Discover the precise gyromagnetic ratio of an orbital electron using our specialized online calculator. This fundamental constant, crucial in quantum mechanics and spectroscopy, represents the ratio of an electron's magnetic dipole moment to its angular momentum, deeply intertwined with the Bohr magneton. Simply input the elementary charge and electron rest mass to get instant results.
Formula:
The Gyromagnetic Ratio (γ) of an orbital electron is a fundamental physical constant defined as the ratio of its magnetic dipole moment to its angular momentum. It can be directly calculated using the elementary charge and the electron's rest mass. This ratio is also inherently linked to the Bohr magneton (μB) and the reduced Planck constant (ħ).
Formula:
γ = -e / (2 * me)
(The negative sign indicates the opposite direction of magnetic moment relative to angular momentum for an electron.)
Alternatively, the magnitude can be expressed as:
|γ| = μB / ħ
Where:
- γ: Gyromagnetic Ratio (Coulombs per kilogram, C/kg)
- e: Elementary Charge (Coulombs, C)
- me: Electron Rest Mass (kilograms, kg)
- μB: Bohr Magneton (Joules per Tesla, J/T or A·m2)
- ħ: Reduced Planck Constant (Joule-seconds, J·s)