Joule to Electronvolt Converter

The electronvolt (symbol: eV) is a unit of energy defined as the amount of kinetic energy gained (or lost) by a single electron when it moves through an electric potential difference of exactly one volt in vacuum.

Fundamental Definition

Mathematical Expression:

1 eV = e × 1 V

Where:

• e = elementary charge = 1.602176634 × 10⁻¹⁹ coulombs (exact, since 2019 SI redefinition)
• V = volt (SI unit of electric potential)

Since 1 volt = 1 joule per coulomb (J/C), we have:

1 eV = (1.602176634 × 10⁻¹⁹ C) × (1 J/C) = 1.602176634 × 10⁻¹⁹ J

This value is now exact by definition following the 2019 SI redefinition.

Physical Interpretation

Imagine a single electron starting at rest:

1. Place electron at negative terminal of a 1-volt battery
2. Let electron accelerate to the positive terminal through the electric field
3. Kinetic energy gained by the electron = 1 electronvolt

The electron's final velocity would be approximately 593 km/s (ignoring relativistic effects), with kinetic energy:

KE = ½mv² = 1 eV = 1.602 × 10⁻¹⁹ J

Common Prefixes and Multiples

Standard SI Prefixes:

• meV (millielectronvolt) = 10⁻³ eV = 1.602 × 10⁻²² J (thermal energies, superconducting gaps)
• eV (electronvolt) = 1.602 × 10⁻¹⁹ J (atomic physics, visible light)
• keV (kiloelectronvolt) = 10³ eV = 1.602 × 10⁻¹⁶ J (X-rays, inner electrons)
• MeV (megaelectronvolt) = 10⁶ eV = 1.602 × 10⁻¹³ J (nuclear physics, gamma rays)
• GeV (gigaelectronvolt) = 10⁹ eV = 1.602 × 10⁻¹⁰ J (particle accelerators, rest masses)
• TeV (teraelectronvolt) = 10¹² eV = 1.602 × 10⁻⁷ J (LHC, highest-energy physics)
• PeV (petaelectronvolt) = 10¹⁵ eV = 0.1602 J (cosmic rays, ultra-high-energy astrophysics)

Electronvolt as Unit of Mass (E=mc²)

Through Einstein's mass-energy equivalence E = mc², the electronvolt can express mass:

Mass Unit: eV/c² (electronvolt divided by speed of light squared)

Conversion:

1 eV/c² = 1.782661921 × 10⁻³⁶ kg

Examples:

• Electron mass: me = 510.9989 keV/c² = 9.109 × 10⁻³¹ kg
• Proton mass: mp = 938.2720 MeV/c² = 1.673 × 10⁻²⁷ kg
• Neutron mass: mn = 939.5654 MeV/c² = 1.675 × 10⁻²⁷ kg
• Higgs boson mass: mH ≈ 125 GeV/c² (discovered 2012, CERN LHC)

Particle physicists routinely express masses in MeV/c² or GeV/c², often abbreviated to just MeV or GeV when context is clear.

The electronvolt's development parallels the history of atomic and nuclear physics in the early 20th century.

Pre-History: Early Electron Research (1897-1920s)

1897: J.J. Thomson discovers the electron using cathode ray tubes, observing electrons accelerated through electric potentials of hundreds of volts.

1909-1913: Robert Millikan's oil drop experiment precisely measures the elementary charge: e ≈ 1.6 × 10⁻¹⁹ C.

1913: Niels Bohr's model of the hydrogen atom calculates ionization energy as 13.6 eV (though he expressed it in ergs or joules).

1920s: Early atomic spectroscopy and quantum mechanics developments naturally worked with energies on the eV scale, though researchers still used CGS units (ergs) or SI joules.

Formalization (1930s-1940s)

Early 1930s: The term "electronvolt" begins appearing in physics literature as particle accelerators (cyclotrons, Van de Graaff generators) accelerate particles through kilovolt and megavolt potentials.

Key Motivation:

• Expressing X-ray energies: 10-100 keV far more intuitive than 10⁻¹⁵ to 10⁻¹⁴ J
• Nuclear reaction energies: Alpha particles with 5 MeV vs. 8 × 10⁻¹³ J
• Particle accelerator beam energies: 1 MeV proton beam vs. 1.6 × 10⁻¹³ J

1932: Carl Anderson discovers the positron (antimatter electron) in cosmic rays, with energies described in MeV.

1930s-1940s: Manhattan Project and nuclear weapons research standardized MeV for nuclear fission and fusion energies.

Post-War Standardization (1950s-1960s)

1948: 9th CGPM (General Conference on Weights and Measures) defines the ampere, indirectly fixing the volt and thus the electronvolt's joule equivalent.

1950s-1960s: Particle physics accelerators (synchrotrons, bevatrons) reach GeV energies:

• Brookhaven Cosmotron (1952): 3 GeV
• Berkeley Bevatron (1954): 6 GeV (first antiproton production)
• CERN Proton Synchrotron (1959): 28 GeV

Standard Practice: By the 1960s, eV/keV/MeV/GeV were universally adopted in atomic, nuclear, and particle physics.

Modern Era (1970s-Present)

1970s-1980s: TeV-scale energies anticipated and achieved:

• Fermilab Tevatron (1983): 1.96 TeV proton-antiproton collisions

2008-Present: CERN Large Hadron Collider (LHC):

• Design energy: 14 TeV (7 TeV per beam)
• Higgs boson discovery (2012): 125 GeV/c² mass
• Current: 13.6 TeV collision energy (2022-2025 Run 3)

2019 SI Redefinition:

• Elementary charge e defined exactly: 1.602176634 × 10⁻¹⁹ C
• Makes 1 eV = 1.602176634 × 10⁻¹⁹ J exact by definition
• Electronvolt recognized in SI Brochure as accepted non-SI unit

Beyond Accelerators:

• Semiconductor physics: Band gaps measured in eV (Si: 1.1 eV, GaN: 3.4 eV)
• Photovoltaics: Solar cell efficiency tied to band gap energies (1.1-1.7 eV optimal)
• Astronomy: Cosmic ray energies up to 10²⁰ eV (Oh-My-God particle, 1991)

Atomic and Molecular Physics

Scientists use eV to describe:

• Ionization energies: Energy required to remove electrons from atoms
• Electron affinity: Energy released when electron attaches to atom
• Molecular orbital energies: HOMO-LUMO gaps, band structures
• Spectroscopy: Photon energies in UV-vis spectroscopy (200-800 nm ≈ 6-1.5 eV)

Example: UV photoelectron spectroscopy (UPS) measures electron binding energies from 0-50 eV.

Nuclear and Particle Physics

The electronvolt (especially MeV, GeV, TeV) is the universal energy unit:

Particle Accelerators:

• Beam energies: "The LHC collides protons at 6.8 TeV per beam"
• Collision center-of-mass energy: √s = 13.6 TeV

Nuclear Reactions:

• Q-values: Energy released/absorbed (e.g., D-T fusion Q = 17.6 MeV)
• Decay energies: Alpha, beta, gamma emissions

Particle Properties:

• Rest masses: Particle Data Group lists masses in MeV/c² or GeV/c²
• Decay channels: Energy distributions of decay products

Semiconductor Device Physics

Band gap energies determine electronic and optical properties:

Applications:

• Solar cells: Optimal band gap ~1.3-1.5 eV for maximum efficiency under solar spectrum
• LEDs: Emission color determined by band gap (red ~1.8 eV, blue ~3.1 eV)
• Transistors: Threshold voltages and switching energies
• Detectors: Ionization energies for particle detection (Si: 3.6 eV per electron-hole pair)

Radiation Dosimetry and Medical Physics

X-ray and gamma-ray energies specified in keV or MeV:

Medical Imaging:

• Mammography: 25-35 keV (soft tissue contrast)
• CT scans: 80-140 keV
• PET scans: 511 keV (positron-electron annihilation photons)

Radiation Therapy:

• External beam: 6-18 MeV photon beams
• Proton therapy: 70-250 MeV proton beams

Astrophysics and Cosmology

Photon energies across the electromagnetic spectrum:

Radio to Infrared: μeV to eV (microwave background ~0.0002 eV) Visible: 1.8-3.1 eV X-ray: keV to MeV (neutron star accretion, supernovae) Gamma-ray: MeV to GeV (active galactic nuclei, gamma-ray bursts) Ultra-high-energy cosmic rays: EeV (10¹⁸ eV) and beyond

Example: Fermi Gamma-ray Space Telescope detects photons from 20 MeV to >300 GeV.

Materials Science and Catalysis

Surface science and chemical reactions:

Techniques:

• XPS (X-ray Photoelectron Spectroscopy): Binding energies 0-1500 eV
• UPS (UV Photoelectron Spectroscopy): Valence band energies 0-50 eV
• Auger Electron Spectroscopy: Electron energies 50-2000 eV

Catalysis:

• Activation barriers: 0.1-3 eV for chemical reactions
• Adsorption energies: 0.5-5 eV for molecules on surfaces