Physics307L F09:People/Ierides/Electron Spin Resonance

Electron Spin Resonance
Please note that Alex Andrego was my lab partner for this lab. You can find her lab summary by following this link.

The purpose of this lab was to find the intrinsic g-factor of an electron by placing a sample of DPPH (a sample with only one free unpaired electron per molecule) in a magnetic field. The magnetic dipole moment of the electron interacts with the magnetic field creating a spin-flip transition for the electron. The electric field of this reaction is given by:
 * $$ E =- \mu_s \times B\,\!$$

Using the energies associated with these transitions and using an oscilloscope, aligning the two different waveforms whilst applying various frequencies and varying the current, we were able to calculate the g-factor.

(A more detailed purpose and setup are shown in the lab notebook )

Data and Analysis
From our trials, we used direct calculations as well as frequency versus current plots to achieve a slope which we used to calculate the g-factor.

From our direct calculations we have:
 * $$ g_{s,mean,small} \simeq 0.9002\pm.0007\,\!$$


 * $$ g_{s,mean,medium} \simeq 0.9226\pm.0025\,\!$$


 * $$ g_{s,mean,large} \simeq 0.8795\pm.0009\,\!$$

From our slope (linest) calculations we have the ranges of:
 * $$0.8965 \leq g_{s,small} \leq 0.9355 \,\!$$


 * $$0.9454 \leq g_{s,medium} \leq 1.0074 \,\!$$


 * $$0.8622 \leq g_{s,large} \leq 0.8952 \,\!$$

Using these values to obtain a mean between each of the three we had a percentage error from the accepted value of the g-factor, $$g_{s,accepted}=2.0023 \,\!$$, of :
 * $$% error_{calculated, mean}\simeq 54.8% \,\!$$


 * $$g_{s,slope,mean}\simeq 53.8% \,\!$$

Conclusions
Although our setup was followed with exact precision and double checked, there seemed to be some systematic error involved with the lab. There was a large amount of noise shown on the oscilloscope during parts of the data taking. When one of the wires was moved it seemed to disturb what was projected onto the screen. We also had a hard time with our aligning of the two different wave patterns.

According to our lab results, our measured values were off by a factor of two relative to the accepted value of the electron g-factor. We believe that this may be due to the fact that we have two coils in parallel series, splitting the current. This could in turn lead to a multiplication of the original equation by two; and even though our errors were so large, I still firmly believe that our data collection was of qualitative measure and precision. We have yet to fully comprehend as to why the factor of two is missing.

Overall, in terms of data collection of data, I believe that this lab was very successful. Perhaps a little more of a discussion pertaining to the coils would be useful for future references.