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. 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 and thus, equivalently, is inversely proportional to the wavelength. 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. 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 rays, as opposed to lower energy photons as in the optical and radio frequency 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 in the SI system) *

h

is the Planck constant *

f

is frequency This equation is known as the Planck relation. 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 in vacuum * ''h'' is the Planck constant 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 SI system. 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 Planck constant, ''c'' is the speed of light, and ''e'' is the elementary charge. 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 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 rays 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, 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, 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 of 35%.

References

{{reflist Foundational quantum physics Electromagnetic spectrum Photons

Formulas

Physics

Electronvolt

Examples

See also

References