How Much Is One Photon

Energy carried by a photon

Photon energy is the energy carried by a unmarried photon. The amount of energy is directly proportional to the photon's electromagnetic 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'due south wavelength, the lower its energy.

Photon energy can be expressed using whatsoever unit of energy. Among the units commonly used to denote photon energy are the electronvolt (eV) and the joule (also as its multiples, such every bit the microjoule). As one joule equals six.24 × x^xviii eV, the larger units may be more useful in denoting the energy of photons with higher frequency and higher energy, such every bit gamma rays, as opposed to lower energy photons as in the optical and radio frequency regions of the electromagnetic spectrum.

Formulas [edit]

Physics [edit]

Photon energy is directly proportional to frequency.^[ane]

E=hf

where

This equation is known as the Planck–Einstein relation.

Additionally,

E={\frac {hc}{\lambda }}

where

E is photon energy
λ is the photon'south wavelength
c is the speed of light in vacuum
h is the Planck abiding

The photon free energy at 1 Hz is equal to 6.62607015 × x⁻³⁴ J

That is equal to iv.135667697 × x^−xv eV

Electronvolt [edit]

Energy is often measured in electronvolts.

To find the photon energy in electronvolts using the wavelength in micrometres, the equation is approximately

E{\text{ (eV)}}={\frac {1.2398}{\lambda {\text{ (μm)}}}}

This equation merely holds if the wavelength is measured in micrometers.

The photon free energy at i μm wavelength, the wavelength of near infrared radiations, is approximately ane.2398 eV.

In chemistry, quantum physics and optical engineering science [edit]

See ^[2]

E=h{\nu }

where

E is photon free energy (joules),
h is the Planck constant
The Greek letter of the alphabet ν (nu) is the photon's frequency.

Examples [edit]

An FM radio station transmitting at 100 MHz emits photons with an free energy of about iv.1357 × 10⁻⁷ eV. This minuscule amount of energy is approximately eight × 10^−xiii times the electron'due south mass (via mass-energy equivalence).

Very-high-free energy gamma rays have photon energies of 100 GeV to over i PeV (10¹¹ to x¹⁵ electronvolts) or sixteen nanojoules to 160 microjoules.^[3] This corresponds to frequencies of 2.42 × 10²⁵ to 2.42 × 10²⁹ Hz.

During photosynthesis, specific chlorophyll molecules absorb ruddy-light photons at a wavelength of 700 nm in the photosystem I, corresponding to an energy of each photon of ≈ ii eV ≈ three × 10⁻¹⁹ J ≈ 75 k _B T, where k _B T denotes the thermal free energy. A minimum of 48 photons is needed for the synthesis of a single glucose molecule from CO_ii and water (chemic potential difference 5 × 10⁻¹⁸ J) with a maximal energy conversion efficiency of 35%.

See besides [edit]

Photon
Electromagnetic radiation
Electromagnetic spectrum
Planck constant
Planck–Einstein relation
Soft photon

References [edit]

^ "Free energy of Photon". Photovoltaic Education Network, pveducation.org. Archived from the original on 2016-07-12. Retrieved 2015-06-21 .
^ Andrew Liddle (27 Apr 2015). An Introduction to Modern Cosmology. John Wiley & Sons. p. 16. ISBN978-1-118-69025-3.
^ Sciences, Chinese Academy of. "Observatory discovers a dozen PeVatrons and photons exceeding one PeV, launches ultra-high-free energy gamma astronomy era". phys.org . Retrieved 2021-11-25 .