Fundamental Physical Constant

Elementary Charge
e = 1.602176634 × 10−19 C

The elementary charge is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron.

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2019 SI Redefinition
1909 First Measured
7 SI Defining Constants
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01

What is the Elementary Charge?

The elementary charge, denoted by e, is a fundamental physical constant that represents the smallest unit of electric charge that can exist freely in nature.

Abstract Physics Visualization

Its exact value, as defined by international convention since May 20, 2019, is 1.602 176 634 × 10−19 coulombs. This value is now one of the seven defining constants of the International System of Units (SI).

A proton carries a positive elementary charge (+e), while an electron carries a negative elementary charge (−e). Although they have opposite charges, the magnitude is identical – a fundamental symmetry in nature that has profound implications for the structure of matter.

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Charge Quantization

All observable electric charges in the universe are integer multiples of the elementary charge. This means an object's charge can be 0, ±1e, ±2e, ±3e, and so on, but never a fraction like 0.5e.

Values in Different Unit Systems

Unit System Value
SI (Coulombs) 1.602 176 634 × 10⁻¹⁹ C
CGS (Statcoulombs) 4.803 204 27 × 10⁻¹⁰ statC
Atomic Units 1 e (by definition)
Planck Units √(4πα) ≈ 0.0854
02

As a Unit

The elementary charge serves as a natural unit of electric charge in many systems of units used in physics.

Natural Unit Systems

In systems of "natural units," the elementary charge is often set to 1 by definition, simplifying equations and highlighting the fundamental nature of physical laws.

Atomic Units

Used in atomic physics and chemistry. The elementary charge e = 1 by definition.

Planck Units

Based on fundamental constants G, ℏ, c, and kB. Charge is related to the fine-structure constant.

Stoney Units

The first system of natural units, proposed by George Stoney in 1881, based on e, G, and c.

The Fine-Structure Constant

α = e²4πε₀ℏc ≈ 1137.036 ≈ 0.00729735

The fine-structure constant (α) is one of the most important dimensionless numbers in physics. It characterizes the strength of the electromagnetic interaction between elementary charged particles.

This remarkable constant appears in the equation relating the elementary charge to other fundamental constants: the permittivity of free space (ε₀), the reduced Planck constant (ℏ), and the speed of light (c).

Why Does α ≈ 1/137 Matter?

  • It determines the size of atoms (Bohr radius ∝ 1/α)
  • It sets the energy scale of atomic spectra
  • It's crucial for quantum electrodynamics (QED) calculations
  • A slightly different value would make carbon-based life impossible
03

Quantization of Charge

Fractional Elementary Charge

While all isolated particles have charges that are integer multiples of e, quarks carry fractional charges.

Quarks and Their Charges

Quarks are fundamental particles that combine to form hadrons (like protons and neutrons). Unlike all other known particles, quarks carry electric charges that are fractions of the elementary charge.

Quark Type Electric Charge
Up (u), Charm (c), Top (t) +⅔ e
Down (d), Strange (s), Bottom (b) −⅓ e
Proton Composition
u+⅔
+
u+⅔
+
d−⅓
=
+1e

A proton consists of 2 up quarks and 1 down quark: (+⅔) + (+⅔) + (−⅓) = +1

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Color Confinement

Quarks can never be observed in isolation due to a phenomenon called "color confinement." The strong force between quarks increases as they are pulled apart, making it energetically impossible to isolate a single quark. If you try to separate quarks, new quark-antiquark pairs are created instead.

Fractional Quantum Hall Effect

In certain two-dimensional systems at very low temperatures and strong magnetic fields, electrons form a highly correlated quantum state where the Hall conductance is quantized at fractional values.

In this fractional quantum Hall effect (FQHE), discovered in 1982, the current is carried by "quasiparticles" that behave as if they have a fractional electric charge (e.g., e/3). These are not fundamental particles but emergent phenomena arising from collective electron behavior.

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Nobel Prize 1998

Robert B. Laughlin, Horst L. Störmer, and Daniel C. Tsui received the Nobel Prize in Physics for their discovery and explanation of the fractional quantum Hall effect.

Dirac's Quantization Condition

In 1931, Paul Dirac proposed a theoretical argument for why electric charge is quantized. He showed that if a single magnetic monopole exists anywhere in the universe, then the quantization of electric charge follows automatically from quantum mechanics.

eg = nℏc2

where e is the elementary charge, g is the magnetic charge, n is an integer

Although magnetic monopoles have never been observed, Dirac's argument remains one of the most elegant theoretical explanations for charge quantization.

04

Experimental Measurements

1909-1913

Millikan Oil Drop Experiment

Robert A. Millikan's oil drop experiment was the first to directly measure the elementary charge with high precision.

How It Worked

  1. Tiny oil droplets were sprayed into a chamber between two metal plates
  2. The droplets became electrically charged by friction or X-ray ionization
  3. An electric field was applied to balance gravity, suspending individual droplets
  4. By measuring the voltage needed to suspend droplets, their charges were calculated
  5. All measured charges were integer multiples of a fundamental value: e ≈ 1.59 × 10⁻¹⁹ C
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Nobel Prize in Physics 1923 - Robert A. Millikan

Millikan Experiment Video
▶

Millikan's Oil Drop Experiment Explained

1962

Josephson Effect

When two superconductors are separated by a thin barrier, quantum tunneling of electron pairs creates a precise relationship between voltage and frequency.

KJ = 2e/h

The Josephson constant provides an extremely precise way to measure the elementary charge and forms the basis for modern voltage standards.

Laboratory Equipment
1980

Quantum Hall Effect

Klaus von Klitzing discovered that in 2D electron systems at low temperatures, the Hall resistance is quantized to precise values.

RK = h/e²

The von Klitzing constant allows precise determination of e and serves as the universal standard for electrical resistance.

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Nobel Prize 1985

2019

SI Redefinition

On May 20, 2019, the International System of Units (SI) was redefined. The elementary charge became one of seven defining constants with an exact value:

e = 1.602 176 634 × 10⁻¹⁹ C (exact)

This change means the ampere is now defined in terms of the elementary charge, rather than through the hypothetical force between infinite parallel wires.

Key Relationship

e = 2RK × KJ

The elementary charge can be precisely determined from the Josephson constant (KJ) and the von Klitzing constant (RK), both measurable with extremely high precision using quantum effects.

05

History & Discovery

1750s

Benjamin Franklin

Franklin proposed that electricity consists of a single fluid, introducing the concepts of positive and negative charge. He conducted famous experiments with lightning and invented the lightning rod.

1874

George Johnstone Stoney

Stoney estimated the magnitude of the "atom of electricity" based on Faraday's laws of electrolysis. In 1891, he coined the term "electron" for this fundamental unit of charge.

1897

J.J. Thomson

Thomson discovered the electron through cathode ray experiments, measuring its charge-to-mass ratio (e/m). This proved that atoms were not indivisible and contained smaller, negatively charged particles.

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Nobel Prize in Physics 1906

1909-1913

Robert A. Millikan

Millikan and Harvey Fletcher performed the oil drop experiment at the University of Chicago, providing the first precise measurement of the elementary charge: e ≈ 1.592 × 10⁻¹⁹ C.

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Nobel Prize in Physics 1923

1962

Brian D. Josephson

Josephson predicted that electron pairs could tunnel between superconductors, creating a precise relationship between voltage and frequency that would enable ultra-precise measurements of the elementary charge.

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Nobel Prize in Physics 1973

1980

Klaus von Klitzing

Von Klitzing discovered the quantum Hall effect, showing that electrical resistance in 2D systems is quantized. This provided another precise method for measuring the elementary charge.

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Nobel Prize in Physics 1985

1982

Fractional Quantum Hall Effect

Störmer and Tsui discovered fractional quantization of Hall conductance, revealing the existence of quasiparticles with fractional charge.

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Nobel Prize in Physics 1998 (with Laughlin)

2019

SI Redefinition

The elementary charge became one of seven defining constants of the SI, with its value fixed exactly. This marked a fundamental shift from artifact-based to constant-based definitions of units.

06

Applications

The elementary charge is fundamental to understanding a vast range of phenomena, from the structure of atoms to the operation of electronic devices.

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Atomic Structure

The electrostatic attraction between positively charged protons and negatively charged electrons, both carrying the elementary charge, holds atoms together and determines their chemical properties.

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Quantum Electrodynamics

QED, called "the jewel of physics," describes how light and matter interact. The elementary charge is the coupling constant that determines the strength of electromagnetic interactions at the quantum level.

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Chemistry & Bonding

Chemical reactions fundamentally involve the transfer or sharing of electrons. Understanding the elementary charge is essential for predicting molecular structures and reaction mechanisms.

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Electronics

Every electronic device relies on the flow of electrons through circuits. The elementary charge determines the fundamental limits of how small and fast electronics can become.

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Particle Physics

The Standard Model of particle physics classifies all known fundamental particles partly by their electric charge, expressed as multiples of e. This helps predict particle interactions and discoveries.

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Metrology

The exact value of the elementary charge now defines the ampere, the SI unit of electric current. This enables unprecedented precision in electrical measurements worldwide.

Coulomb's Law

The force between two charged particles is one of the most important equations in physics, and the elementary charge appears centrally in it:

F = 14πε₀ × q₁q₂r²

For two electrons separated by 1 nanometer, this force is about 2.3 × 10⁻¹⁰ N – tiny by everyday standards, but enormous at the atomic scale, about 1000 times stronger than the gravitational force between them.

08

References & Further Reading

📚 Wikipedia Articles

🏛️ Official Sources

🏆 Nobel Prize Lectures

🎬 Educational Videos

📝 How to Cite This Page

"Elementary Charge." 1.602176634.xyz. Accessed [Date]. https://1.602176634.xyz/