# Definition:Fine-Structure Constant

## Definition

The fine-structure constant is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.

It is related to the strength of the coupling of an elementary charge $\E$ with the electromagnetic field, by the formula:

$\alpha = \dfrac {\E^2} {2 \pi \epsilon_0 h c}$

where:

$\E$ is the elementary charge: $1.60217 \, 6634 \times 10^{-19} \, \mathrm C$
$h$ is Planck's constant: $6.62607 \, 015 \times 10^{-34} \, \mathrm J \, \mathrm s$
$c$ is the speed of light: $299 \, 792 \, 458 \, \mathrm m \, \mathrm s^{-1}$
$\epsilon_0$ is the vacuum permittivity: $8.85418 \, 78128(13) \times 10^{-12} \, \mathrm F \, \mathrm m^{-1}$

### Value

 $\ds \alpha$ $\approx$ $\ds 7 \cdotp 29735 \, 25693 \times 10^{-3}$ This sequence is A003673 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008). $\ds \dfrac 1 \alpha$ $\approx$ $\ds 1 \cdotp 37035 \, 99908 \, 4 \times 10^2$ This sequence is A005600 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

### Symbol

$\alpha$

The symbol for the fine-structure constant is $\alpha$.

The $\LaTeX$ code for $\alpha$ is \alpha .

## Also known as

The fine-structure constant is also (rarely) known as the Sommerfeld constant, for Arnold Johannes Wilhelm Sommerfeld.

Some sources do not hyphenate: fine structure constant.