13 Jul 2026

Determination of Magnetic Field Strength and Resonance Frequency Using ESR

practical pg-iii esr g-factor magnetic-resonance

Aim

To determine the resonance frequency and magnetic field strength of a paramagnetic sample using electron spin resonance, and to calculate 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 atom or ion with an unpaired electron possesses a spin magnetic moment. In an applied magnetic field the two allowed orientations of the electron spin have different energies; this Zeeman splitting is

\[\Delta E=g\mu_BB.\]

When microwave radiation is applied, the spin can change orientation if one microwave quantum supplies exactly this energy. Resonance therefore occurs when

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

Measuring the resonant field at a known frequency gives

\[g=\frac{h\nu}{\mu_BB}.\]

The spectrometer sweeps the magnetic field through resonance and records the field at which the absorption peak occurs.

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 resonance condition is observed by sweeping the magnetic field at each microwave frequency. 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.