Theelementary charge, usually denoted bye, is a fundamentalphysical constant, defined as theelectric chargecarried by a singleproton (+1e) or, equivalently, the magnitude of the negative electric charge carried by a singleelectron, which has charge −1 e.[2][a]
InSI units, thecoulomb is defined such that the value of the elementary charge is exactlye = 1.602176634×10−19 C[1] or 160.2176634zeptocoulombs (zC).[3] Since the2019 revision of the SI, the sevenSI base units are defined in terms of seven fundamental physical constants, of which the elementary charge is one.
In somenatural unit systems, such as the system ofatomic units,e functions as theunit ofelectric charge. The use of elementary charge as a unit was promoted byGeorge Johnstone Stoney in 1874 for the first system of natural units, calledStoney units.[7] Later, he proposed the nameelectron for this unit. At the time, the particle we now call theelectron was not yet discovered and the difference between the particleelectron and the unit of chargeelectron was still blurred. Later, the nameelectron was assigned to the particle and the unit of chargee lost its name. However, the unit of energyelectronvolt (eV) is a remnant of the fact that the elementary charge was once calledelectron.
Charge quantization is the principle that the charge of any object is aninteger multiple of the elementary charge. Thus, an object's charge can be exactly 0 e, or exactly 1 e, −1 e, 2 e, etc., but not1/2e, or −3.8 e, etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
This is the reason for the terminology "elementary charge": it is meant to imply that it is an indivisible unit of charge.
There are two known sorts of exceptions to the indivisibility of the elementary charge:quarks andquasiparticles.
Quarks, first posited in the 1960s, have quantized charge, but the charge is quantized into multiples of1/3e. However, quarks cannot be isolated; they exist only in groupings, and stable groupings of quarks (such as aproton, which consists of three quarks) all have charges that are integer multiples ofe. For this reason, either 1 e or1/3e can be justifiably considered to be "thequantum of charge", depending on the context. This charge commensurability, "charge quantization", has partially motivatedgrand unified theories.
Quasiparticles are not particles as such, but rather anemergent entity in a complex material system that behaves like a particle. In 1982Robert Laughlin explained thefractional quantum Hall effect by postulating the existence of fractionally chargedquasiparticles. This theory is now widely accepted, but this is not considered to be a violation of the principle of charge quantization, since quasiparticles are notelementary particles.
All knownelementary particles, including quarks, have charges that are integer multiples of1/3e. Therefore, the "quantum of charge" is1/3e. In this case, one says that the "elementary charge" is three times as large as the "quantum of charge".
On the other hand, allisolatable particles have charges that are integer multiples ofe. (Quarks cannot be isolated: they exist only in collective states like protons that have total charges that are integer multiples ofe.) Therefore, the "quantum of charge" ise, 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.[8] 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 refers to a quantity of charge equal to that of a proton.
Paul Dirac argued in 1931 that ifmagnetic monopoles exist, then electric charge must be quantized; however, it is unknown whether magnetic monopoles actually exist.[9][10] It is currently unknown why isolatable particles are restricted to integer charges; much of thestring theory landscape appears to admit fractional charges.[11][12]
The elementary charge is exactly defined since 20 May 2019 by theInternational System of Units. Prior to this change, the elementary charge was a measured quantity whose magnitude was determined experimentally. This section summarizes these historical experimental measurements.
In terms of the Avogadro constant and Faraday constant
If theAvogadro constantNA and theFaraday constantF are independently known, the value of the elementary charge can be deduced using the formula(In other words, the charge of onemole of electrons, divided by the number of electrons in a mole, equals the charge of a single electron.)
This method isnot how themost accurate values are measured today. Nevertheless, it is a legitimate and still quite accurate method, and experimental methodologies are described below.
The value of the Avogadro constantNA was first approximated byJohann Josef Loschmidt 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.[13] Today the value ofNA can be measured at very high accuracy by taking an extremely pure crystal (oftensilicon), measuring how far apart the atoms are spaced usingX-ray diffraction or another method, and accurately measuring the density of the crystal. From this information, one can deduce the mass (m) of a single atom; and since themolar mass (M) is known, the number of atoms in a mole can be calculated:NA =M/m.
The value ofF can be measured directly usingFaraday's laws of electrolysis. Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published byMichael Faraday in 1834.[14] In anelectrolysis 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 ofelectric current), and also taking into account the molar mass of the ions, one can deduceF.[1]
The limit to the precision of the method is the measurement ofF: the best experimental value has a relative uncertainty of 1.6 ppm, about thirty times higher than other modern methods of measuring or calculating the elementary charge.[15]
A famous method for measuringe is Millikan's oil-drop experiment. A small drop of oil in an electric field would move at a rate that balanced the forces ofgravity,viscosity (of traveling through the air), andelectric 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, namelye.
The necessity of measuring the size of the oil droplets can be eliminated by using tiny plastic spheres of a uniform size. The force due to viscosity can be eliminated by adjusting the strength of the electric field so that the sphere hovers motionless.
Anyelectric current will be associated withnoise from a variety of sources, one of which isshot noise. Shot noise exists because a current is not a smooth continual flow; instead, a current is made up of discrete electrons that pass by one at a time. By carefully analyzing the noise of a current, the charge of an electron can be calculated. This method, first proposed byWalter H. Schottky, can determine a value ofe of which the accuracy is limited to a few percent.[16] However, it was used in the first direct observation ofLaughlinquasiparticles, implicated in thefractional quantum Hall effect.[17]
Another accurate method for measuring the elementary charge is by inferring it from measurements of two effects inquantum mechanics: TheJosephson effect, voltage oscillations that arise in certainsuperconducting structures; and thequantum Hall effect, a quantum effect of electrons at low temperatures, strong magnetic fields, and confinement into two dimensions. TheJosephson constant iswhereh is thePlanck constant. It can be measured directly using theJosephson effect.
by combining the best measured value of the antiproton charge (below) with the low limit placed on antihydrogen's net charge by theALPHA Collaboration atCERN.[19]
Hori et al.[20] as cited in antiproton/proton charge difference listing of theParticle Data Group[21] The Particle Data Group article has a link to the current online version of the particle data.
^The symbole has another useful mathematical meaning due to which its use as label for elementary charge is avoided intheoretical physics. For example, inquantum mechanics one wants to be able to write compactlyplane waves with the use ofEuler's number. In the US,Euler's number is often denotede (italicized), while it is usually denoted e (roman type) in the UK and Continental Europe. Somewhat confusingly, inatomic physics,e sometimes denotes the electron charge, i.e. thenegative of the elementary charge. The symbolqe is also used for the charge of an electron.
^This is derived from theCODATA 2018 value, since one coulomb corresponds to exactly2997924580 statcoulombs. The conversion factor is ten times the numerical value ofspeed of light inmetres per second.
^Millikan, R. A. (1910). "The isolation of an ion, a precision measurement of its charge, and the correction of Stokes's law".Science.32 (822):436–448.doi:10.1126/science.32.822.436.
^Fletcher, Harvey (1982). "My work with Millikan on the oil-drop experiment".Physics Today.35 (6):43–47.doi:10.1063/1.2915126.
^Bressi, G.; Carugno, G.; Della Valle, F.; Galeazzi, G.; Sartori, G. (2011). "Testing the neutrality of matter by acoustic means in a spherical resonator".Physical Review A.83 (5) 052101.arXiv:1102.2766.doi:10.1103/PhysRevA.83.052101.S2CID118579475.
