electron mass

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The electron mass (symbol: ''m''e) is the
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
of a stationary
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
, also known as the
invariant mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an physical body, object or physical system, system of objects that is independent of the overall motion ...
of the electron. It is one of the fundamental constants of
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
. It has a value of about or about , which has an energy-equivalent of about or about

# Terminology

The term "rest mass" is sometimes used because in
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between Spacetime, space and time. In Albert Einstein's original treatment, the theory is based on two Postulates of ...
the mass of an object can be said to increase in a frame of reference that is moving relative to that object (or if the object is moving in a given frame of reference). Most practical measurements are carried out on moving electrons. If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass. Such correction becomes substantial for electrons accelerated by voltages of over . For example, the relativistic expression for the total energy, ''E'', of an electron moving at speed $v$ is :$E = \gamma m_\text c^2 ,$ where the Lorentz factor is $\gamma = 1/\sqrt$. In this expression ''m''e is the "rest mass", or more simply just the "mass" of the electron. This quantity ''m''e is frame invariant and velocity independent. However, some texts group the Lorentz factor with the mass factor to define a new quantity called the ''relativistic mass'', .

# Determination

Since the electron mass determines a number of observed effects in atomic physics, there are potentially many ways to determine its mass from an experiment, if the values of other physical constants are already considered known. Historically, the mass of the electron was determined directly from combining two measurements. The mass-to-charge ratio of the electron was first estimated by Arthur Schuster in 1890 by measuring the deflection of "cathode rays" due to a known magnetic field in a
cathode ray tube A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns, which emit electron beams that are manipulated to display images on a Phosphorescence, phosphorescent screen. The images may represent electrical waveforms (osci ...
. Seven years later J. J. Thomson showed that cathode rays consist of streams of particles, to be called electrons, and made more precise measurements of their mass-to-charge ratio again using a cathode ray tube. The second measurement was of the charge of the electron. This was determined with a precision of better than 1% by Robert A. Millikan in his oil drop experiment in 1909. Together with the mass-to-charge ratio, the electron mass was determined with reasonable precision. The value of mass that was found for the electron was initially met with surprise by physicists, since it was so small (less than 0.1%) compared to the known mass of a hydrogen atom. The electron rest mass can be calculated from the Rydberg constant ''R'' and the fine-structure constant ''α'' obtained through spectroscopic measurements. Using the definition of the Rydberg constant: :$R_ = \frac ,$ thus :$m_ = \frac ,$ where ''c'' is the speed of light and ''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
. The relative uncertainty, 5 in the 2006
CODATA The Committee on Data of the International Science Council (CODATA) was established in 1966 as the Committee on Data for Science and Technology, originally part of the International Council of Scientific Unions, now part of the International ...
recommended value, is due entirely to the uncertainty in the value of the Planck constant. With the re-definition of kilogram in 2019, there is no uncertainty by definition left in Planck constant anymore. The electron relative atomic mass can be measured directly in a Penning trap. It can also be inferred from the spectra of antiprotonic helium atoms (
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol (chemistry), symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas gr ...
atoms where one of the electrons has been replaced by an antiproton) or from measurements of the electron ''g''-factor in the hydrogenic ions 12C5+ or 16O7+. The electron relative atomic mass is an adjusted parameter in the CODATA set of fundamental physical constants, while the electron rest mass in kilograms is calculated from the values of the Planck constant, the fine-structure constant and the Rydberg constant, as detailed above.

# Relationship to other physical constants

The electron mass is used to calculate the Avogadro constant ''N''A: :$N_ = \frac = \frac .$ Hence it is also related to the atomic mass constant ''m''u: :$m_ = \frac = \frac = \frac ,$ where ''M''u is the molar mass constant (defined in SI) and ''A''r(e) is a directly measured quantity, the relative atomic mass of the electron. Note that ''m''u is defined in terms of ''A''r(e), and not the other way round, and so the name "electron mass in atomic mass units" for ''A''r(e) involves a circular definition (at least in terms of practical measurements). The electron relative atomic mass also enters into the calculation of all other relative atomic masses. By convention, relative atomic masses are quoted for neutral atoms, but the actual measurements are made on positive ions, either in a mass spectrometer or a Penning trap. Hence the mass of the electrons must be added back on to the measured values before tabulation. A correction must also be made for the mass equivalent of the binding energy ''E''b. Taking the simplest case of complete ionization of all electrons, for a nuclide X of
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
''Z'', :$A_\left(\right) = A_\left(^\right) + ZA_\left(\right) - E_/m_c^2\,$ As relative atomic masses are measured as ratios of masses, the corrections must be applied to both ions: the uncertainties in the corrections are negligible, as illustrated below for hydrogen 1 and oxygen 16. The principle can be shown by the determination of the electron relative atomic mass by Farnham ''et al.'' at the University of Washington (1995). It involves the measurement of the frequencies of the cyclotron radiation emitted by electrons and by 12C6+ ions in a Penning trap. The ratio of the two frequencies is equal to six times the inverse ratio of the masses of the two particles (the heavier the particle, the lower the frequency of the cyclotron radiation; the higher the charge on the particle, the higher the frequency): :$\frac = \frac = 0.000\,274\,365\,185\,89\left(58\right)$ As the relative atomic mass of 12C6+ ions is very nearly 12, the ratio of frequencies can be used to calculate a first approximation to ''A''r(e), . This approximate value is then used to calculate a first approximation to ''A''r(12C6+), knowing that ''E''b(12C)/''m''u''c''2 (from the sum of the six ionization energies of carbon) is : . This value is then used to calculate a new approximation to ''A''r(e), and the process repeated until the values no longer vary (given the relative uncertainty of the measurement, 2.1): this happens by the fourth cycle of iterations for these results, giving for these data.

# References

{{reflist Electron Mass Physical constants