# Definition:Fine-Structure Constant

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## 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`

.

### Dimension

The **fine-structure constant** is dimensionless.

## 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**.

## Sources

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