# Photon energy

**Photon energy** is the energy carried by a single photon, the quantum of electromagnetic radiation, given by the Planck–Einstein relation \( E = hf \), where \( h \) is the [Planck constant](https://www.edgepedia.org/planck-constant) and \( f \) is the photon's frequency. Equivalently, \( E = hc/\lambda \) in terms of wavelength \( \lambda \). A photon's energy depends only on its frequency: brighter light of the same color contains more photons, not more energetic ones.<sup>[1](https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect)</sup>

| Key fact | Detail |
|---|---|
| Defining relation | \( E = hf = hc/\lambda \), with \( \lambda f = c \) in vacuum<sup>[2](https://openstax.org/books/university-physics-volume-3/pages/6-3-the-compton-effect)</sup> |
| Planck constant | \( h = 6.626\ 070\ 15 \times 10^{-34} \) J·s, exact by SI definition since 20 May 2019<sup>[3](https://www.bipm.org/en/measurement-units/si-defining-constants)</sup> |
| Convenient constant | \( hc = 1240 \) eV·nm, so a 430 nm violet photon carries 2.88 eV<sup>[1](https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect)</sup> |
| Electronvolt | 1 eV = 1.602 176 634 × 10⁻¹⁹ J (exact); the standard energy unit for photons<sup>[4](https://physics.nist.gov/cgi-bin/cuu/Value?evj%7Csearch_for=electron-neutron)</sup> |
| Momentum link | \( p = E/c = h/\lambda \); a photon is massless, so energy and momentum are locked together<sup>[2](https://openstax.org/books/university-physics-volume-3/pages/6-3-the-compton-effect)</sup> |
| Spectrum span | Photon energies from below 2 × 10⁻²⁴ J (radio) to more than 2 × 10⁻¹⁴ J (gamma rays)<sup>[5](https://imagine.gsfc.nasa.gov/science/toolbox/spectrum_chart.html)</sup> |
| Highest detected | A cosmic photon of about 400 TeV has been recorded, and individual gamma-ray sources have been detected up to about 5 × 10¹² eV<sup>[6](https://heasarc.gsfc.nasa.gov/docs/heasarc/headates/spectrum.html)</sup><sup> • </sup><sup>[7](https://imagine.gsfc.nasa.gov/ask_astro/xrays.html)</sup> |

## The relation and its constants

The energy quantum of radiation, \( \Delta E = hf \), was introduced in 1900 by the German physicist [Max Planck](https://www.edgepedia.org/max-planck) to explain blackbody radiation. [Albert Einstein](https://www.edgepedia.org/albert-einstein) extended the idea in 1905, proposing that light itself consists of energy quanta, which he used to explain the photoelectric effect; the term photon came later.<sup>[8](https://openstax.org/books/university-physics-volume-3/pages/6-introduction)</sup>

**Exact constants.** Since the 2019 revision of the SI, the Planck constant is a defining constant with the exact value \( h = 6.626\ 070\ 15 \times 10^{-34} \) J·s, and the speed of light in vacuum is exactly \( c = 299\ 792\ 458 \) m/s.<sup>[3](https://www.bipm.org/en/measurement-units/si-defining-constants)</sup> The electronvolt, the kinetic energy an electron gains through a potential difference of one volt in vacuum, is exactly \( 1.602\ 176\ 634 \times 10^{-19} \) J because the elementary charge is also a defining constant.<sup>[4](https://physics.nist.gov/cgi-bin/cuu/Value?evj%7Csearch_for=electron-neutron)</sup> Photon energies are usually quoted in eV or its multiples (keV, MeV, GeV, TeV) rather than joules.

The product \( hc \) is a practical shortcut: \( hc = 1240 \) eV·nm, so photon energy in electronvolts is 1240 divided by the wavelength in nanometers. A 430 nm violet photon therefore carries \( 1240/430 = 2.88 \) eV.<sup>[1](https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect)</sup>

## Energy and momentum

A photon is massless, so its energy cannot be written as \( mc^2 \) with a rest mass. Setting \( m_0 = 0 \) in the relativistic energy equation \( E^2 = p^2c^2 + m_0^2c^4 \) gives \( E = pc \), so the photon's momentum is \( p = E/c = h/\lambda \).<sup>[2](https://openstax.org/books/university-physics-volume-3/pages/6-3-the-compton-effect)</sup> Energy and momentum are rigidly proportional: fixing one fixes the other, and neither can change without the other.<sup>[9](https://giophysics.com/university-physics/topics/photon-energy-momentum-massless-limit/)</sup>

This link is what makes photon energy measurable in scattering. In the Compton effect, studied by [Arthur H. Compton](https://www.edgepedia.org/arthur-h-compton) and explained in 1923, X-rays scattered off materials such as graphite emerge with longer wavelengths than the incident beam, because a photon transfers part of its energy to an electron. The explanation convinced the physics community that electromagnetic waves behave as streams of photons.<sup>[2](https://openstax.org/books/university-physics-volume-3/pages/6-3-the-compton-effect)</sup>

## Evidence from the photoelectric effect

The photoelectric effect shows photon energy directly. Each photon transfers all of its energy to a single electron in an all-or-nothing interaction, and the maximum kinetic energy of the ejected electron is

\[ K_{\max} = hf - \varphi, \]

where \( \varphi \) is the work function of the metal, the energy needed to detach an electron from the surface.<sup>[1](https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect)</sup> Three features of the effect cannot be explained classically: there is no time lag even at very low intensity, the electron kinetic energy does not depend on the light's intensity, and there is a cut-off frequency \( f_c = \varphi/h \) below which no electrons appear at all.<sup>[1](https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect)</sup>

Work functions are a few electronvolts, so visible and ultraviolet photons are in the right energy range. Silver, with \( \varphi = 4.73 \) eV, has a cut-off wavelength of 262 nm; 300 nm radiation ejects nothing, while photons shorter than 262 nm eject electrons.<sup>[1](https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect)</sup>

## Photon energies across the spectrum

NASA's reference chart gives approximate energy limits for the regions of the electromagnetic spectrum:<sup>[5](https://imagine.gsfc.nasa.gov/science/toolbox/spectrum_chart.html)</sup>

| Region | Energy (J) |
|---|---|
| Radio | < 2 × 10⁻²⁴ |
| Microwave | 2 × 10⁻²⁴ – 2 × 10⁻²² |
| Infrared | 2 × 10⁻²² – 3 × 10⁻¹⁹ |
| Optical | 3 × 10⁻¹⁹ – 5 × 10⁻¹⁹ |
| Ultraviolet | 5 × 10⁻¹⁹ – 2 × 10⁻¹⁷ |
| X-ray | 2 × 10⁻¹⁷ – 2 × 10⁻¹⁴ |
| Gamma-ray | > 2 × 10⁻¹⁴ |

The only real difference between a gamma-ray photon and a visible-light photon is the energy.<sup>[10](https://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html)</sup> The boundaries between the ultraviolet, extreme-ultraviolet, X-ray, and gamma-ray bands are a matter of definition rather than science and are somewhat debated; astronomers studying high-energy sources typically place the X-ray band at 0.12–50 keV and gamma rays above 50 keV.<sup>[6](https://heasarc.gsfc.nasa.gov/docs/heasarc/headates/spectrum.html)</sup>

**Extreme energies.** Observations of cosmic sources span more than 21 decades in photon energy.<sup>[6](https://heasarc.gsfc.nasa.gov/docs/heasarc/headates/spectrum.html)</sup> Reliable detections of very high energy gamma rays from individual sources, including a couple of active galaxies and the [Crab Nebula](https://www.edgepedia.org/crab-nebula), extend to about \( 10^{27} \) Hz, corresponding to \( 5 \times 10^{12} \) eV.<sup>[7](https://imagine.gsfc.nasa.gov/ask_astro/xrays.html)</sup> The highest-energy cosmic photon listed by NASA's high-energy astrophysics archive is about 400 TeV.<sup>[6](https://heasarc.gsfc.nasa.gov/docs/heasarc/headates/spectrum.html)</sup>

## What changes energy and what does not

Photon energy is tied to frequency, and frequency is the quantity that survives a change of medium. When light passes from air into water or glass, its speed drops to \( c/n \) and its wavelength shortens to \( \lambda/n \), but the frequency stays the same, so the photon energy \( E = hf \) is unchanged.<sup>[11](https://openstax.org/books/physics/pages/16-2-refraction)</sup><sup> • </sup><sup>[12](https://openstax.org/books/physics/pages/17-key-equations)</sup> A photon's energy does change when the photon itself is transformed: in [Compton scattering](https://www.edgepedia.org/compton-scattering) the photon survives with less energy and a longer wavelength after transferring energy to an electron, and in emission or absorption an atomic transition produces or consumes a photon whose energy equals the energy difference between the two levels, \( hf = |E_n - E_m| \).<sup>[2](https://openstax.org/books/university-physics-volume-3/pages/6-3-the-compton-effect)</sup><sup> • </sup><sup>[13](https://openstax.org/books/university-physics-volume-3/pages/6-key-equations)</sup>

## References

1. [6.2 Photoelectric Effect, University Physics Volume 3, OpenStax](https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect)
2. [6.3 The Compton Effect, University Physics Volume 3, OpenStax](https://openstax.org/books/university-physics-volume-3/pages/6-3-the-compton-effect)
3. [SI Defining Constants, BIPM](https://www.bipm.org/en/measurement-units/si-defining-constants)
4. [CODATA Value: electron volt, NIST](https://physics.nist.gov/cgi-bin/cuu/Value?evj%7Csearch_for=electron-neutron)
5. [Wavelength, Frequency, and Energy: Regions of the Electromagnetic Spectrum, NASA Imagine the Universe](https://imagine.gsfc.nasa.gov/science/toolbox/spectrum_chart.html)
6. [What are the Energy Range Definitions for EM Radiation?, NASA HEASARC](https://heasarc.gsfc.nasa.gov/docs/heasarc/headates/spectrum.html)
7. [Imagine the Universe! Ask an Astrophysicist, NASA](https://imagine.gsfc.nasa.gov/ask_astro/xrays.html)
8. [Ch. 6 Introduction, University Physics Volume 3, OpenStax](https://openstax.org/books/university-physics-volume-3/pages/6-introduction)
9. [Photon Energy, Momentum & the Massless Limit, GioPhysics](https://giophysics.com/university-physics/topics/photon-energy-momentum-massless-limit/)
10. [Electromagnetic Spectrum Introduction, NASA Imagine the Universe](https://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html)
11. [16.2 Refraction, Physics, OpenStax](https://openstax.org/books/physics/pages/16-2-refraction)
12. [Ch. 17 Key Equations, Physics, OpenStax](https://openstax.org/books/physics/pages/17-key-equations)
13. [Ch. 6 Key Equations, University Physics Volume 3, OpenStax](https://openstax.org/books/university-physics-volume-3/pages/6-key-equations)

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*Topic: Encyclopedia › Physical world and mathematics › Physics › Classical physics › Electromagnetism › Electromagnetic radiation and waves*

*Initially written Sep 17, 2026 · Reviewed: Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*

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