Planck relation

The Planck relation (referred to as Planck's energy–frequency relation, the Planck–Einstein relation, Planck equation, and Planck formula, though the latter might also refer to <a href="/facts/Planck%2527s_law/7Umkdb9m">Planck's law</a>) is a fundamental equation in <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a> which states that the <a href="/facts/Energy/wd8PrQM7">energy</a> E of a <a href="/facts/Photon/mFNhAEzA">photon</a>, known as <a href="/facts/Photon_energy/Gy4zEAaE">photon energy</a>, is proportional to its <a href="/facts/Frequency/QUSbPaW8">frequency</a> ν:

E
        =
        h
        ν
        .
      
    
    {\displaystyle E=h\nu .}

The <a href="/facts/Constant_of_proportionality/xDQmfh6t">constant of proportionality</a>, h, is known as the <a href="/facts/Planck_constant/qGHAe3qq">Planck constant</a>. Several equivalent forms of the relation exist, including in terms of <a href="/facts/Angular_frequency/VqLm3L3R">angular frequency</a> ω:

E
        =
        ℏ
        ω
        ,
      
    
    {\displaystyle E=\hbar \omega ,}

where 
  
    
      
        ℏ
        =
        h
        
          /
        
        2
        π
      
    
    {\displaystyle \hbar =h/2\pi }
  
.  Written using the symbol f for frequency, the relation is

E
        =
        h
        f
        .
      
    
    {\displaystyle E=hf.}

The relation accounts for the <a href="/facts/Quantum/4x5QTxGB">quantized nature of light</a> and plays a key role in understanding phenomena such as the <a href="/facts/Photoelectric_effect/gIDcdm5U">photoelectric effect</a> and <a href="/facts/Black-body_radiation/K4YKPKXL">black-body radiation</a> (where the related <a href="/facts/Planck_postulate/MjMTMIKl">Planck postulate</a> can be used to derive <a href="/facts/Planck%2527s_law/7Umkdb9m">Planck's law</a>).

Planck relation open-in-new

Planck relation