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 unit of energy. 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 × 10¹⁸ 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, such as those in the radio frequency region of the electromagnetic spectrum.

Formulas

Physics

Photon energy is directly proportional to frequency.

$E=hf$

Where

$E$ is energy (J)

$h$ is Planck's constant: 6.62606957 × 10⁻³⁴ (m²kgs^-1)

$f$ is frequency (Hz)

This equation is known as the Planck-Einstein relation.

Additionally,

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

Where

E is photon energy (Joules),

λ is the photon's wavelength (metres),

c is the speed of light in vacuum - 3x10⁸ metres per second

h is the Planck constant - 6.62606957 × 10⁻³⁴ (m²kgs^-1)

The photon energy at 1 Hz is equal to 6.62606957 × 10⁻³⁴ J

That is equal to 4.135667516 × 10⁻¹⁵ eV (electronvolts)

Electronvolts

Energy is often measured in electronvolts.

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

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

Please note: this equation only holds if the wavelength is measured in micrometers.

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

In chemistry and optical engineering,

$E=h{\nu }$

Where

E is photon energy (Joules),

h is the Planck constant - 6.62606957 × 10⁻³⁴ (m²kgs^-1)

The Greek letter ν (nu) is the photon's frequency.

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 (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, 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 x 10⁻¹⁹ J ≈ 75 k_BT, where k_BT denotes the thermal energy. A minimum of 48 photons is needed for the synthesis of a single glucose molecule from CO₂ and water (chemical potential difference 5 x 10⁻¹⁸ J) with a maximal energy conversion efficiency of 35%

See also

• Photon
• Electromagnetic radiation
• Electromagnetic spectrum
• Planck constant and Planck units
• Planck–Einstein relation
• Soft photon