User:Chad A McCoy/Notebook/Jr. Lab/2008/12/06

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Electron Spin Lab: 11/24-12/1/2008

 * The lab for this week was measuring the g-factor for the intrinsic spin of an electron.


 * Raw data and notes on procedure can be found here

$$\mathrm{B}=\frac{\mu\,{R}^{2}N I}{({R}^{2}+{x}^{2})^{3/2}}$$
 * As the apparatus included Helmholtz coils, we had to calculate the magnetic field between the coils using the formula:


 * For our coils, $$R=.0675 m$$, $$x=R/2$$, and $$\mu=4 \pi * 10^{-7}$$


 * Plugging those values in, we came out with the result that $$\mathrm{B}=0.004263{I}$$


 * As the objective of this lab was to find the g-factor for the spin of the electron, we could relate the energy difference between the spin-up and spin-down states with the energy of the resonance photon.


 * That relationship is given by: $${h}{\nu}={g_{s}}{\mu_{B}}{B}$$, where h is Planck's constant, g is the spin factor, mu_B is the Bohr magneton, and B is the magnetic field strength.


 * Therefore $$g_{s}=\frac{h}{.004263 \mu_{B}} \frac{\nu}{I}=1.677*10^{-8}\frac{\nu}{I}$$


 * Doing the calculations I came out with a value of g being .8498, with error being .0072.


 * Calculating off a linear fit, the generated value of g was .796 with error .013.


 * Using the calculated value as my final answer, gives me the final value as:

$$g_{s}=.8498(72)$$


 * If I compare this value to the accepted value of g, being 2.0023, I find that my answer differs from the accepted value by over 100 times the standard error, meaning that it is very likely that there was a major systematic error that resulted in my answer being that extreme.




 * The excel file that contains all my calculations can be found at [[Media:Electron Spin Resonance.xls]]


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