Photon energy

<h2 id="formulas">Formulas</h2>
<h3>Physics</h3>
Photon energy is directly proportional to frequency.<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a>

E
        =
        h
        f
      
    
    {\displaystyle E=hf}

where

<ul><li>
 
 
 
 E
 
 
 {\displaystyle E}
 
 is energy (<a href="/facts/Joule/9ndq9jD2">joules</a> in the <a href="/facts/International_system_of_units/S7YLglNz">SI system</a>)<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a></li>
<li>
 
 
 
 h
 
 
 {\displaystyle h}
 
 is the <a href="/facts/Planck_constant/qGHAe3qq">Planck constant</a></li>
<li>
 
 
 
 f
 
 
 {\displaystyle f}
 
 is frequency<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a></li></ul>
This equation is known as the <a href="/facts/Planck_relation/KR8u3qPV">Planck relation</a>.
Additionally, using equation f = c/λ,

E
        =
        
          
            
              h
              c
            
            λ
          
        
      
    
    {\displaystyle E={\frac {hc}{\lambda }}}

where

<ul><li>E is the photon's energy</li>
<li>λ is the photon's wavelength</li>
<li>c is the <a href="/facts/Speed_of_light/sKSQwdNx">speed of light</a> in vacuum</li>
<li>h is the <a href="/facts/Planck_constant/qGHAe3qq">Planck constant</a></li></ul>
The photon energy at 1 Hz is equal to 6.62607015×10−34 J, which is equal to 4.135667697×10−15 eV.

<h3>Electronvolt</h3>
Photon energy is often measured in electronvolts. One electronvolt (eV) is exactly 1.602176634×10−19 J‍<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a> or, using the atto prefix, 0.1602176634 aJ, in the <a href="/facts/International_system_of_units/S7YLglNz">SI system</a>. To find the photon energy in electronvolt using the wavelength in <a href="/facts/Micrometre/7eDFxD2L">micrometres</a>, the equation is approximately

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

since 
 
 
 
 h
 c
 
 /
 
 e
 
 
 {\displaystyle hc/e}
 
 = 1.239841984...×10−6 eV⋅m<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> where h is the <a href="/facts/Planck_constant/qGHAe3qq">Planck constant</a>, c is the <a href="/facts/Speed_of_light/sKSQwdNx">speed of light</a>, and e is the <a href="/facts/Elementary_charge/lPcj6CoQ">elementary charge</a>.
The photon energy of near <a href="/facts/Infrared/44XdJNcc">infrared</a> radiation at 1 μm wavelength is approximately 1.2398 eV.

<h2 id="examples">Examples</h2>
An <a href="/facts/FM_broadcasting/TpKl3FJv">FM</a> <a href="/facts/Radio/XFr909M2">radio</a> station transmitting at 100 <a href="/facts/Megahertz/6Wshj5qm">MHz</a> emits photons with an energy of about 4.1357×10−7 eV. This minuscule amount of energy is approximately 8×10−13 times the <a href="/facts/Electron/L0KBo5cW">electron</a>'s mass (via mass–energy equivalence).
<a href="/facts/Very-high-energy_gamma_ray/6DLpFxw8">Very-high-energy gamma rays</a> have photon energies of 100 GeV to over 1 PeV (1011 to 1015 electronvolts) or 16 nJ to 160 μJ.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> This corresponds to frequencies of 2.42×1025 Hz to 2.42×1029 Hz.
During <a href="/facts/Photosynthesis/TMV7w693">photosynthesis</a>, specific <a href="/facts/Chlorophyll/1Sb0NyyM">chlorophyll</a> molecules absorb red-light photons at a wavelength of 700 nm in the <a href="/facts/Photosystem_I/z9hRH0kt">photosystem I</a>, corresponding to an energy of each photon of ≈ 2 eV ≈ 3×10−19 J ≈ 75 kBT, where kBT denotes the thermal energy. A minimum of 48 photons is needed for the synthesis of a single <a href="/facts/Glucose/oUSkoLCD">glucose</a> molecule from CO2 and water (chemical potential difference 5×10−18 J) with a maximal <a href="/facts/Energy_conversion_efficiency/gSqXlWoI">energy conversion efficiency</a> of 35%.

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Electromagnetic_radiation/Ynx7ujCW">Electromagnetic radiation</a></li>
<li><a href="/facts/Electromagnetic_spectrum/24LARvFY">Electromagnetic spectrum</a></li>
<li><a href="/facts/Planck_relation/KR8u3qPV">Planck relation</a></li>
<li><a href="/facts/Soft_photon/lBeczPBP">Soft photon</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">"Energy of Photon". Photovoltaic Education Network, pveducation.org. <a href="https://www.pveducation.org/pvcdrom/properties-of-sunlight/energy-of-photon" target="_blank">https://www.pveducation.org/pvcdrom/properties-of-sunlight/energy-of-photon</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">"6.3 How is energy related to the wavelength of radiation? | METEO 300: Fundamentals of Atmospheric Science". <a href="https://www.e-education.psu.edu/meteo300/node/682" target="_blank">https://www.e-education.psu.edu/meteo300/node/682</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">"6.3 How is energy related to the wavelength of radiation? | METEO 300: Fundamentals of Atmospheric Science". <a href="https://www.e-education.psu.edu/meteo300/node/682" target="_blank">https://www.e-education.psu.edu/meteo300/node/682</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">"2022 CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18. <a href="https://physics.nist.gov/cgi-bin/cuu/Value?evj" target="_blank">https://physics.nist.gov/cgi-bin/cuu/Value?evj</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">"NIST table of fundamental physical constants". Retrieved 27 June 2023. <a href="https://physics.nist.gov/cuu/Constants/index.html" target="_blank">https://physics.nist.gov/cuu/Constants/index.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Sciences, Chinese Academy of. "Observatory discovers a dozen PeVatrons and photons exceeding 1 PeV, launches ultra-high-energy gamma astronomy era". phys.org. Retrieved 2021-11-25. <a href="https://phys.org/news/2021-05-observatory-dozen-pevatrons-photons-exceeding.html" target="_blank">https://phys.org/news/2021-05-observatory-dozen-pevatrons-photons-exceeding.html</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
</ol>

Photon energy open-in-new

Photon energy