The big idea: The joule (J) is huge for a single particle. Atomic and nuclear energies are tiny fractions of a joule, so physicists use a smaller unit: the electronvolt (eV).
One electronvolt is the energy gained by one electron (charge e) when it is pushed through a potential difference of one volt.
That works out to a fixed amount of energy:
1 eV = 1.60 × 10⁻¹⁹ J
Spot it: The eV is just a unit of energy, like the joule — not a new kind of energy.
The number 1.60 × 10⁻¹⁹ is the elementary charge e in coulombs. That is no coincidence: energy = charge × voltage, so e coulombs × 1 volt = 1.60 × 10⁻¹⁹ J.
Bigger eV units: Like metres → kilometres, the eV has bigger cousins:
- 1 keV (kilo-electronvolt) = 10³ eV - 1 MeV (mega-electronvolt) = 10⁶ eV
Atomic-transition energies are a few eV; nuclear (decay, binding) energies are a few MeV.
Everything rests on one given number: 1 eV = 1.60 × 10⁻¹⁹ J. To go each way:
The two directions
- eV → J: multiply by 1.60 × 10⁻¹⁹ (you have many eV, each worth a tiny number of joules)
- J → eV: divide by 1.60 × 10⁻¹⁹ (you are counting how many eV fit into the energy)
- the energy expressed in joules (J)
- the same energy expressed in electronvolts (eV)
- the joules in one electronvolt — the elementary charge e in coulombs
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Worked example — eV to joules
An electron in an atom drops between two energy levels and emits a photon of energy 2.5 eV. Express this energy in joules.
Solution
- Going eV → J, so use the given conversion:
- Put in 2.5 eV:
- Work it out — keep the unit:
Final answer
E = 4.0 × 10⁻¹⁹ J. (A few eV is a tiny fraction of a joule — that is why we use the eV.)
Worked example — joules to MeV
A nuclear decay releases 8.0 × 10⁻¹³ J of energy. Express this in MeV.
Solution
- Going J → eV, so divide by the given conversion:
- Put in 8.0 × 10⁻¹³ J:
- Convert eV → MeV (divide by 10⁶):
Final answer
E = 5.0 MeV — a typical nuclear-decay energy.
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How this is tested: The electronvolt rarely gets its own question — instead it is the unit you answer in across Theme E and the fields topics.
- Paper 1A: photon energies and transition energies are quoted in eV; you may need to convert to joules before using E = hf or E = hc/λ. - Paper 2: a part often says 'state, in eV' the energy of a particle, or quotes a nuclear energy in MeV.
Classic trap: multiplying when you should divide. eV → J multiply by 1.60 × 10⁻¹⁹; J → eV divide.
Convert first, then use the formula: Planck's equation E = hf gives the energy in joules. If the answer is wanted in eV, work in joules, then divide by 1.60 × 10⁻¹⁹ at the end.
- energy of the photon (J)
- Planck constant, 6.63×10⁻³⁴ J s (given)
- frequency of the light (Hz)
- speed of light, 3.00×10⁸ m s⁻¹ (given)
- wavelength of the light (m)
IB-style question — photon energy in eV
An atom emits a photon of light of wavelength 4.4 × 10⁻⁷ m (violet light). Find the energy of the photon in electronvolts. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹.)
Solution
- The wavelength is given, so use the given photon equation:
- Put in the numbers (this gives the energy in joules):
- Work out the energy in joules:
- Now convert J → eV by dividing by 1.60 × 10⁻¹⁹:
Final answer
E ≈ 2.8 eV. (Visible-light photons carry a few eV — right for an atomic transition.)