The electronvolt

The big idea: You wouldn't price a single sweet in millions of dollars — the unit would be absurdly big for the job. In the same way the joule (J) is far too big for the energy of one particle, 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:

How this is tested — the electronvolt is rarely its own question; it is the unit you answer in across Theme E and the fields topics:

The 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.