OCR Specification focus:
‘The electronvolt (eV) is the energy gained by charge e through potential difference of one volt.’
In physics, energy is often expressed in joules, but for processes involving individual particles, such as electrons or photons, this unit becomes impractically large. The electronvolt (eV) provides a more convenient and intuitive scale, allowing physicists to describe and compare microscopic energy exchanges that occur in atomic and quantum phenomena with clarity and precision.
Understanding the Electronvolt
Definition of the Electronvolt
Electronvolt (eV): The energy gained by an electron (charge e) when it moves through an electric potential difference of one volt.
When an electron is accelerated by a potential difference, it experiences a change in energy equal to the product of its charge and the voltage.
Electron accelerated between charged plates. The diagram shows an electron gun where an electron moves from the negatively charged plate to the positively charged plate, gaining kinetic energy KE=qVKE = qVKE=qV equal to the loss of electric potential energy. This illustrates the electronvolt as the energy gained through a 1 V potential difference, matching the definition used in quantum physics. Source.
This makes the electronvolt a practical unit for measuring small energy changes that occur within atoms, molecules, and subatomic particles.
Relationship to the Joule
While the joule (J) is the SI unit of energy, it is far too large for describing quantum-scale processes. The conversion factor between these units bridges the microscopic and macroscopic scales:
EQUATION
—-----------------------------------------------------------------
Energy Conversion
1 eV = 1.602 × 10⁻¹⁹ J
e = Elementary charge = 1.602 × 10⁻¹⁹ C
V = Potential difference = 1 V
—-----------------------------------------------------------------
Thus, one electronvolt represents a minuscule amount of energy — approximately one quintillionth of a joule — yet it is still significant at the atomic level.
Why the Electronvolt is Useful
The electronvolt is used throughout atomic physics, nuclear physics, and quantum mechanics because it directly relates the potential energy of a charged particle to an easily measurable electrical quantity. This eliminates the need for repeated conversions between joules and volts in experimental work.
Practical Benefits
Simplifies calculations involving energy changes due to electrical potentials.
Scales appropriately for subatomic energies — electrons in atoms, for example, typically have binding energies of a few eV.
Facilitates comparison between energies of different phenomena, such as photon energies and atomic transitions.
Common unit in spectroscopy, photoelectric experiments, and semiconductor physics.
For instance, the visible spectrum of light corresponds to photon energies of roughly 1.6 eV (red) to 3.1 eV (violet), making the electronvolt ideal for describing these energies.
Visible photon energies in electronvolts. The graphic maps colours from red to violet onto a horizontal energy scale in eV, visually connecting wavelength and photon energy via E=hf=hc/λE = hf = hc/\lambdaE=hf=hc/λ. This directly supports using the electronvolt for optical photons; the diagram includes only visible-range values and is deliberately uncluttered. Source.
Relating Electronvolts to Charge and Voltage
Energy Gain of a Charged Particle
The relationship between a charged particle’s energy change and the potential difference it experiences can be expressed as:
EQUATION
—-----------------------------------------------------------------
Energy from Potential Difference
E = qV
E = Energy gained or lost (J)
q = Charge on the particle (C)
V = Potential difference (V)
—-----------------------------------------------------------------
For an electron (charge = e), this becomes E = eV, meaning that when it moves through a potential difference of 1 volt, it gains or loses 1 electronvolt of energy. This direct proportionality allows the electronvolt to link electrical and mechanical perspectives of energy effortlessly.
Use of the Electronvolt in Quantum Physics
Photon Energies
In quantum physics, light is described as discrete packets of energy called photons. The energy of a photon is related to its frequency or wavelength by:
EQUATION
—-----------------------------------------------------------------
Photon Energy Equation
E = hf = hc/λ
E = Photon energy (J or eV)
h = Planck’s constant = 6.63 × 10⁻³⁴ J·s
f = Frequency (Hz)
c = Speed of light = 3.00 × 10⁸ m/s
λ = Wavelength (m)
—-----------------------------------------------------------------
Physicists often express E in electronvolts rather than joules, as it aligns more naturally with the energy ranges observed in experiments. For example, a green photon with a wavelength of 500 nm has an energy of about 2.5 eV — a much more practical figure than its joule equivalent.
Atomic and Nuclear Energy Scales
Different physical processes operate over characteristic energy ranges, conveniently expressed in eV multiples:
Atomic binding energies: typically 1–10 eV.
Ionisation energies: tens of eV.
Nuclear binding energies: millions of eV, or MeV (mega-electronvolts).
High-energy particle physics: billions of eV, or GeV (giga-electronvolts).
These extended units allow for consistent scaling without changing the base unit concept.
Electronvolt Multiples:
1 keV = 10³ eV
1 MeV = 10⁶ eV
1 GeV = 10⁹ eV
Each step represents three orders of magnitude, enabling concise expression of both atomic and cosmic energies.
Measuring and Interpreting Energy in eV
In Experimental Contexts
When designing or analysing experiments involving electrons, photons, or other charged particles, energies are frequently measured in eV. Examples include:
Determining the work function of a metal surface in the photoelectric effect, where photon energy must exceed this threshold to release electrons.
Measuring excitation and ionisation energies in spectroscopy, where energy levels of atoms are separated by discrete electronvolt differences.
Describing semiconductor band gaps, typically a few eV wide, dictating electrical properties of materials used in LEDs and solar cells.
Visualising the Scale
An energy change of a few electronvolts corresponds to motion of individual electrons in atoms, while mega- or giga-electronvolts describe processes involving nuclei or subatomic particles in accelerators. This adaptability across scales makes the electronvolt a cornerstone of modern physics language.
Summary of Key Points
Although not an SI unit, the electronvolt (eV) is universally accepted in physics due to its direct link between electric potential and energy and its suitability for microscopic scales. It provides a bridge between measurable electrical quantities and the energy of quantum processes, fulfilling the OCR specification requirement:
“The electronvolt (eV) is the energy gained by charge e through potential difference of one volt.”
FAQ
The electronvolt is not part of the International System of Units (SI) because it is defined using the elementary charge and volt, which are derived from SI units rather than being fundamental.
However, it is accepted for use alongside SI units due to its practicality in expressing microscopic energies. The electronvolt conveniently matches the scale of energy changes in atoms, photons, and subatomic particles, whereas the joule is too large for these processes.
Yes. Any particle with a single elementary charge (+e or –e) gains or loses 1 eV of energy when moving through a potential difference of 1 V.
Particles with multiple charges gain energy in proportion to their charge:
A proton (+e) gains 1 eV through 1 V.
An alpha particle (+2e) gains 2 eV through 1 V.
Thus, the electronvolt measures energy per unit charge, not specifically for electrons.
Energies at atomic, nuclear, and particle levels span wide ranges. Expressing all values in plain eV would involve awkwardly large numbers.
keV (10³ eV) suits X-ray photon or electron energies.
MeV (10⁶ eV) fits nuclear binding energies and radioactivity.
GeV (10⁹ eV) is typical for high-energy particle physics.
Using these multiples keeps numbers manageable and allows for quick comparison between phenomena across different energy scales.
The electronvolt can be connected to temperature through the Boltzmann constant (k), where 1 eV ≈ 1.16 × 10⁴ K.
This means that particles with thermal energy of 1 eV have an equivalent temperature of about 11,600 K.
This relationship is useful in plasma physics and astrophysics, where temperatures are so high that thermal energies are better expressed in electronvolts rather than kelvin.
Energy levels in atoms and molecules are often separated by values in the order of electronvolts.
Ionisation energies (energy required to remove an electron) typically range from 3–25 eV.
Electronic transitions between atomic orbitals often involve fractions or a few eV.
This makes the electronvolt ideal for quantifying the discrete energy differences observed in spectroscopy and explaining how photons of specific energies correspond to emitted or absorbed light.
Practice Questions
Question 1 (2 marks)
Define the electronvolt (eV) and state its value in joules.
Mark scheme:
• 1 mark for stating that the electronvolt is the energy gained by an electron when it moves through a potential difference of one volt.
• 1 mark for quoting or calculating the correct conversion value: 1 eV = 1.602 × 10⁻¹⁹ J.
Question 2 (5 marks)
An electron is accelerated from rest through a potential difference of 5000 V.
(a) Calculate the energy gained by the electron in electronvolts.
(b) Convert this energy into joules.
(c) Explain why the electronvolt is a more convenient unit than the joule for describing energy changes at the atomic or subatomic scale.
Mark scheme:
(a) Energy in eV = 5000 eV (1 mark for using E = eV).
(b) Energy in J = 5000 × 1.602 × 10⁻¹⁹ = 8.01 × 10⁻¹⁶ J (1 mark for correct substitution, 1 mark for correct answer and units).
(c)
• 1 mark for stating that the electronvolt is more suitable for very small energies typical of electrons, atoms, or photons.
• 1 mark for explaining that values expressed in joules are inconveniently small (e.g. 10⁻¹⁹ J range).
• 1 mark for recognising that using eV simplifies comparison and calculation in quantum and atomic physics.
