# Photon energy

**Photon energy** is the energy carried by a single 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'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 (eV) and the joule (as well as its multiples, such as the microjoule). As one joule equals 6.24×10^{18} eV, 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.

## Formulas

### Physics

Photon energy is directly proportional to frequency.^{[1]}

- is energy (typically in joules)
^{[2]} - is the Planck constant
- is frequency (typically in hertz)
^{[2]}

This equation is known as the Planck–Einstein relation.

Additionally,

*E*is photon 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 6.62607015×10^{−34} J, which is equal to 4.135667697×10^{−15} eV.

### Electronvolt

Photon energy is often measured in electronvolts. To find the photon energy in electronvolt using the wavelength in micrometres, the equation is approximately

since = 1.239841984...×10^{−6} eV⋅m^{[3]} where *h* is the Planck constant, *c* is the speed of light, and *e* is the elementary charge.

The photon energy of near infrared radiation at 1 μm wavelength is approximately 1.2398 eV.

## Examples

An FM radio 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's mass (via mass–energy equivalence).

Very-high-energy gamma rays have photon energies of 100 GeV to over 1 PeV (10^{11} to 10^{15} electronvolts) or 16 nJ to 160 μJ.^{[4]} This corresponds to frequencies of 2.42×10^{25} Hz to 2.42×10^{29} Hz.

During photosynthesis, specific chlorophyll 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 molecule from CO_{2} and water (chemical potential difference 5×10^{−18} J) with a maximal energy conversion efficiency of 35%.

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