photon energy

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Photon energy is the
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
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 particle, massless ...
. The amount of energy is directly proportional to the photon's electromagnetic
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in Hertz (unit), hertz (H ...
and thus, equivalently, is inversely proportional to the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adjac ...
. 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
unit of energy Energy is defined via Mechanical work, work, so the SI unit of energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundame ...
. 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 from rest through an Voltage, electric potential difference of one volt i ...
(eV) and the
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units, International System of Units (SI). It is equal to the amount of Work (physics), work done when a force of 1 Newton (unit), newton displaces a mass through ...
(as well as its multiples, such as the microjoule). As one joule equals 6.24 × 1018 eV, 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 γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nucleus, atomic nuclei. It consists of the shortest wavelength electromagnetic wav ...
s, as opposed to lower energy photons as in the optical and
radio frequency Radio frequency (RF) is the oscillation rate of an Alternating current, alternating electric current or voltage or of a Magnetic field, magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around ...
regions of the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular ...
.

# Formulas

## Physics

Photon energy is directly proportional to frequency. $E = hf$ where *$E$ is energy *$h$ is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
*$f$ is frequency This equation is known as the
Planck–Einstein 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 relation, Planck equation, and Planck formula, ...
. Additionally, $E = \frac$ where *''E'' is photon 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 that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
in vacuum *''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
The photon energy at 1 Hz is equal to 6.62607015 × 10−34 J That is equal to 4.135667697 × 10−15 eV

## Electronvolt

Energy is often measured in electronvolts. To find the photon energy in
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 from rest through an Voltage, electric potential difference of one volt i ...
s using the wavelength in
micrometre The micrometre (American and British English spelling differences#-re, -er, international spelling as used by the International Bureau of Weights and Measures; SI symbol: μm) or micrometer (American and British English spelling differences# ...
s, the equation is approximately :$E\text = \frac$ This equation only holds if the wavelength is measured in micrometers. The photon energy at 1 μm wavelength, the wavelength of near
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...

## In chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ..., quantum physics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ... and optical engineering

See $E = h$ where *''E'' is photon energy (joules), *''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
*The
Greek letter The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as ...
''ν'' ( nu) is the photon's
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in Hertz (unit), hertz (H ...
.

# Examples

An FM
radio Radio is the technology of signaling and telecommunication, communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device ...
station transmitting at 100  MHz emits photons with an energy of about 4.1357 × 10−7 eV. This minuscule amount of energy is approximately 8 × 10−13 times the
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
's mass (via mass-energy equivalence). Very-high-energy gamma rays have photon energies of 100 GeV to over 1 PeV (1011 to 1015 electronvolts) or 16 nanojoules to 160 microjoules. This corresponds to frequencies of 2.42 × 1025 to 2.42 × 1029 Hz. During
photosynthesis Photosynthesis is a process used by plants and other organisms to Energy transformation, convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemica ...
, specific
chlorophyll Chlorophyll (also chlorophyl) is any of several related green pigments found in cyanobacteria and in the chloroplasts of algae and plants. Its name is derived from the Ancient Greek, Greek words , ("pale green") and , ("leaf"). Chlorophyll al ...
molecules absorb red-light photons at a wavelength of 700 nm in the photosystem I, corresponding to an energy of each photon of ≈ 2 eV ≈ 3 × 10−19 J ≈ 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 simple sugar with the Chemical formula#Molecular formula, molecular formula . Glucose is overall the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis f ...
molecule from CO2 and water (chemical potential difference 5 × 10−18 J) with a maximal energy conversion efficiency of 35%.

*
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 particle, massless ...
*
Electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
*
Electromagnetic spectrum The electromagnetic spectrum is the range of frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular ...
*
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
*
Planck–Einstein 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 relation, Planck equation, and Planck formula, ...
* Soft photon

# References

{{Reflist Foundational quantum physics Electromagnetic spectrum Photons