Volts to Electron-Volts Conversion Guide

Introduction

Converting voltage to electron-volts (eV) bridges classical electrical engineering and quantum physics, providing a fundamental energy unit for atomic and subatomic processes. For a single electron, the conversion is direct: 1 volt equals 1 electron-volt exactly (E(eV) = V(V)). The electron-volt is defined as the energy gained by a single electron accelerated through 1 volt potential difference, equal to 1.602176634 × 10⁻¹⁹ joules. This unit is essential for understanding semiconductors, particle accelerators, X-ray systems, spectroscopy, and quantum phenomena because joules are impractically small for atomic-scale processes. Understanding this conversion enables engineers to calculate photon energies from wavelengths, determine semiconductor bandgaps, analyze particle accelerator energies, and design LED and solar cell systems based on quantum energy relationships.

This guide is designed for electrical engineers, physicists, and students working with quantum physics, semiconductors, spectroscopy, and particle physics applications. You will learn the fundamental conversion relationship, photon energy formulas, semiconductor bandgap calculations, particle accelerator energy scales, and standards for electron-volt measurements per CODATA 2018 and ISO 80000-1.

Quick Answer: How to Convert Volts to Electron-Volts?

For a single electron, volts convert directly to electron-volts: 1 volt = 1 eV exactly. The relationship is E(eV) = V(V) for single electrons.

Core Formula

$E\ (\text{eV}) = V$

For single electron: 1 volt = 1 eV exactly

Additional Formulas

Worked Examples

Reference Table

Key Standards

Converting volts to electron-volts bridges the gap between classical electrical engineering and quantum physics. The electron-volt (eV) is the fundamental energy unit for atomic and subatomic processes, essential for understanding semiconductors, particle accelerators, X-ray systems, spectroscopy, and quantum phenomena. This guide explains the physics behind this conversion and its applications in modern technology.

Understanding the Electron-Volt

What is an Electron-Volt?

An electron-volt (eV) is a unit of energy equal to the amount of kinetic energy gained by a single electron when accelerated through an electric potential difference of one volt in vacuum.

Definition:

$1 eV = e \times 1 V$

Where e is the elementary charge:

$e = 1.602176634 \times 10^{-19} coulombs (C)$

Therefore:

$1 eV = 1.602176634 \times 10^{-19} joules (J)$

Why Use Electron-Volts?

Joules are impractically small for atomic-scale phenomena:

• Energy to ionize hydrogen atom: $2.18 \times 10^{-18}$ J = 13.6 eV
• Photon of visible light: $3.2 \times 10^{-19}$ J = 2 eV
• X-ray photon: $1.6 \times 10^{-15}$ J = 10,000 eV = 10 keV

Electron-volts provide convenient, manageable numbers for quantum physics.

The Elementary Charge Constant

The elementary charge (e) is one of the fundamental physical constants:

$e = 1.602176634 \times 10^{-19} C (exact)$

As of May 20, 2019, this value is exact by definition in the revised SI system. Previously measured experimentally, it's now a defining constant.

Historical note: Robert Millikan's famous oil drop experiment (1909) first measured e with high precision, earning him the 1923 Nobel Prize.

Fundamental Volt to eV Conversion Formula

Single Electron Acceleration

When a single electron (charge = e) moves through potential difference V:

$E(eV) = V(V) \times \frac{e(C)}{e(C)} = V(V)$

Result: The numerical value is identical!

$E(eV) = V(V)$

Examples:

• 1 volt → 1 eV
• 100 volts → 100 eV
• 1000 volts → 1000 eV = 1 keV
• 1,000,000 volts → 1,000,000 eV = 1 MeV

Energy in Joules

To find absolute energy in joules:

$E(J) = V(V) \times e(C)$

$E(J) = V(V) \times 1.602176634 \times 10^{-19}$

Example: 5 V potential

$E = 5 \times 1.602176634 \times 10^{-19} = 8.011 \times 10^{-19} J$

Multiple Electrons or Ions

For particles with charge $q = n \times e$, where $n$ is the number of elementary charges:

$E(eV) = V(V) \times n$

Where:

• $n$ = Number of elementary charges (1 for electron/proton, 2 for He²⁺, 3 for N³⁺, etc.)
• $q = n \times e$ = Total particle charge
• $e = 1.602176634 \times 10^{-19}$ C = Elementary charge

Physical Explanation: When a particle with charge $q = n \times e$ is accelerated through potential difference $V$, it gains energy: $E = q \times V = n \times e \times V$

Since $1 \text{ eV} = e \times 1 \text{ V}$, the energy in electron-volts is: $E(eV) = \frac{n \times e \times V}{e \times 1 \text{ V}} = n \times V$

Examples:

• Doubly ionized helium (He²⁺, $n=2$): 100 V → $E = 100 \times 2 = 200$ eV
• Triply ionized nitrogen (N³⁺, $n=3$): 1000 V → $E = 1000 \times 3 = 3000$ eV = 3 keV
• Proton ($n=1$): Same as electron, 5000 V → $E = 5000 \times 1 = 5000$ eV = 5 keV
• Alpha particle (He²⁺, $n=2$): 1 MV → $E = 1,000,000 \times 2 = 2$ MeV

Important Note: The electron-volt is defined for a single electron. For multiply charged ions, the energy in eV is multiplied by the charge number $n$, but the unit "eV" still refers to the energy a single electron would gain.

Energy Ranges and Applications

The electron-volt scale spans enormous ranges across different physical phenomena:

Energy Scale Table

Thermal Energy at Room Temperature

At temperature $T$, average thermal energy:

$E_{\text{thermal}} = k_B T$

Where:

• $k_B = 1.380649 \times 10^{-23}$ J/K (Boltzmann constant)
• $T$ = Absolute temperature (kelvin)

At 300 K (27°C):

$E_{\text{thermal}} = 1.380649 \times 10^{-23} \times 300 = 4.142 \times 10^{-21} \text{ J}$

Convert to eV:

$E_{\text{thermal}} = \frac{4.142 \times 10^{-21}}{1.602176634 \times 10^{-19}} = 0.02586 \text{ eV} \approx 26 \text{ meV}$

Commonly stated: $kT \approx 0.026 \text{ eV}$ at room temperature.

This is why semiconductor devices are sensitive to temperature—thermal energy approaches operating energies! At room temperature, $kT$ is approximately 26 meV, which is comparable to the thermal voltage ($V_T = \frac{kT}{e} \approx 26$ mV) used in semiconductor device equations.

Photon Energy and Wavelength

Photons (light particles) have energy related to their wavelength and frequency.

Photon Energy Formula

$E = h \nu = \frac{hc}{\lambda}$

Where:

• h = Planck's constant = $6.62607015 \times 10^{-34}$ J·s
• $\nu$ (nu) = Frequency (Hz)
• c = Speed of light = $2.998 \times 10^8$ m/s
• $\lambda$ (lambda) = Wavelength (m)

Practical Formula in eV

For wavelength in nanometers (nm):

$E(eV) = \frac{1239.84}{\lambda(nm)}$

This is one of the most useful formulas in optics and spectroscopy!

Derivation

$E = \frac{hc}{\lambda} = \frac{6.62607015 \times 10^{-34} \times 2.998 \times 10^8}{\lambda}$

$E = \frac{1.98645 \times 10^{-25}}{\lambda}$

Convert to eV:

$E(eV) = \frac{1.98645 \times 10^{-25}}{\lambda \times 1.602176634 \times 10^{-19}} = \frac{1239.84 \times 10^{-9}}{\lambda}$

For $\lambda$ in nm:

$E(eV) = \frac{1239.84}{\lambda(nm)}$

Rounded versions:

• 1240/$\lambda$ (nm) — Most common
• 1240 eV·nm — Energy-wavelength constant

Visible Light Spectrum

Example: Green light at 520 nm

$E = \frac{1239.84}{520} = 2.38 eV$

Electromagnetic Spectrum Energy Ranges

Practical Examples

Example 1: Cathode Ray Tube (CRT)

Scenario: CRT television accelerates electrons through 25,000 V (25 kV). What energy do electrons gain?

Solution:

$E = 25000 eV = 25 keV$

In joules:

$E = 25000 \times 1.602176634 \times 10^{-19} = 4.005 \times 10^{-15} J$

Velocity (non-relativistic approximation):

$v = \sqrt{\frac{2E}{m_e}} = \sqrt{\frac{2 \times 4.005 \times 10^{-15}}{9.109 \times 10^{-31}}} = 9.38 \times 10^7 m/s$

Result: Electrons travel at 31% the speed of light!

Example 2: LED Emission

Scenario: Red LED emits 650 nm light. What is the photon energy?

Solution:

$E = \frac{1239.84}{650} = 1.91 eV$

This energy corresponds to the semiconductor bandgap. Electrons dropping across this bandgap emit red photons.

Forward potential: Approximately 1.9-2.0 V (matches photon energy!)

Example 3: Solar Cell Bandgap

Scenario: Silicon solar cell has bandgap of 1.12 eV. What wavelength photons can it absorb?

Solution: Rearrange photon energy formula:

$\lambda = \frac{1239.84}{E(eV)} = \frac{1239.84}{1.12} = 1107 nm$

Result: Silicon absorbs photons up to 1107 nm (near-infrared).

Implication: Longer wavelength infrared photons ($\lambda$ > 1107 nm) pass through without generating electricity—fundamental limit of silicon solar cells.

Example 4: Medical X-Ray Machine

Scenario: X-ray tube operates at 80 kV. What is the maximum X-ray photon energy?

Solution:

$E_{\text{max}} = 80000 eV = 80 keV$

Minimum wavelength (highest energy photons):

$\lambda_{\text{min}} = \frac{1239.84}{80000} = 0.0155 nm$

Note: This is the Duane-Hunt limit. Most X-ray photons have lower energies (continuous spectrum), but none exceed this maximum.

Example 5: Particle Accelerator

Scenario: Large Hadron Collider (LHC) accelerates protons to 6.5 TeV (6.5 trillion eV). What electrical potential would give this energy?

Theoretical V value:

$V = 6.5 \times 10^{12} V = 6.5 TV (teravolts)$

Practical reality: Impossible to create 6.5 trillion volt potential! Instead, LHC uses repeated acceleration through many lower voltages in circular path. Protons pass through accelerating sections millions of times.

In joules:

$E = 6.5 \times 10^{12} \times 1.602 \times 10^{-19} = 1.04 \times 10^{-6} J$

Comparison: This is comparable to kinetic energy of a flying mosquito (macroscopic!), but concentrated in a single subatomic particle!

Example 6: Photoelectric Effect

Scenario: Cesium work function is 2.14 eV. What minimum wavelength light causes photoemission?

Solution: Photon energy must exceed work function:

$E_{\text{photon}} \geq 2.14 eV$

$\lambda_{\text{max}} = \frac{1239.84}{2.14} = 579 nm$

Result: Yellow light (579 nm) or shorter wavelengths (higher energy) eject electrons. Red/orange light (longer $\lambda$, lower E) cannot, regardless of intensity.

This is the photoelectric effect that Einstein explained (Nobel Prize 1921), proving light's particle nature.

Semiconductor Applications

Energy Band Diagrams

Semiconductors are characterized by:

• Valence band: Filled with electrons
• Conduction band: Empty at 0 K
• Bandgap (Eg): Energy separation (in eV)

LED Color Selection

LED color is determined by semiconductor bandgap:

Red LED (AlGaAs): Eg = 1.9 eV → $\lambda$ = 650 nm Green LED (GaP): Eg = 2.26 eV → $\lambda$ = 549 nm Blue LED (GaN): Eg = 2.7 eV → $\lambda$ = 460 nm

Forward electric tension $\approx$ Bandgap energy (in volts numerically equals eV)

Solar Cell Selection

Ideal solar cell bandgap: 1.34 eV (Shockley-Queisser limit, 33.7% maximum efficiency).

Common materials:

• Silicon (1.12 eV): 29.4% max efficiency (theoretical)
• GaAs (1.43 eV): 33.5% max performance
• Perovskites (1.5-1.7 eV): Tunable, emerging technology

Spectroscopy and Analytical Applications

X-Ray Fluorescence (XRF)

Elements emit characteristic X-rays at specific energies:

Application: Material identification, coating thickness measurement.

Auger Electron Spectroscopy (AES)

Surface analysis technique measuring electron energies 50-2000 eV.

Example: Carbon KLL Auger peak at 272 eV identifies carbon on surface.

Photoelectron Spectroscopy (XPS/UPS)

Measures electron binding energies to identify chemical states.

Core level binding energies (eV):

• Carbon C 1s: 285
• Oxygen O 1s: 532
• Nitrogen N 1s: 400
• Iron Fe 2p₃/₂: 707

Ionization and Chemical Bonds

Ionization Energies

Energy to remove electron from atom:

Example: To ionize hydrogen (H → H⁺ + e⁻), electron must gain 13.6 eV.

Volt level equivalent: Accelerating electron through 13.6 V gives enough energy to ionize hydrogen.

Chemical Bond Energies

Conversion: 1 eV/molecule = 96.485 kJ/mol

Mass-Energy Equivalence

Einstein's famous equation in eV units:

$E = mc^2$

Electron rest mass energy:

$m_e c^2 = 0.511 MeV = 511 keV$

Proton rest mass energy:

$m_p c^2 = 938.3 MeV = 938,300 keV$

Neutron rest mass energy:

$m_n c^2 = 939.6 MeV$

High-energy physics notation: Particle masses often expressed in eV/c²:

• Electron: 511 keV/c²
• Proton: 938.3 MeV/c²
• Higgs boson: 125 GeV/c²

Temperature Conversion to eV

Thermal energy in electron-volts:

$E(eV) = \frac{k_B T}{e} = \frac{k_B}{e} \times T(K)$

Where $\frac{k_B}{e} = 8.617333 \times 10^{-5}$ eV/K

Formula:

$E(eV) = 8.617 \times 10^{-5} \times T(K)$

Examples:

Practical Calculations

Calculate Voltage Needed for Specific Energy

Problem: What potential accelerates electrons to 1 MeV?

Solution:

$V = 1,000,000 V = 1 MV (megavolt)$

Equipment: Medical linear accelerators (LINAC) for cancer therapy use 4-25 MV.

Calculate Photon Wavelength from Voltage

Problem: 100 kV X-ray tube produces maximum energy photons. What wavelength?

Step 1: Energy in eV

$E = 100,000 eV = 100 keV$

Step 2: Calculate wavelength

$\lambda = \frac{1239.84}{100000} = 0.0124 nm$

Result: 0.0124 nm (hard X-rays)

Calculate Required Photon Energy for Semiconductor

Problem: Design UV LED emitting at 365 nm. What bandgap semiconductor needed?

Solution:

$E_g = \frac{1239.84}{365} = 3.40 eV$

Material selection: GaN (3.44 eV) or AlGaN alloy—perfect match!

What Are the Advanced Topics in?

Relativistic Effects

At high energies (E $\approx$ mec² = 511 keV for electrons), relativistic corrections needed:

Total energy:

$E_{total} = \gamma m_e c^2$

Where:

$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$

Kinetic energy:

$E_{kinetic} = (\gamma - 1) m_e c^2$

Example: 1 MeV electron

$E_{kinetic} = 1 MeV, \quad m_e c^2 = 0.511 MeV$

$\gamma = 1 + \frac{1}{0.511} = 2.96$

$v = c\sqrt{1 - \frac{1}{\gamma^2}} = 0.94c$

Result: 94% speed of light—definitely relativistic!

Compton Scattering

High-energy photons scatter off electrons, losing energy:

$\lambda' - \lambda = \frac{h}{m_e c}(1 - \cos \theta)$

Compton wavelength: h/(mec) = 0.00243 nm

Significant for X-rays and gamma rays.

Pair Production

Photons with energy > 1.022 MeV (2mec²) can create electron-positron pairs:

$\gamma \to e^- + e^+$

Threshold: 1.022 MeV = twice electron rest mass energy

Standards and References

This guide follows:

• CODATA 2018: Recommended values of fundamental physical constants
• SI Brochure 9th Edition: International System of Units
• NIST Special Publication 330: The International System of Units (SI)
• ISO 80000-1: Quantities and Units
• IUPAC: Quantities, Units and Symbols in Physical Chemistry

Use our free Volts to Electron-Volts Calculator for instant conversions with photon wavelength calculations and CODATA 2018 compliant formulas.

Related quantum and energy tools:

• Joule to Watt Calculator - Convert energy over time to power
• Volt to Joule Calculator - Convert electrical potential to energy
• Volt to Watt Calculator - Compute power from voltage and current

Our calculations follow industry best practices and have been validated against real-world scenarios.

Conclusion

Converting volts to electron-volts reveals the quantum nature of electrical energy. For a single electron, the conversion is direct: E(eV) = V(V), where 1 volt equals 1 electron-volt exactly. The electron-volt is defined as the energy gained by a single electron accelerated through 1 volt potential difference, equal to 1.602176634 × 10⁻¹⁹ joules. This unit is essential for atomic and subatomic processes because joules are impractically small for quantum-scale phenomena. The photon energy formula E(eV) = 1239.84 / λ(nm) connects wavelength to energy, fundamental for LED design, solar cells, and spectroscopy. Semiconductor bandgap energy (in eV) numerically equals LED forward voltage (in volts), enabling direct conversion between quantum energy and electrical potential. Understanding this relationship enables proper design of quantum devices, particle accelerators, X-ray systems, and optoelectronic components.

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Key Takeaways

• Convert volts to electron-volts directly—for a single electron, 1 volt equals 1 electron-volt exactly (E(eV) = V(V)); this is the fundamental relationship
• Understand the elementary charge constant—e = 1.602176634 × 10⁻¹⁹ C exactly (no uncertainty); since 2019 SI redefinition, e is a defining constant
• Calculate photon energy from wavelength—E(eV) = 1239.84 / λ(nm) connects wavelength to energy; fundamental for LED design, solar cells, and spectroscopy
• Relate semiconductor bandgaps to voltage—bandgap energy (in eV) numerically equals LED forward voltage (in volts); electrons dropping across bandgap emit photons
• Use correct energy scales—meV (thermal), eV (chemistry), keV (X-rays), MeV (nuclear), GeV (particle accelerators); eV spans 15+ orders of magnitude
• Account for multiple charges—for multiply charged ions, E(eV) = V × n, where n is the number of elementary charges
• Apply to practical applications—LED color determined by bandgap (wavelength = 1240/Eg(eV)), solar cell absorption limits, X-ray photon energies

Further Learning

• Volt to Joule Guide - Converting voltage to energy in joules
• Volt to Watt Guide - Converting voltage to power
• Joule to Watt Guide - Converting energy to power
• Capacitor Energy Guide - Understanding energy storage
• Volt to eV Calculator - Interactive calculator for electron-volt conversion

References & Standards

This guide follows established engineering principles and standards. For detailed requirements, always consult the current adopted edition in your jurisdiction.

Primary Standards

CODATA 2018 Recommended values of fundamental physical constants. Defines elementary charge e = 1.602176634 × 10⁻¹⁹ C exactly (no uncertainty). Since the 2019 SI redefinition, e is a defining constant. The electron-volt is defined as 1 eV = e × 1 V = 1.602176634 × 10⁻¹⁹ J.

ISO 80000-1 Quantities and units. Defines electron-volt (eV) as an accepted non-SI unit for energy, commonly used in atomic, nuclear, and particle physics.

SI Brochure 9th Edition The International System of Units (SI). Provides official definitions of SI units and accepted non-SI units including the electron-volt.

Supporting Standards & Guidelines

IEC 60050 - International Electrotechnical Vocabulary International standards for electrical terminology and definitions, including quantum physics terms.

Further Reading

• NIST Special Publication 330 - The International System of Units (SI) - Official NIST guide to SI units

Note: Standards and codes are regularly updated. Always verify you're using the current adopted edition applicable to your project's location. Consult with local authorities having jurisdiction (AHJ) for specific requirements.

Disclaimer: This guide provides general technical information based on international electrical and physics standards. Always verify calculations with applicable standards (CODATA, ISO, SI) and consult licensed professionals for actual applications. Component ratings and specifications may vary by manufacturer.