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 $4π ε 0 ħcα = e 2$ . 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);
$ε 0$ is the electric constant or permittivity o free space;
$µ 0$ is the magnetic constant or permeability o free space;
$k e$ is the Coulomb constant;
$R K$ is the von Klitzing constant;
$Z 0$ is the vacuum impedance or impedance o free space.

The defineetion reflects the fact thae $α$ is relatit tae the permeability o free space $µ 0$ , whilk equals $\mu _{0}={\frac {2\alpha }{e^{2}}}{\frac {h}{c}}.$ in the 2019 redefineetion of SI base units, 4 $π$ × 1.000 000 000 82 (20) 10⁻⁷ H·m⁻¹ is the value for $µ 0$ based upo' mair accurat meisurements o the fine structur constant.^[1]^[2]^[3]

See anaw

fine structur

References

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