13 Jul 2026

Electron Spin Resonance and Determination of the g-Factor

practical pg-iii esr g-factor magnetic-resonance

Aim

To observe electron spin resonance in a paramagnetic sample and determine the electron $g$-factor.

Apparatus

ESR spectrometer, microwave source, Helmholtz coils, Hall probe, paramagnetic sample, and frequency meter.

Figure

Microwave excitation of the paramagnetic sample while the magnetic field is swept and measured.

Theory

An unpaired electron has spin magnetic moment. In a magnetic field its two spin orientations have an energy separation $\Delta E=g\mu_BB$. Resonance occurs when microwave energy equals this separation:

\[h\nu=g\mu_BB.\]

Measuring the resonant field at known frequency therefore gives $g=h\nu/(\mu_BB)$.

Observations

Microwave frequency (GHz)	Resonance field (mT)	$g$
9.10	324.5	2.00
9.20	328.0	2.01
9.30	331.5	2.00

Graph

Resonance field plotted against microwave frequency.

Result

The mean electron $g$-factor of the sample is

\[\boxed{g=2.00}.\]

Viva Questions

1. Why is a paramagnetic sample used? It contains unpaired spins that can absorb microwave energy.
2. What is resonance? Absorption when the radiation energy equals the spin-level separation.
3. Why is a Hall probe used? To calibrate the magnetic field at the sample position.

Maxima Code

Download the Maxima calculation file.