Electron spin resonance (ESR) is an effect that can be seen in molecules that have a single unpaired electron attached to one of the atoms of the molecule. In this lab, we will use a sample of diphenyl-picryl-hydrazine (DPPH), an organic compound with an unpaired electron on one of its nitrogen atoms.
The electron has intrinsic spin angular momentum and hence an intrinsic magnetic moment. The electron has quantum spin 1/2. Hence, in the presence of an external magnetic field (B), the electron's magnetic moment can assume two different orientations relative to the external field. Each of these orientations represent a slightly different energy level given by
where µs is the electron magnetic moment, related to the intrinsic spin S by
µs = g e/2m S
The constant g is the Lande' g-factor. The similar, classically-derived expression relating the orbital magnetic moment (µL) to the orbital angular momentum (L) requires g to be 1. (Review sections 7.5 and 7.8 of the your text, Modern Physics, by Krane) This agrees with experiment. However, for electron spin, experiment shows g = 2.0 within about .1%. It will be your task to determine g from the data of this experiment.
The Experiment
The Lande' g-factor can be determined if we can measure the energy difference between the two electron spin orientations in the presence of an external magnetic field (B). This can be done by immersing the DPPH sample in the external field while simultaneously bathing the sample with high frequency RF radiation. When the energy of the "RF photons" match the energy difference between the the two spin states, the unpaired electrons in the DPPH molecules can absorb the photons.
The equipment for this experiment includes
The Helmholtz coils will be powered by an AC current, so the external field will follow a sinewave form. The RF frequency will be held fixed. As the external field value rises, the energy difference between the the two spin states will widen. When this gap matches the RF photon energy, the resonance will be seen in the output of the RF circuit providing the RF field. This should occur four times during a complete cycle, provided the maximum value of the external field is high enough.
The setup is shown below. You will be provided with a more detailed description of the experiment in the lab. The oscilloscope trace shows the external field on the lower trace and the RF output on the upper trace. Note that resonance will be observed at the four points where the energy gap matches the RF photon energy.