# Physics307L F09:People/Andrego/Electron Spin Resonance

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## Contents

## ELECTRON SPIN RESONANCE LAB SUMMARY

^{SJK Incomplete Feedback Notice}

Please note that Anastasia Ierides was my lab partner for this lab. You can find her lab summary by following this link.

### Brief Overview

- The purpose of this lab was to measure the "g-factor" of the electron using Electron Spin Resonance. We accomplished this by looking for the
*spin-flip*transition of an unpaired free electron under the influence of our induced magnetic field, by placing a sample of Diphenyl-Picryl-Hydrazyl that has a total angular momentum equal to zero and one unpaired electron. - The magnetic field interacts with the magnetic dipole moment of the electron to create an electric field given by the equation:
- [math] E =- \mu_s \times B\,\![/math]

- The two energies associated with the two orientations of the electron are given by:
- [math]E = E_0 \pm g_s \mu_B B\,\![/math]

- where [math]E_0\,\![/math] is the rest energy of the electron and [math]g_s\,\![/math] is the g-factor.

- We were able to use an oscilloscope to view the two different wave patterns and match up their frequencies in order to obtain our data.

### Data Results

- The following values are our best guess using direct calculations:

- [math] g_{s,mean,small} \simeq 0.9002\pm.0007\,\![/math]

- [math] g_{s,mean,medium} \simeq 0.9226\pm.0025\,\![/math]

- [math] g_{s,mean,large} \simeq 0.8795\pm.0009\,\![/math]

- The following values are our best guess using our linest slope calculations:

- [math]0.8965 \leq g_{s,small} \leq 0.9355 \,\![/math]

- [math]0.9454 \leq g_{s,medium} \leq 1.0074 \,\![/math]

- [math]0.8622 \leq g_{s,large} \leq 0.8952 \,\![/math]

### Error

For ALL RECORDED accounts of error in our experiment methods and procedures please see the Notes about Our Uncertainty section in our Electron Spin Resonance Lab Notebook.

- The accepted g-factor value is given as:
- [math]g_{s,accepted}=2.0023 \,\![/math]

- The percentage error of our mean direct calculated and slope calculated values relative to the accepted value of the g-factor are:

- [math]% error_{calculated, mean}\simeq 54.8% \,\![/math]

- [math]% error_{s,slope}\simeq 53.8% \,\![/math]

### Conclusions

^{SJK 17:06, 18 December 2009 (EST)}

- According to our error results, our calculated values of the g-factor are off by about a factor of two. We believe that this may be due to the misunderstanding of our initial equation and how the Helmholtz coils fit into that calculation. We do know that we had two Helmholtz coils connected in parallel which means that the current we calculated is twice the amount that travels through the Helmholtz coils individually, however we are not certain that this is where we went wrong in our calculations. We also are lead to believe that due to the complexity of the setup for this lab we may have been an elevated amount of systematic error in our data. We were kind of caught off guard by this large amount of error and realization that our data was off by a factor of two because we felt as though our data was consistent and that we did a very careful setup and execution of our lab. When we further investigated this matter in relation to other, and past student's work we were relived to know that we are not the only ones who not only experienced this factor of 2 error, but also that it has yet to be fully understood.