# Physics307L:People/Osinski/ESR

^{SJK 17:31, 18 December 2008 (EST)}## Calculating g-factor from Measured Electron Spin Resonance

-Boleszek Osinski, Chad McCoy-

## A Brief Introduction

An electron in the presence of a magnetic field will exhibit a difference in energies for its spin up and spin down states equal to **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle g_s \mu_B B }**
. If a photon with energy equal to this difference is incident upon an electron in the lower energy state that electron will acquire just enough energy to flip into its other spin energy state. This spin flip is termed electron spin resonance.

Given that the g-factor plays a role in the mathematical formulation of the electromagnetic properties of electrons we were able to find it by measuring the resonance pulses that result from the change in permeability (responsiveness to a B field) that occurs during periodically occurring moments of resonance and setting the expression for energy difference equal to the photon energy hv. Further details concerning the use of an RF generator and experimental setup is available in the lab notebook.

## Results

The accepted value for the unitless g-factor is

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle g_s ≈ 2.0023\,}**

From the application of the formula to each pair of data we obtain an average g-factor of

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle g_s=0.84(70)\,}**

From a linear least squares fit applied to data using small, medium, and large inducting coils we obtain

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle g_s=0.8907\,}**

It is quite obvious that our results diverge from the accepted value (it would require an addition of 165.714 sdms to reach the value to be exact). Tn my opinion this drastic error is due in part to the interference of EM waves produced by the metal encasing of the probe unit, but is mostly due to our failure to position the Helmholtz coils correctly. Discussions about this and other subjects have been provided at the end of the lab notebook.