Fine-structur constant

In physics, the fine-structure constant, kent as Sommerfeld's constant anaw, commonly scrieved by α (the Greek letter alpha), is a dimensionless physical constant chairacterisin the strenth of the electromagnetic interaction atween elementary chairged pairticles. It is relatit tae the elementary chairge e, that chairacterises the strenth o couplin o an elementary chairged pairticle wi tha electromagnetic field, bi the formula 4πε₀ħcα = e². Being a dimensionless quantity, it hae the sel an same nummerical vailyie in aw seestems o units, that is approximately 1/137 .

Defineetion

Some equivalent defineetions o α in terms o ither fundamental pheesical constants are:

$\alpha ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {e^{2}}{\hbar c}}={\frac {\mu _{0}}{4\pi }}{\frac {e^{2}c}{\hbar }}={\frac {k_{\text{e}}e^{2}}{\hbar c}}={\frac {c\mu _{0}}{2R_{\text{K}}}}={\frac {e^{2}}{4\pi }}{\frac {Z_{0}}{\hbar }}$

whaur:

• e is the elementary chairge (:= 1.602176634×10⁻¹⁹ C);
• π is the mathematical constant pi;
• ħ = h/2π is tha reduiced Planck constant (:= 6.62607015×10⁻³⁴/2π J s);
• c is the speed of light in vacuum (:= 299792458 m/s);
• ε₀ is the electric constant or permittivity o free space;
• µ₀ is the magnetic constant or permeability o free space;
• k_e is the Coulomb constant;
• R_K is the von Klitzing constant;
• Z₀ is the vacuum impedance or impedance o free space.

The defineetion reflects the fact thae α is relatit tae the permeability o free space µ₀, whilk equals $\mu _{0}={\frac {2\alpha }{e^{2}}}{\frac {h}{c}}.$in the 2019 redefineetion of SI base units, 4π × 1.000 000 000 82 (20) 10⁻⁷ H·m⁻¹ is the value for µ₀ based upo' mair accurat meisurements o the fine structur constant.

See anaw

• fine structur