constant

electron mass

Rest mass of an electron, a fundamental physical constant.
Value
\(m_{e} = 9.1093837015 \times 10^{-31}\)kilogram
13 related articles · 6 formulas

Description

The electron mass is the rest mass of the electron, a fundamental constant of nature. It is approximately 9.109 × 10⁻³¹ kilograms, or about 0.511 MeV/c² in particle physics units. This value is crucial because the electron is the lightest charged lepton, and its mass influences the structure of atoms, the behavior of matter, and the dynamics of many physical processes.

History

The electron was discovered by J.J. Thomson in 1897, and its mass was first measured by him using deflection in electric and magnetic fields. The modern precise value was established through decades of increasingly refined experiments, with the current best value coming from measurements in the 2010s.

How it works

The electron mass is not derived from a more fundamental theory but is measured experimentally. It is determined through a variety of techniques, including Penning traps that measure the cyclotron frequency of a single electron in a magnetic field, and through precision spectroscopy of hydrogen-like atoms, where the electron's mass affects the energy levels. The most accurate measurements combine these methods with quantum electrodynamics calculations.

In practice

The electron mass is essential in fields like semiconductor physics, where it determines the behavior of electrons in materials, and in metrology, where it links the kilogram to fundamental constants.

Fun fact

The electron is so light that about 1,836 electrons would be needed to equal the mass of a single proton.

Concept graph →

Formulas

$$\text{RM} = \frac{e^3}{2\pi m_e^2 c^4} \int n_e B_\parallel \, dl$$
Rotation measure is proportional to the integral of electron density times parallel magnetic field along the line of sight.
What is in the formula
n_evariableelectron number density — electron number density per cubic metre
B_parallelvariablemagnetic field component along line of sight — magnetic flux density tesla
dlvariableinfinitesimal path element along line of sight metre
econstantelementary charge — elementary charge = 1.602176634e-19 coulomb
m_econstantelectron rest mass — electron mass = 9.1093837015e-31 kilogram
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
∫operatorsummation over the line of sight — integral operator
$$a_0 = \frac{e E_0}{m_e c \omega}$$
Dimensionless parameter comparing electron oscillation energy to rest mass.
What is in the formula
a_0variablerelativistic intensity parameter (normalized vector potential) — relativistic parameter
E_0variablepeak electric field amplitude of the laser — electric field volt per metre
ωvariableangular frequency of the laser — angular frequency radian per second
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
m_econstantmass of an electron at rest — electron mass = 9.1093837015e-31 kilogram
cconstantuniversal speed limit of light in vacuum — speed of light = 299792458 metre per second
$$\mathrm{RM} = \frac{e^3}{2\pi m_e^2 c^4} \int_0^L n_e(s) B_\parallel(s) \, ds$$
Rotation measure quantifies Faraday rotation in plasma.
What is in the formula
RMvariableRotation measure — rotation measure radian per metre squared
n_evariableElectron number density — number density per metre cubed
B_parallelvariableMagnetic field component along line of sight — magnetic field tesla
svariablePath length along line of sight — length metre
LvariableTotal path length through plasma — length metre
econstantCharge of a single electron — elementary charge = 1.602176634e-19 coulomb
m_econstantRest mass of an electron — electron mass = 9.1093837015e-31 kilogram
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
∫operatorIntegration along the line of sight — integral operator
$$\Delta t = \frac{e^2}{2\pi m_e c} \mathrm{DM} \left(\nu_1^{-2} - \nu_2^{-2}\right)$$
Time delay between frequencies due to plasma dispersion.
What is in the formula
ΔtvariableTime delay between two frequencies — time second
DMvariableDispersion measure (column density of free electrons) — dispersion measure parsec per cubic centimetre
ν_1variableHigher frequency of the signal — frequency hertz
ν_2variableLower frequency of the signal — frequency hertz
econstantThe fundamental charge carried by a single proton or electron. — elementary charge = 1.602176634e-19 coulomb
m_econstantThe rest mass of an electron. — electron mass = 9.1093837015e-31 kilogram
cconstantThe universal speed limit for massless particles and information. — speed of light = 299792458 metre per second
$$E_\nu = \sqrt{c^2 p_z^2 + m_e^2 c^4 (1 + 2\nu B)}$$
Energy of electron in magnetic field with Landau quantization.
What is in the formula
E_νvariableEnergy of electron in Landau level ν — energy joule
p_zvariableElectron momentum along magnetic field — momentum kilogram metre per second
νvariableLandau quantum number (0,1,2,...) — landau level number
BvariableMagnetic field strength — magnetic flux density tesla
cconstantUniversal speed limit for massless particles — speed of light = 299792458 metre per second
m_econstantMass of an electron at rest — electron mass = 9.1093837015e-31 kilogram
$$-\frac{dE}{dx} = \frac{4\pi N_A r_e^2 m_e c^2 \rho z^2}{A \beta^2} \left[ \ln\left(\frac{2m_e \gamma^2 v^2 W_{\text{max}}}{I^2}\right) - 2\beta^2 - \delta - 2\frac{C}{Z} \right]$$
Energy loss of charged particles due to ionization in matter.
What is in the formula
EvariableKinetic energy of the charged particle — energy joule
xvariablePath length in the material — length metre
\rhovariableDensity of the absorbing material — density kilogram per cubic metre
zvariableCharge number of the incident particle — charge number
AvariableAtomic mass number of the absorber — atomic mass number
\betavariableSpeed of the particle relative to the speed of light — velocity ratio
\gammavariableLorentz factor of the particle — lorentz factor
vvariableSpeed of the particle — velocity metre per second
W_{\text{max}}variableMaximum energy transfer in a single collision — energy joule
IvariableMean excitation potential of the absorber — energy joule
\deltavariableDensity correction factor — density correction
CvariableShell correction factor — shell correction
ZvariableAtomic number of the absorber — atomic number
N_AconstantNumber of constituent particles per mole — avogadro constant = 6.02214076e23 per mole
r_econstantRadius of a classical electron — classical electron radius = 2.8179403262e-15 metre
m_econstantRest mass of the electron — electron mass = 9.1093837015e-31 kilogram
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
-\frac{d}{dx}operatorNegative derivative with respect to path length — negative derivative
\lnoperatorNatural logarithm — natural logarithm

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