Fine-structur constant

In pheesics, the fine-structure constant, anaw kent as Sommerfeld's constant, commonly scrieved by Template:Math (the Greek letter alpha), is a dimensionless pheesical constant chairacterisin the strenth of the electromagnetic interaction atween elementary chairged pairticles. It is relatit tae the elementary chairge Template:Math, whilk chairacterises the strenth o couplin o an elementary chairged pairticle wi tha electromagnetic field, bi the formula Template:Math. Being a dimensionless quantity, it hae the sel an same nummerical vailyie in aw seestems o units, whilk is approximately Template:Sfrac .

Defineetion

Some equivalent defineetions o Template:Math 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:

• Template:Math is the elementary chairge (:= 1.602176634×10⁻¹⁹ C);
• Template:Math is the mathematical constant pi;
• Template:Math is tha reduiced Planck constant (:= Template:Sfrac J s);
• Template:Math is the speed of light in vacuum (:= 299792458 m/s);
• Template:Math is the electric constant or permittivity o free space;
• Template:Math is the magnetic constant or permeability o free space;
• Template:Math is the Coulomb constant;
• Template:Math is the von Klitzing constant;
• Template:Math is the vacuum impedance or impedance o free space.

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

See anaw

• fine structur