Einstein unit: Counting Light by the Mole
In 1905, Albert Einstein proposed that light itself carried energy in discrete packets. His work on the photoelectric effect helped establish the idea behind the photon, and his name later became attached to a quantity used in physical chemistry. The Einstein unit denotes one mole of photons, including the photons carried by a beam of monochromatic light. It has also been used for the energy associated with that quantity of light. The name brings together two scientific histories: the discovery of light's particle behavior and the chemist's method of expressing enormous numbers of tiny entities through the mole.
Einstein built on Max Planck's work on the exchange of energy between matter and electromagnetic radiation. Planck treated energy stored in a material object as discrete, equal-sized parts. Einstein extended quantization to the radiation itself, proposing independently moving, localized energy quanta. Acceptance came gradually. His predicted energy relationship had been verified experimentally by 1916, but the particle interpretation remained contentious. Arthur Compton's experiment in 1922 showed that photons carried momentum related to their wave number. Compton received the Nobel Prize in 1927 for his scattering research, while Gilbert N. Lewis popularized the name photon in 1926.
The energy associated with an Einstein unit depends on the light's frequency. Each photon carries energy equal to the Planck constant multiplied by frequency; an equivalent relationship uses the speed of light divided by wavelength. Higher frequency means more energy per photon, while longer wavelength means less. A monochromatic beam has a single frequency, allowing its photons to share the same energy. The amount of photons and their energy therefore describe different properties of the beam. A mole specifies the number of entities, while frequency or wavelength determines the energy associated with each of those entities.
The photon has no electric charge and is considered massless, moving at the speed of light in a vacuum. It belongs to the boson family and exhibits both wave and particle behavior. When a single photon passes through a double slit, its energy arrives at a point on a screen, while the distribution of possible arrival positions displays interference. Photons also carry momentum and can exert pressure. Atoms, molecules, and nuclei emit photons when they move to lower energy levels, producing characteristic energies across a range extending from radio waves to gamma rays.
The mole in the Einstein unit belongs to a chemical tradition that developed through the study of relative atomic masses. John Dalton published a table of standard atomic weights in 1805 using hydrogen as the reference. Jons Jacob Berzelius later improved atomic mass measurements and used oxygen as a standard, assigning it a value of 100. Other chemists, including Stanislao Cannizzaro, helped resolve uncertainties about the composition of compounds. Wilhelm Ostwald coined the German term Mol, and the English name mole followed as a translation in 1897.
The standard behind the mole changed as measurement techniques developed. Physicists used oxygen-16 while chemists kept natural oxygen as the reference, before carbon-12 became the common basis during the 1960s. Under the carbon definition, a mole contained as many elementary entities as there were atoms in twelve grams of carbon-12. The mole became the seventh SI base unit in 1971. Because the gram and the atomic mass unit were not mathematically tied together, the number of entities in a mole still had to be established experimentally. The Avogadro constant expressed that connection between laboratory quantities and individual atoms or molecules.
A later revision changed the numerical foundation behind every Einstein unit. Scientists from more than 60 countries met in Versailles, France, on 16 November 2018, when SI base units were defined through physical constants. The changes took effect on 20 May 2019. The mole then contained exactly 6.02214076 times ten to the twenty-third elementary entities. Those entities can be photons as well as atoms or molecules. The fixed number made the mole independent of a particular physical sample, giving photon quantities the same exact numerical basis used for amounts of chemical substances.
Individual photons also became detectable events in laboratory instruments. In a photomultiplier tube, a sufficiently energetic photon strikes a metal plate and releases an electron, beginning an amplified cascade of electrons. Semiconductor charge-coupled devices register a charge generated by an arriving photon. Geiger counters detect changes in gas conductivity when photons ionize gas molecules. Photon absorption can even break chemical bonds, including those in chlorine. In molecular biology, fluorescence resonance energy transfer follows interactions between suitable proteins as one system absorbs light and a nearby system takes the energy and emits a photon at another frequency.