electronvolt

Non-SI unit accepted for use with the SI

Name	Symbol	Quantity		SI units
electronvolt	eV	energy	1.602 176 634 × 10⁻¹⁹ J
The electronvolt, symbol eV, is a non-SI unit of energy accepted for use with the SI. One electronvolt is equal to the kinetic energy acquired by one electron in passing through a potential difference of one volt in vacuum.
Definition				h Δν_Cs
$1 \mspace{4mu} \text{eV} \mspace{6mu} = \dfrac{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}\\ \\ \\ 1 \mspace{4mu} \text{eV} \mspace{6mu} \approx 2.630 \mspace{4mu} 355 \mspace{4mu} 813 \mspace{4mu} 855 \mspace{4mu} 163 \mspace{4mu} 441 \times10^{4} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}$

One volt is equal to one joule per coulomb. It follows that the value of one electronvolt, in terms of joules, can be found by multiplying the magnitude of the charge carried by one electron, expressed in coulombs, by one volt.

Defining constants

The volt is defined by the equation:

$1 \mspace{4mu} \text{V} \mspace{6mu} = \dfrac{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} \dfrac{h \mspace{4mu} \Delta \nu _{Cs}}{e}$

Multiplying both sides of this equation by the elementary charge, e, gives the SI definition for the electronvolt:

$1 \mspace{4mu} \text{eV} \mspace{6mu} = \dfrac{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}$

Similarly, the joule is defined by the equation:

$1 \mspace{4mu} \text{J} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}$

Multiplying both sides of this equation by the numeric value of the elementary charge gives the definition for the value of one electronvolt in joules:

$1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19} \mspace{4mu} \text{J} \mspace{6mu} = \dfrac{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}$

Particle physics

The magnitude of the charge on one electron is equal to the elementary charge, e, which is defined as 1.602 176 634 × 10⁻¹⁹ C.

The electronvolt is often combined with the SI prefixes, and is typically used to measure the energies of elementary particles.

Unit of mass

Since mass is related to energy through Einstein’s mass-energy equivalence equation, E = mc², the masses of elementary particles can be expressed in terms of electronvolts, and c, where c is the speed of light in vacuum.

$1 \mspace{4mu} \text{eV}/c^2 \mspace{18mu} = \mspace{4mu} \dfrac{1.602\ 176\ 634 \times 10^{-19}\ \text{J}} {(299\ 792\ 458\ \text{m s}^{-1})^2}\\ \\ \\ 1 \mspace{4mu} \text{eV}/c^2 \mspace{19mu} = \mspace{4mu} 1.782\ 661\ 921\ 627... \times 10^{-36} \mspace{6mu} \text{kg}\\ \\ 1 \mspace{4mu} \text{MeV}/c^2 \mspace{4mu} = \mspace{4mu} 1.782\ 661\ 921\ 627... \times 10^{-30} \mspace{6mu} \text{kg}\\ \\ 1 \mspace{4mu} \text{GeV}/c^2 \mspace{6mu} = \mspace{4mu} 1.782\ 661\ 921\ 627... \times 10^{-27} \mspace{6mu} \text{kg}$

The eV/c² is not accepted for use with the SI.

Examples of masses of elementary particles

Quarks

Name	Mass in MeV/c²	Mass in SI units
up	2.2	3.92 × 10⁻³⁰ kg
down	4.6	8.2 × 10⁻³⁰ kg
charm	1 280	2.28 × 10⁻²⁷ kg
strange	96	1.71 × 10⁻²⁸ kg
top	173 100	3.086 × 10⁻²⁵ kg
bottom	4 180	7.45 × 10⁻²⁷ kg
Leptons
electron	0.511	9.109 × 10⁻³¹ kg
muon	105.658	1.883 52 × 10⁻²⁸ kg
tau	1 776.86	3.167 54 × 10⁻²⁷ kg
Bosons
Name	Mass in GeV/c²	Mass in SI units
W boson	80.369	1.432 708 × 10⁻²⁵ kg
Z boson	91.1880	1.625 573 × 10⁻²⁵ kg
Higgs boson	125.11	2.230 288 × 10⁻²⁵ kg