other words, the charge of one mole of electrons, divided by the number of electrons in a mole, equals the charge of a single electron.)
In practice, this method is
not how the
most accurate values are measured today. Instead of calculating
e from
F and
NA, in fact
NA is calculated from
F and
e, while
e is measured independently by a different method. Nevertheless, this is a legitimate and still quite accurate method, and experimental methodologies are described below:
Measuring the Faraday constant
The value of
F can be measured directly using
Faraday's laws of electrolysisFaraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by Michael Faraday in 1834.-Statements of the laws:Several versions of the laws can be found in textbooks and the scientific literature...
. Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by
Michael FaradayMichael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....
in 1834.
In an
electrolysisIn chemistry and manufacturing, electrolysis is a method of using an electric current to drive an otherwise non-spontaneous chemical reaction. Electrolysis is commercially highly important as a stage in the separation of elements from naturally-occurring sources such as ores using an electrolytic...
experiment, there is a one-to-one correspondence between the electrons passing through the anode-to-cathode wire and the ions that plate onto or off of the anode or cathode. Measuring the mass change of the anode or cathode, and the total charge passing through the wire (which can be measured as the time-integral of
electric currentElectric current can mean, depending on the context, a flow of electric charge or the rate of flow of electric charge ....
), and also taking into account the
molar massMolar mass, symbol M, is the mass of one mole of a substance . It is a physical property which is characteristic of each pure substance...
of the ions, one can deduce
F.
Measuring the Avogadro constant
The value of the Avogadro constant
NA was first approximated by
Johann Josef LoschmidtJan or Johann Josef Loschmidt , who referred to himself mostly as 'Josef' , was a notable Austrian scientist who performed groundbreaking work in chemistry, physics , and crystal forms.Born of poor Bohemian farming stock in Počerny , now part of Karlovy Vary, Czech Republic,...
who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas.
Today the value of
NA can be measured at very high accuracy by taking an extremely pure crystal (in practice, often
siliconSilicon is the most common metalloid. It is a chemical element, which has the symbol Si and atomic number 14. A tetravalent metalloid, silicon is less reactive than its chemical analog carbon...
), measuring how far apart the atoms are spaced using X-ray diffraction or another method, and accurately measuring the density of the crystal. From this information, one can deduce the weight (in grams) of a single atom; and since the molar mass is known, the number of atoms in a mole can be calculated.
Oil-drop experiment
A famous method for measuring
e is Millikan's oil-drop experiment. A small drop of oil in an electric field would move at a rate that balanced the forces of gravity,
viscosityViscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness." Thus, water is "thin," having a lower viscosity, while honey is "thick," having a higher viscosity...
(of traveling through the air), and electric force. The forces due to gravity and viscosity could be calculated based on the size and velocity of the oil drop, so electric force could be deduced. Since electric force, in turn, is the product of the electric charge and the known electric field, the electric charge of the oil drop could be accurately computed. By measuring the charges of many different oil drops, it can be seen that the charges are all integer multiples of a single small charge, namely
e.
Shot noise
Any
electric currentElectric current can mean, depending on the context, a flow of electric charge or the rate of flow of electric charge ....
will be associated with
noiseElectronic noise is a random signal characteristic of all electronic circuits. Depending on the circuit, the noise generated by electronic devices can vary greatly. Noise can be produced by several different effects. Thermal noise and shot noise are inherent to all devices...
from a variety of sources. One of these sources,
shot noiseShot noise is a type of electronic noise that occurs when the finite number of particles that carry energy, such as electrons in an electronic circuit or photons in an optical device, is small enough to give rise to detectable statistical fluctuations in a measurement...
, is due to the fact that the current is not a smooth continual flow, but rather consists of discrete electrons which pass through one at a time. By carefully analyzing the noise of a current, the charge of an electron can be calculated. This method can give a value of
e accurate to a few percent.
From the Josephson and von Klitzing constants
Currently, the most accurate method for measuring the elementary charge is by inferring it from measurements of two effects in
quantum mechanicsQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
: The
Josephson effectThe Josephson effect is the phenomenon of current flow across two weakly coupled superconductors, separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting barrier—is known as a Josephson junction; the current that crosses the barrier is the...
, voltage oscillations that arise in certain superconducting structures; and the
quantum Hall effectThe quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized valueswhere e is the elementary charge and h is Planck's constant...
, a quantum effect of electrons at low temperatures, strong magnetic fields, and confinement into two dimensions.
The Josephson constant is
(where
h is Planck's constant). It can be measured directly using the
Josephson effectThe Josephson effect is the phenomenon of current flow across two weakly coupled superconductors, separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting barrier—is known as a Josephson junction; the current that crosses the barrier is the...
.
The von Klitzing constant is.
It can be measured directly using the
quantum Hall effectThe quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized valueswhere e is the elementary charge and h is Planck's constant...
.
From these two constants, the elementary charge can be deduced:.