Classical electron radius

The classical electron radius is a combination of fundamental <a href="/facts/Physical_quantity/S8pWBEpK">physical quantities</a> that define a length scale for problems involving an electron interacting with <a href="/facts/Electromagnetic_radiation/Ynx7ujCW">electromagnetic radiation</a>. It links the classical electrostatic self-interaction energy of a homogeneous charge distribution to the electron's relativistic mass-energy. According to modern understanding, the electron is a <a href="/facts/Point_particle/4MPToN8W">point particle</a> with a <a href="/facts/Point_particle/4MPToN8W">point charge</a> and no spatial extent. Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems. The classical electron radius is given as

r
          
            e
          
        
        =
        
          
            1
            
              4
              π
              
                ε
                
                  0
                
              
            
          
        
        
          
            
              e
              
                2
              
            
            
              
                m
                
                  e
                
              
              
                c
                
                  2
                
              
            
          
        
        =
        2.8179403227
        (
        19
        )
        ×
        
          10
          
            −
            15
          
        
        
           m
        
        =
        2.8179403227
        (
        19
        )
        
           fm
        
        ,
      
    
    {\displaystyle r_{\text{e}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {e^{2}}{m_{\text{e}}c^{2}}}=2.8179403227(19)\times 10^{-15}{\text{ m}}=2.8179403227(19){\text{ fm}},}

where 
 
 
 
 e
 
 
 {\displaystyle e}
 
 is the <a href="/facts/Elementary_charge/lPcj6CoQ">elementary charge</a>, 
 
 
 
 
 m
 
 e
 
 
 
 
 {\displaystyle m_{\text{e}}}
 
 is the <a href="/facts/Electron_mass/xlG83aQl">electron mass</a>, 
 
 
 
 c
 
 
 {\displaystyle c}
 
 is the <a href="/facts/Speed_of_light/sKSQwdNx">speed of light</a>, and 
 
 
 
 
 ε
 
 0
 
 
 
 
 {\displaystyle \varepsilon _{0}}
 
 is the <a href="/facts/Vacuum_permittivity/gWRUhPGY">permittivity of free space</a>. This numerical value is several times larger than the <a href="/facts/Proton_radius/clCjepXP">radius of the proton</a>.
In <a href="/facts/Gaussian_units/1mtqI96c">cgs units</a>, the permittivity factor and 
 
 
 
 
 
 1
 
 4
 π
 
 
 
 
 
 {\displaystyle {\frac {1}{4\pi }}}
 
 do not enter, but the classical electron radius has the same value.
The classical electron radius is sometimes known as the <a href="/facts/Hendrik_Lorentz/JbBpKFyr">Lorentz</a> radius or the <a href="/facts/Thomson_scattering/hUj6gSgB">Thomson scattering</a> length. It is one of a trio of related scales of length, the other two being the <a href="/facts/Bohr_radius/vvP1lghl">Bohr radius</a> 
 
 
 
 
 a
 
 0
 
 
 
 
 {\displaystyle a_{0}}
 
 and the <a href="/facts/Reduced_Compton_wavelength/og2h1J2q">reduced Compton wavelength</a> of the electron ƛe. Any one of these three length scales can be written in terms of any other using the <a href="/facts/Fine-structure_constant/zyzpmTJV">fine-structure constant</a> 
 
 
 
 α
 
 
 {\displaystyle \alpha }
 
:

r
 
 e
 
 
 =
 
 
 {\displaystyle r_{\text{e}}=}
 
 ƛe 
 
 
 
 
 α
 
 
 =
 
 
 a
 
 0
 
 
 
 α
 
 2
 
 
 .
 
 
 {\displaystyle \alpha }={a_{0}\alpha ^{2}.}

Classical electron radius open-in-new

Classical electron radius