# Sebastian e/m Ratio

## Contents

# Partner

# Purpose

The purpose of this lab was to calculate the charge to mass ratio for an electron traveling though an electric field of known potential difference and deflected by a magnetic field of known magnitude (calculated from the current passing through the Helmholtz coils). This is an important constant to study, because as stated in Prof Gold's Lab Manual, it is "...the electron’s existence, and its charge-to-mass ratio, that lead to the concept of the ﬁrst atomic particle" (15).

# Lab Data

My Lab Notebook

e/m Ratio - December 12, 2010

# Equipment

- SOAR DC Power Supply Model PS-3630 (Electron Gun Heater)
- e/m Experimental Apparatus -composed of a tube of dilute helium gas, an electron heater, focusing magnets, and a Helmholtz coil used to provide a constant magnetic field (this description is from Brian Josey's lab notbook - a link can be found in the references section of my primary notebook)
- Gelman Instrument Company: Deluxe Regulated Power Supply
- Hewlett Packard 6384A DC Power Supply (Helmholtz Coils)
- Multiple BNC cables
- 3 voltmeters (one of which was used as an ammeter)

# Lab Summary

For this lab, my partner Matthew Cordova and I had to connect all the experimental and data recording devices to the power supplies because they had all been removed. We managed to connect everything correctly except for one ammeter that should have been connected in series with the Helmholtz Coils and the Power Supply. Matt initially had the correct correction, but I overruled him and had him connect it differently. After only obtaining a beam of electrons that would only remain horizontal, we asked Prof. Koch to verify that our connections were correct. He quickly saw the problem and corrected our mistake. We then powered everything on and saw that our beam bent around into a circular shape as we adjusted the current through the coils. Initially the beam bent downward so we had to switch the cables so that it would bend upward.

After obtaining the correct beam behavior, we fiddled with the current in the coils and the accelerating voltage to see how this affected the electron beam. Of course, the circular shape of the beam just changed in radius as it should.

Next, we began the data taking portion of the lab which proved to be the hardest part. We had to record the radius of the beam for different values of coil current and accelerating voltage (all three values were recorded and can be found in my primary lab notebook). We had to align the right hand side of the beam with its reflection from the mirrored ruler (which measured in cm), which was hard due to the fact that the ruler was not aligned vertically with the center of the beam. We did the same with the left side of the circular beam.
We recorded 11 data points where we kept the accelerating voltage constant and varied the current in the coils. Then we took 11 more data points in which we kept the coil current constant and varied the accelerating voltage. after only taking a few measurements for the radius, we quickly noticed that the ruler was not centered with the center of the ring, so we had to take one half of the sum of the right hand side radius and the left hand side radius.

A description of the data analysis part of this lab can be found in my lab notebook.

# Calculations and Results

I obtained four different values for [math]\frac{e}{m}[/math], one more than what is called for in the lab manual. My results are as follows:

For Constant Accelerating Voltage:Numerical Calculation: [math]\frac{e}{m} = ( 2.4 \pm 0.3 )\times 10^{11}\frac{C}{kg} [/math] Graphical Calculation: [math]2.4\times10^{11}\frac{C}{kg}\leq \frac{e}{m}\leq 2.5\times10^{11}\frac{C}{kg}\,\![/math]

For Constant Coil Current:Numerical Calculation: [math]\frac{e}{m} = ( 2.4 \pm 0.7 )\times 10^{11}\frac{C}{kg} [/math] Graphical Calculation: [math]2.3\times10^{11}\frac{C}{kg}\leq \frac{e}{m}\leq 2.4\times10^{11}\frac{C}{kg}\,\![/math]

## Accepted Value

The accepted value for the charge to mass ratio is: [math]\frac{e}{m} = 1.76 \times 10^{11} \frac{C}{kg}[/math].

## Comparison

**For Constant Accelerating Voltage:**

Numerical Calculation: About 2 SEM's away from accepted value with a percent error of about 36%.

Graphical Calculation: About 36% percent error

**For Constant Coil Current:**

Numerical Calculation: About 1 SEM away from accepted value with a percent error of about 36% error.

Graphical Calculation: About 34% error

# Conclusions

Although my calculations were to the right order of magnitude, I feel like our value of about 2.4 was off from the accepted value due the the method in which we measured both the left and right radii. Not only were we "eyeballing" the measurement, where was no way of centering the ruler vertically. Also the thickness of the beam could have added to our error. The beam had a finite width, so maybe if we would have measured the beam at a different point, we would obtain something closer to the accepted value. The focus knob could only refine the resolution of the bam so much, so I would think that there would always be some error associated with the beam itself. (Steve Koch 22:02, 21 December 2010 (EST):There are other, unavoidable, sources of systematic error in this lab, and looks like you did close to as good as possible as far as taking data.)