 # Fine Structure Constant

In advanced physics, the fine structure constant is synonymous to Sommerfeld’s constant. Denoted by Greek letter 𝜶 (alpha). It is a dimensionless physical constant. Fine-Structure Constant characterises the strength of electromagnetic interactions between any two elementary charged particles.

## Measurement

Being a dimensionless quantity, Fine-Structure Constant has the same numerical value in all system of units. Which is approximately

$$\alpha =\frac{1}{137}$$ = 0.0072973525664(17).

## Definition

Fine-Structure Constant characterises the strength or magnitude of coupling of any elementary charged particle(e) with the given electromagnetic field. Mathematically 𝜶 can be expressed in terms of other fundamental physical constants as follows-

$$\alpha =\frac{1}{4\pi \epsilon _{0}}\frac{e^{2}}{\left ( \frac{h}{2\pi } \right )c}=\frac{\mu _{0}}{4\pi }\frac{e^{2}c}{\left ( \frac{h}{2\pi } \right )}=\frac{k_{e}e^{2}}{\left ( \frac{h}{2\pi } \right )c}=\frac{c\mu _{0}}{2R_{K}}=\frac{e^{2}}{4\pi }\frac{Z_{0}}{\left ( \frac{h}{2\pi } \right )}$$

Where,

• ħ=\left ( \frac{h}{2\pi } \right ) is the reduced Plank constant.
• e is the elementary charge (e=1.602176634 × 10-19C)
• c is the velocity of light in vacuum (c=299792458 m/s)
• ε0 is the permittivity of free space.
• µ0 is the Permeability of free space.
• Ke is the Coulomb constant.
• RK is the von Klitzing constant.
• Z0 is the impedance of free space.

## In non-SI units

Value of this dimensionless physical quantity can be expressed in many units.

### Electrostatic CGS unit

In electrostatic CGS units, electric charge is measured using statcoulomb and is defined assuming permittivity factor 4πε0 or Coulomb constant ke is 1 and is dimensionless. Thus, the value of fine structure constant turns out to be-

$$\alpha =\frac{e^{e}}{\left ( \frac{h}{2\pi } \right )c}$$

### Natural unit

High energy physics commonly use natural units, where ε0 = c = ħ = 1. here, ε0 is the permittivity of free space. Thus the value of fine structure constant turns out to be-

$$\alpha =\frac{e^{e}}{4\pi }$$

### Atomic units

According to atomic units, $$\epsilon _{0} =\frac{1}{4\pi }$$ and e = me = ħ = 1, thus the fine structure constant turns out to be-

$$\alpha =\frac{1}{c}$$

## Physical interpretations

The physical interpretation of Fine Structure Constant is plenty. Some are listed below-

• In quantum electrodynamics, Fine Structure Constant 𝜶 is directly related to coupling constant.
• In solid state physics and electrical engineering, 𝜶 is one-fourth product of the characteristic impedance of free space.
• Within the Bohr model, 𝜶 gives the maximum positive charge of an atomic nucleus that will allow a stable-orbit around it.
• 𝜶 gives the probability about emission or absorption of an electron by a photon.
• It also has got wide applications in low energy physics, particularly in electroweak theory. Also, some properties of subatomic particles exhibit a strong correlation with 𝜶.

Hope you have understood about fine structure constant(𝜶). Including, definition, formula, terms along with units, values in non-SI units and physical interpretation of alpha.

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