| Electronvolts (eV) | Calories (cal) |
|---|---|
| 1 Electronvolt | 3.82929405832 × 10-20 cal |
| 2 Electronvolts | 7.65858811663 × 10-20 cal |
| 3 Electronvolts | 1.1487882175 × 10-19 cal |
| 4 Electronvolts | 1.53171762333 × 10-19 cal |
| 5 Electronvolts | 1.91464702916 × 10-19 cal |
| 10 Electronvolts | 3.82929405832 × 10-19 cal |
| 20 Electronvolts | 7.65858811663 × 10-19 cal |
| 25 Electronvolts | 9.57323514579 × 10-19 cal |
| 50 Electronvolts | 1.91464702916 × 10-18 cal |
| 100 Electronvolts | 3.82929405832 × 10-18 cal |
| Reference | Electronvolts (eV) | Calories (cal) |
|---|---|---|
| One food calorie (kcal) | 2.61145 × 1022 eV | 1000 cal |
| An AA alkaline battery | 6.24151 × 1022 eV | 2390.06 cal |
| Daily adult food intake | 5.22289 × 1025 eV | 2000000 cal |
| One unit on an electricity bill | 2.24694 × 1025 eV | 860421 cal |
| A lightning strike | 6.24151 × 1027 eV | 239005736 cal |
The electronvolt is a unit of energy equal to the work done on a single electron moved through a potential difference of one volt. Its symbol is eV. Since the 2019 redefinition of the SI it has an exact value, 1.602176634 times ten to the power minus nineteen joules, because the elementary charge itself is now a defined constant.
It exists because the joule is hopelessly large for the atomic world. A single visible photon carries between about 1.6 and 3.3 electronvolts, and expressing that in joules requires nineteen leading zeros. Working in electronvolts lets a physicist state the energy of a chemical bond, an atomic transition or a subatomic collision as a number between one and a few, which is what a unit is supposed to do.
The scale organises whole disciplines. Chemistry lives at a few electronvolts, the energy of bonds and of the visible and ultraviolet photons that break them. X-rays occupy kiloelectronvolts. Nuclear physics works in megaelectronvolts, the scale of binding energies and radioactive decay. Particle physics uses gigaelectronvolts, where the proton's rest mass is 0.938, and teraelectronvolts at the Large Hadron Collider, whose protons carry 6.8 each.
Mass is quoted in the same unit through the mass-energy relation. A particle's rest mass is given in electronvolts divided by the speed of light squared, and physicists routinely drop the divisor and simply say that the electron is 511 kiloelectronvolts. The Higgs boson is 125 gigaelectronvolts on the same convention.
Semiconductor engineering depends on it. The band gap that determines what a material does electrically and optically is an energy in electronvolts: about 1.1 for silicon, 3.4 for gallium nitride, and this single number decides whether a device is a solar cell, a transistor or a blue light-emitting diode.
Astronomy inherits the convention for high-energy photons, so gamma-ray telescopes report observations in gigaelectronvolts and teraelectronvolts rather than in wavelengths.
Particle accelerators are named after the energies they reach, which is why their names track the prefixes. The Cockcroft-Walton machine that first split a nucleus in 1932 worked at a few hundred kiloelectronvolts; the Bevatron of the 1950s reached billions and found the antiproton; and the Large Hadron Collider brings protons to 6.8 teraelectronvolts each. Cosmic rays put all of this in perspective by arriving with energies up to 10 to the twentieth electronvolts, tens of millions of times more than any machine can produce, though only a handful of such particles strike the Earth in a century over a square kilometre.
One electronvolt equals about 1.602 times ten to the power minus nineteen joules, or roughly 3.83 times ten to the power minus twenty calories.
The calorie is a unit of energy equal to 4.184 joules. Its symbol is cal. It was originally defined as the heat needed to raise the temperature of one gram of water by one degree Celsius, and it is not an SI unit, though it survives almost everywhere that food and heat are discussed.
The original definition was awkward because the answer depends on the starting temperature. Water takes slightly more heat to warm from 14.5 to 15.5 degrees than from 19.5 to 20.5, so several competing calories existed: the fifteen-degree calorie, the mean calorie and the International Steam Table calorie among them. The thermochemical calorie now used is simply defined as exactly 4.184 joules, cutting the link to water entirely and ending the ambiguity.
The greater confusion is one of scale. The calorie printed on food packaging in the United States is not this unit at all but the kilocalorie, a thousand times larger, sometimes distinguished by a capital C. A biscuit described as containing sixty calories in fact contains sixty thousand of the unit described here. The convention is entrenched and unlikely to change, so nutritional figures and physical ones must be read in different registers.
Chemistry retained the calorie long after physics moved on. Enthalpies of reaction, bond energies and heats of formation were tabulated in kilocalories per mole for most of the twentieth century, and older literature and some current American textbooks still are. The equivalent SI figure in kilojoules per mole is larger by a factor of 4.184, and misreading which is meant produces errors that look plausible.
Nutrition science uses it because human energy balance happens to sit at a convenient scale in kilocalories, with a daily requirement of around two thousand. In joules the same figure is roughly eight and a half million, which is accurate but harder to reason with.
Air conditioning and refrigeration in some countries still rate capacity in kilocalories per hour, and heating values of fuels appear in calories per gram in older engineering tables.
One calorie equals exactly 4.184 joules, 0.001 kilocalories, or about 0.00116 watt-hours.