elementary charge

SI defining constant

Name	Symbol	Base units
elementary charge	e	s A
The elementary charge, symbol e, is a physical constant. It is the electric charge carried by a single proton or, equivalently, the magnitude of the electric charge carried by a single electron, which has charge −e. The numerical value of the elementary charge, symbol e, is defined to be exactly 1.602 176 634 × 10⁻¹⁹ when expressed in the unit coulomb, symbol C, or s A.
$e = 1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19} \mspace{6mu} \text{C}$

Electric charge

The fixed numerical value of the elementary charge, e, is defined exactly:

$e \mspace{4mu} = 1.602\ 176\ 634 \times 10^{-19} \ \text{C}$

Inverting this relation gives an exact expression for the unit of electric charge, the coulomb, in terms of the elementary charge, e :

$1 \mspace{4mu} \text{C} \mspace{6mu} = \dfrac{1}{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}} \mspace{6mu} e$

Electric current

The elementary charge, e, together with the caesium frequency, Δν_Cs, forms the basis for the definition of the unit of electric current, the ampere.

The definition of the ampere implies the exact relation:

$\Delta \nu _{Cs} \mspace{4mu} e \mspace{4mu} = (9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}) \ \text{A}$

Inverting this relation gives an exact expression for the ampere in terms of the elementary charge, e, and the caesium frequency, Δν_Cs :

$1 \mspace{4mu} \text{A} \mspace{4mu} = \dfrac{1}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})} \mspace{4mu} \Delta \nu _{Cs} \mspace{4mu} e\\$

The Faraday constant

The Faraday constant, symbol F, is the molar equivalent of the elementary charge. It is named after the English scientist Michael Faraday.

It is equal to the total electric charge of one mole of particles, each with an electric charge equal to the elementary charge, e.

The Faraday constant is equal to the product of two of the SI defining constants – the elementary charge, e, and the Avogadro constant, N_A.

$F \ = e \mspace{4mu} N_A \\ \\ F \ = 1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19} \mspace{4mu} \text{C} \mspace{4mu} \times \mspace{4mu} 6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23} \mspace{4mu} \text{mol}^{-1} \\ \\ F \ = 9.648 \mspace{4mu} 533 \mspace{4mu} 212 \mspace{4mu} 331 \mspace{4mu} 001 \mspace{4mu} 84 \times 10^4 \mspace{6mu} \text{C} \mspace{4mu} \text{mol}^{-1}$

The Josephson constant

The relation between the elementary charge, e, and the Planck constant, h, forms the definition of the Josephson constant, K_J, named after British physicist Brian D. Josephson:

$K_{J} = \dfrac{2e} {h}\\ \\ \\ K_{J} = \dfrac{2 \times (1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19} \ \text{C})} {6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34} \mspace{4mu} \text{J} \ \text{s}}\\ \\ \\ K_{J} = 483 \mspace{4mu} 597.848 \mspace{4mu} 416 \mspace{4mu} 983 \mspace{4mu} 632 \mspace{4mu} 447 \mspace{4mu} 658 \mspace{4mu} 285 \mspace{4mu} \text{...} \mspace{4mu} \text{GHz} / \text{V}$

When two superconductors are weakly coupled, e.g. by separating them with an insulating layer just a few nanometres thick, they form a Josephson junction. Exposure of a Josephson junction to microwaves creates voltage levels between the superconductors in exactly quantized steps. This phenomenon is known as the Josephson effect.

The magnitude of the voltage generated at each quantized step is directly proportional to the quotient ^h⁄_2e, and therefore indirectly proportional to the Josephson constant.

The von Klitzing constant

The relation between the elementary charge, e, and the Planck constant, h, also forms the definition of the von Klitzing constant, R_K, named after German physicist Klaus von Klitzing:

$R_{K} = \dfrac{h} {e^2}\\ \\ \\ R_{K} = \dfrac{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34} \mspace{4mu} \text{J} \ \text{s}} {(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19} \ \text{C})^2}\\ \\ \\ R_{K} = 25 \mspace{4mu} 812.807 \mspace{4mu} 459 \mspace{4mu} 304 \mspace{4mu} 506 \mspace{4mu} 660 \mspace{4mu} 045 \mspace{4mu} \text{...} \mspace{4mu} \Omega$

If a current of ultracold electrons, flowing in the form of a sheet thin enough to be regarded as two-dimensional, is exposed to a strong magnetic field perpendicular to the sheet, electrical resistance across the width of the current stream develops in exactly quantized steps. This phenomenon is known as the quantum Hall effect.

The magnitude of the resistance at each quantized step is directly proportional to the von Klitzing constant.

Resistance

The von Klitzing constant forms the basis for the definition of the unit of electrical resistance, the ohm:

Expressed in SI units, the quotient ^h⁄_e² has the exact value:

$\dfrac{h}{e^2} \mspace{6mu} = \dfrac{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}}{(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2} \mspace{6mu} \Omega$

Inverting this relation gives an exact expression for the ohm in terms of the elementary charge, e, and the Planck constant, h :

$1 \mspace{4mu} \Omega \mspace{6mu} = \dfrac{(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2}{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}} \mspace{6mu} \dfrac{h}{e^2}$

Particle physics

Atoms are composed of subatomic particles called protons, neutrons and electrons. These particles have electric charge of either +e, –e or 0.

Particle	Charge in e	Charge in SI units
electron	-1	-1.602 176 634 × 10⁻¹⁹ C
proton	+1	1.602 176 634 × 10⁻¹⁹ C
neutron	0	0 C

The Standard Model of particle physics describes 6 subatomic particles called quarks. These particles have electric charge of either +⅔e or -⅓e. The exact numerical value of the electric charge of these particles expressed in coulombs follows from the definition of the value of e:

Quark	Charge in e	Charge in SI units
up	+⅔	1.068 117 756 × 10⁻¹⁹ C
down	-⅓	-0.534 058 878 × 10⁻¹⁹ C
charm	+⅔	1.068 117 756 × 10⁻¹⁹ C
strange	-⅓	-0.534 058 878 × 10⁻¹⁹ C
top	+⅔	1.068 117 756 × 10⁻¹⁹ C
bottom	-⅓	-0.534 058 878 × 10⁻¹⁹ C

A proton is composed of two up quarks of charge +⅔e and one down quark of charge –⅓e, giving a total charge of +1e. A neutron is composed of one up quark of charge +⅔e and two down quarks of charge –⅓e, giving a total charge of 0e.