\[\alpha=\frac{e^2}{4\pi\varepsilon_0\hbar c}\]
Variables
alpha[α]fine-structure constant
eelementary charge (C)
epsilon0[ε0]vacuum permittivity (F/m)
hbar[ℏ]reduced Planck constant (J·s)
cspeed of light (m/s)
Description
What is this formula?
The fine-structure constant is a dimensionless physical constant that characterizes the strength of electromagnetic interactions between charged particles. It is one of the most important constants in modern physics.
When to use it
Use this formula when studying atomic physics, quantum electrodynamics, electromagnetic interactions, and fundamental constants.
Example
Data:
e=1.602×10^-19 C
ε0=8.854×10^-12 F/m
ℏ=1.055×10^-34 J·s
c=3×10^8 m/s
Formula:
α=e²/(4πε0ℏc)
Substitution:
α=((1.602×10^-19)²)/(4π(8.854×10^-12)(1.055×10^-34)(3×10^8))
Result:
α≈0.007297
α≈1/137
Applications
- Quantum electrodynamics
- Atomic physics
- Fundamental physics
- Spectroscopy
- Particle physics
- Electromagnetic theory