# Physics307L:People/Le/esr

## Purpose/Procedure

The purpose of this lab was to discover the "spin factor", gs, of an electron buy finding its resonance frequencies in a magnetic field.

We excite electrons with a Radio Frequency generator and place them in an external magnetic field. Observing the energy levels with an oscilloscope, when we see a dip in energies, thats where the electron has aligned itself with the field (thus observing the spin orientation)

For a detailed procedure and pictures of the setup please see my lab notebook [1]

## Data

We measured the frequency of the RF generator and the current going through the Helmholtz Coils to find the magnetic field. Graphing the frequency vs the strength of the magnetic field, and then taking the slope, we can find the gs factor http://openwetware.org/images/5/5d/Esr.JPG

We found the number to be 1.68±.021

SJK 00:16, 4 December 2007 (CST)
00:16, 4 December 2007 (CST)
Nice data!

## Errors

Comparing our number to the accepted value of 2.0023

${\displaystyle \%error={\frac {|Actual-Experimental|}{|Actual|}}x100}$

${\displaystyle \%error={\frac {|2.0023-1.6858|}{|2.0023|}}x100}$

${\displaystyle \%error=15.8}$

#### Possible Sources of Error

• The Helmholtz coils may not have been aligned exactly parallel. One may have been higher than the other. Also, the lab notebook wanted then 1 radius apart, but the best we could do is have the stands touching each other as the closest spot
• This could mess up the uniformity of the B field
• The Helmholtz Coils get hotter as the current flows in them, changing their resistances, possibly changing the B field
• The RF coil had to be in the middle of the B field (where the field is most uniform) but could only be in about 40% of the way (since we could not separate the coils to make more room).
• The RF coil is metal, which attracts B fields, which could have skewed the field itself
• The Earth's and surrounding electronics' B fields could interfere with the Helmholtz's (although it is assumed that the coils' field is strong enough to negate any outside fields).
• Calibrating the oscilloscope and making sure the graphs lined up required alot of "eyeballing" which may lead to human errors

## Final Thoughts

The experiment was the most complex one I have done to date. Just setting up the circuit was a task. The results came out fairly well, after we got the hang of taking measurements.

#### Possible Fixes

Since I feel that most of the error comes from the perturbation of the magnetic field, larger coils will produce a larger, more stable magnetic field, and allow the coils themselves to be placed further apart to allow the RF coil to be more in the middle.