Mass
By mass–energy equivalence, the electronvolt is also a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c^{2}, where c is the speed of light in vacuum (from E = mc^{2}). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with c set to 1.^{[6]} The mass equivalent of 7000100000000000000♠1 eV/c^{2} is
- $1\;{\text{eV}}/c^{2}={\frac {(1.60217646\times 10^{-19}\;{\text{C}})\cdot 1\;{\text{V}}}{(2.99792458\times 10^{8}\;{\text{m}}/{\text{s}})^{2}}}=1.783\times 10^{-36}\;{\text{kg}}.$
For example, an electron and a positron, each with a mass of 6999511000000000000♠0.511 MeV/c^{2}, can annihilate to yield 6987163742436971400♠1.022 MeV of energy. The proton has a mass of 6999938000000000000♠0.938 GeV/c^{2}. In general, the masses of all hadrons are of the order of 7000100000000000000♠1 GeV/c^{2}, which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:
- 7000100000000000000♠1 GeV/c^{2} = 6973178300000000000♠1.783×10^{−27} kg.
The unified atomic mass unit (u), 1 gram divided by Avogadro's number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula:
- 1 u = 7002931494100000000♠931.4941 MeV/c^{2} = 6999931494100000000♠0.9314941 GeV/c^{2}.
Momentum
In high-energy physics, the electronvolt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., 6981160217648700000♠1 eV). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.
The dimensions of momentum units are LMT^{−1}. The dimensions of energy units are L^{2}MT^{−2}. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (LT^{−1}), facilitates the required conversion of using energy units to describe momentum. In the field of high-energy particle physics, the fundamental velocity unit is the speed of light in vacuum c.
By dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c.^{[7]} ^{[8]}
The fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity. For example, if the momentum p of an electron is said to be 6990160217648700000♠1 GeV, then the conversion to MKS can be achieved by:
- $p=1\;{\text{GeV}}/c={\frac {(1\times 10^{9})\cdot (1.60217646\times 10^{-19}\;{\text{C}})\cdot (1\;{\text{V}})}{(2.99792458\times 10^{8}\;{\text{m}}/{\text{s}})}}=5.344286\times 10^{-19}\;{\text{kg}}\cdot {\text{m}}/{\text{s}}.$
Distance
In particle physics, a system of "natural units" in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see mass–energy equivalence). In particular, particle scattering lengths are often presented in units of inverse particle masses.
Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:
- $\hbar ={{h} \over {2\pi }}=1.054\ 571\ 726(47)\times 10^{-34}\ {\mbox{J s}}=6.582\ 119\ 28(15)\times 10^{-16}\ {\mbox{eV s}}.$
The above relations also allow expressing the mean lifetime τ of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via Γ = ħ/τ. For example, the B^{0} meson has a lifetime of 1.530(9) picoseconds, mean decay length is cτ = 6996459699999999999♠459.7 μm, or a decay width of 6977689256324707400♠(4.302±25)×10^{−4} eV.
Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.
Energy in electronvolts is sometimes expressed through the wavelength of light with photons of the same energy: 1 eV = 8065.544005(49) cm^{−1}.
Temperature
In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to the Kelvin scale is defined by using k_{B}, the Boltzmann constant:
- ${1 \over k_{\text{B}}}={1.602\,176\,53(14)\times 10^{-19}{\text{ J/eV}} \over 1.380\,6505(24)\times 10^{-23}{\text{ J/K}}}=11\,604.505(20){\text{ K/eV}}.$
For example, a typical magnetic confinement fusion plasma is 6985240326473049999♠15 keV, or 170 MK.
As an approximation: k_{B}T is about 6979400544121750000♠0.025 eV (≈ 290 K/11604 K/eV) at a temperature of 7002293150000000000♠20 °C.
Properties
Energy of photons in the visible spectrum in eV
Graph of wavelength (nm) to energy (eV)
The energy E, frequency v, and wavelength λ of a photon are related by
- $E=h\nu ={\frac {hc}{\lambda }}$ $={\frac {(4.13566\,7516\times 10^{-15}\,{\mbox{eV}}\,{\mbox{s}})(299\,792\,458\,{\mbox{m/s}})}{\lambda }}$
where h is the Planck constant, c is the speed of light. This reduces to
- $E{\mbox{(eV)}}=4.13566\,7516\,{\mbox{feVs}}\cdot \nu \ {\mbox{(PHz)}}$ $={\frac {1\,239.84193\,{\mbox{eV}}\,{\mbox{nm}}}{\lambda \ {\mbox{(nm)}}}}.$^{[9]}
A photon with a wavelength of 6993532000000000000♠532 nm (green light) would have an energy of approximately 6981373307121471000♠2.33 eV. Similarly, 6981160217648700000♠1 eV would correspond to an infrared photon of wavelength 6994124000000000000♠1240 nm or frequency 7014241800000000000♠241.8 THz.
Scattering experiments
In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by scintillation light. For example, the yield of a phototube is measured in phe/keVee (photoelectrons per keV electron-equivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.
Energy comparisons
Photon frequency vs. energy particle in electronvolts. The
energy of a photon varies only with the frequency of the photon, related by speed of light constant. This contrasts with a massive particle of which the energy depends on its velocity and
rest mass.
^{[10]}^{[11]}^{[12]} Legend
- 7013841142655675000♠5.25×10^{32} eV: total energy released from a 20 kt nuclear fission device
- 7009195465531414000♠1.22×10^{28} eV: the Planck energy
- 10 YeV (7006160217648700000♠1×10^{25} eV): the approximate grand unification energy
- ~624 EeV (7001999758127888000♠6.24×10^{20} eV): energy consumed by a single 100-watt light bulb in one second (7002100000000000000♠100 W = 7002100000000000000♠100 J/s ≈ 7001999758127888000♠6.24×10^{20} eV/s)
- 300 EeV (7001480652946100000♠3×10^{20} eV = ~7001500000000000000♠50 J):^{[13]} the so-called Oh-My-God particle (the most energetic cosmic ray particle ever observed)
- 6996320435297400000♠2 PeV: two petaelectronvolts, the most high-energetic neutrino detected by the IceCube neutrino telescope in Antarctica^{[14]}
- 6994224304708180000♠14 TeV: the designed proton collision energy at the Large Hadron Collider (operated at about half of this energy since 30 March 2010, reached 13 TeV in May 2015)
- 6993160217648700000♠1 TeV: a trillion electronvolts, or 6993160200000000000♠1.602×10^{−7} J, about the kinetic energy of a flying mosquito^{[15]}
- 125.1±0.2 GeV: the energy corresponding to the mass of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma^{[16]}
- 6989336457062270000♠210 MeV: the average energy released in fission of one Pu-239 atom
- 6989320435297400000♠200 MeV: the average energy released in nuclear fission of one U-235 atom
- 6988281983061712000♠17.6 MeV: the average energy released in the fusion of deuterium and tritium to form He-4; this is 7014410000000000000♠0.41 PJ per kilogram of product produced
- 6987160217648700000♠1 MeV (6987160200000000000♠1.602×10^{−13} J): about twice the rest energy of an electron
- 6982217896002232000♠13.6 eV: the energy required to ionize atomic hydrogen; molecular bond energies are on the order of 6981160217648700000♠1 eV to 6982160217648700000♠10 eV per bond
- 6981256348237920000♠1.6 eV to 6981544740005580000♠3.4 eV: the photon energy of visible light
- 6981176239413570000♠1.1 eV: the energy E_{G} required to break a covalent bond in silicon
- 6981115356707063999♠720 meV: the energy E_{G} required to break a covalent bond in germanium
- 6979400544121749999♠25 meV: the thermal energy k_{B}T at room temperature; one air molecule has an average kinetic energy 6979608827065059999♠38 meV
- 7002230000000000000♠230 µeV: the thermal energy k_{B}T of the cosmic microwave background
Per mole
One mole of particles given 1 eV of energy has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F ≈ 7004964850000000000♠96485 C mol^{−1}) where the energy in joules of N moles of particles each with energy X eV is X·F·N.
See also
Notes and references
- ^ IUPAC Gold Book Archived 2009-01-03 at the Wayback Machine., p. 75
- ^ SI brochure, Sec. 4.1 Table 7 Archived July 16, 2012, at the Wayback Machine.
- ^ "CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-22.
2014 CODATA recommended values
- ^ "CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-22.
2014 CODATA recommended values
- ^ "Definitions of the SI units: Non-SI units". Archived from the original on 2009-10-31.
- ^ Barrow, J. D. "Natural Units Before Planck." Quarterly Journal of the Royal Astronomical Society 24 (1983): 24.
- ^ "Units in particle physics". Associate Teacher Institute Toolkit. Fermilab. 22 March 2002. Archived from the original on 14 May 2011. Retrieved 13 February 2011.
- ^ "Special Relativity". Virtual Visitor Center. SLAC. 15 June 2009. Retrieved 13 February 2011.
- ^ "CODATA Value: Planck constant in eV s". Archived from the original on 22 January 2015. Retrieved 30 March 2015.
- ^ What is Light? Archived December 5, 2013, at the Wayback Machine. – UC Davis lecture slides
- ^ Elert, Glenn. "Electromagnetic Spectrum, The Physics Hypertextbook". hypertextbook.com. Archived from the original on 2016-07-29. Retrieved 2016-07-30.
- ^ "Definition of frequency bands on". Vlf.it. Archived from the original on 2010-04-30. Retrieved 2010-10-16.
- ^ Open Questions in Physics. Archived 2014-08-08 at the Wayback Machine. German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.
- ^ "A growing astrophysical neutrino signal in IceCube now features a 2-PeV neutrino". Archived from the original on 2015-03-19.
- ^ Glossary Archived 2014-09-15 at the Wayback Machine. - CMS Collaboration, CERN
- ^ ATLAS; CMS (26 March 2015). "Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments". Physical Review Letters. 114 (19): 191803. arXiv:1503.07589 . Bibcode:2015PhRvL.114s1803A. doi:10.1103/PhysRevLett.114.191803 . PMID 26024162.
External links