Photon energy is the

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

carried by a single

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...

. The amount of energy is directly proportional to the photon's

electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

and thus, equivalently, is inversely proportional to the

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy. Photon energy can be expressed using any

energy unit Energy () is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy sta ...

. Among the units commonly used to denote photon energy are the

electronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an Voltage, electric potential difference of one volt in vacuum ...

(eV) and the

joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...

(as well as its multiples, such as the microjoule). As one joule equals , the larger units may be more useful in denoting the energy of photons with higher frequency and higher energy, such as

gamma ray A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...

s, as opposed to lower energy photons as in the optical and

radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the u ...

regions of the

electromagnetic spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...

Formulas

Physics

Photon energy is directly proportional to frequency.

E = hf

where *

E

is energy (

joules The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work don ...

in the

SI system The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...

) *

h

is the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

f

is frequency This equation is known as the

Planck relation The Planck relationFrench & Taylor (1978), pp. 24, 55.Cohen-Tannoudji, Diu & Laloë (1973/1977), pp. 10–11. (referred to as Planck's energy–frequency relation,Schwinger (2001), p. 203. the Planck–Einstein relation, Planck equation, and Plan ...

. Additionally, using equation ''f'' = ''c''/''λ'',

E = \frac

where * ''E'' is the photon's energy * ''λ'' is the photon's wavelength * ''c'' is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

in vacuum * ''h'' is the

The photon energy at 1 Hz is equal to , which is equal to .

Electronvolt

Photon energy is often measured in electronvolts. One electronvolt (eV) is exactly or, using the atto prefix, , in the

. To find the photon energy in electronvolt using the wavelength in

micrometre The micrometre (English in the Commonwealth of Nations, Commonwealth English as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American English), also commonly known by the non-SI term micron, is a uni ...

s, the equation is approximately :

E\text = \frac

since

hc/e

= where ''h'' is the

, ''c'' is the

, and ''e'' is the

elementary charge The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, ...

. The photon energy of near

infrared Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...

radiation at 1 μm wavelength is approximately 1.2398 eV.

Examples

An FM

radio Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...

station transmitting at 100

MHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base u ...

emits photons with an energy of about . This minuscule amount of energy is approximately times the

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

's mass (via mass–energy equivalence).

Very-high-energy gamma ray A very-high-energy gamma ray (VHEGR) is Gamma ray, gamma radiation with photon energy, photon energies of 100 GeV (gigaelectronvolt) to 100 TeV (teraelectronvolt), i.e., 1011 to 1014 electronvolts. This is approximately equal to wavelengths betwe ...

s have photon energies of 100 GeV to over 1 PeV (10¹¹ to 10¹⁵ electronvolts) or 16 nJ to 160 μJ. This corresponds to frequencies of to . During

photosynthesis Photosynthesis ( ) is a system of biological processes by which photosynthetic organisms, such as most plants, algae, and cyanobacteria, convert light energy, typically from sunlight, into the chemical energy necessary to fuel their metabo ...

, specific

chlorophyll Chlorophyll is any of several related green pigments found in cyanobacteria and in the chloroplasts of algae and plants. Its name is derived from the Greek words (, "pale green") and (, "leaf"). Chlorophyll allows plants to absorb energy ...

molecules absorb red-light photons at a wavelength of 700 nm in the

photosystem I Photosystem I (PSI, or plastocyanin–ferredoxin oxidoreductase) is one of two photosystems in the Light-dependent reactions, photosynthetic light reactions of algae, plants, and cyanobacteria. Photosystem I is an integral membrane ...

, corresponding to an energy of each photon of ≈ 2 eV ≈ ≈ 75 ''k''_B''T'', where ''k''_B''T'' denotes the thermal energy. A minimum of 48 photons is needed for the synthesis of a single

glucose Glucose is a sugar with the Chemical formula#Molecular formula, molecular formula , which is often abbreviated as Glc. It is overall the most abundant monosaccharide, a subcategory of carbohydrates. It is mainly made by plants and most algae d ...

molecule from CO₂ and water (chemical potential difference ) with a maximal

energy conversion efficiency Energy conversion efficiency (''η'') is the ratio between the useful output of an energy conversion machine and the input, in energy terms. The input, as well as the useful output may be chemical, electric power, mechanical work, light (radi ...

of 35%.

References

{{reflist Foundational quantum physics Electromagnetic spectrum Photons

Formulas

Physics

Electronvolt

Examples

See also

References