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Electron gyromagnetic ratio

γe=1.76085962784×1011 s−1⋅T−1\gamma_{\mathrm{e}} = 1.76085962784 \times 10^{11}\ \text{s}^{-1}{\cdot}\text{T}^{-1}
Value1.76085962784e11 s⁻¹·T⁻¹
StatusMeasured: ± 55 s⁻¹·T⁻¹ (3.1e-10 relative)
SourceCODATA 2022
CategoriesElectromagneticphysicsatomicmagnetism

Learning zone

The electron precesses in a magnetic field for the same reason the proton does, but 658 times faster, because its mass is 1836 times smaller and its g-factor about 2. Divided by 2π it is 28.025 GHz per tesla, which puts electron spin resonance squarely in the microwave X-band: a benchtop EPR spectrometer at 9.5 GHz needs only about 0.34 T, a magnet you can lift.

Yevgeny Zavoisky observed the resonance in Kazan in 1944, two years before nuclear magnetic resonance, working with wartime radar equipment and a homemade magnet. Because only unpaired electrons respond, EPR is a selective probe of free radicals, transition-metal centres and defects in crystals. The same constant now sets the control frequency for spin qubits in silicon and for the nitrogen-vacancy centres in diamond used as nanoscale magnetometers.