Physics307L:People/Barron/labsum~e over m
e/m Ratio Lab Summary
^{SJK 03:00, 23 October 2008 (EDT)}Here is the lab manual page.
Here are my lab notes.
Partner: Justin Muehlmeyer
Introduction
In this lab, we take advantage of the Lorentz force to measure the charge-to-mass ratio of the electron: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{e}{m}.} We do this with the help of a bulb of He gas, through which an electron gun fires a steady stream of particles, exciting the He and making it fluoresce in the boundaries of the path (roughly). The bulb is in the magnetic field created by Helmoltz coils. Through a series of trials differing in Helmholtz current and electron gun potential, we take data on the radius of the electron path and each path's corresponding V and I values. From this data we can obtain an experimental value for the ratio.
Approach
Dr. Gold's Lab Manual outlines a manual data-taking approach involving averaging data from two sets of measurements using an anti-parallax error ruler mounted behind the bulb. We decided against this, with the urging of Aram Gragossian, and instead used a digital camera at a set angle and distance from the experiment so that the mounted ruler and electron path could be clearly related at a pixel level of resulting images. Some image editing software could be used to process the pictures, make the electron path clearer, and accurately measure each radius. We took data sets: one with constant gun potential, and one varying potential and current at once.
I utilized three methods to obtain Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{e}{m}.} I simply utilized the formula Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{q}{m} = \frac{2V}{(RB)^2} = \frac{2V}{R^2(kI)^2}} on both data sets, with a mock 68% confidence interval (mock due to inconsistent error propagation). For constant potential, I also used a slope-calculation method outlined in Dr. Gold's manual. I don't have an error on this value, due to seemingly insignificant measurement uncertainty. All computation and analysis can be found in my notes.
Final Results
e/m Ratio Constant Voltage | e/m Ratio Changing Voltage, Current | e/m Ratio Constant Voltage, Slope Method |
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{q}{m}} = 4.6573e11 ± 4.9646e10 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{C}{kg}} |
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{q}{m}} = 4.3653e11 ± 5.9377e10 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{C}{kg}} |
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{q}{m}} = 1.2014e10 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{C}{kg}} |
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \%_{error} = 165\%} |
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \%_{error} = 149\%} |
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \%_{error} = 93.2\%} |
Near 100% error is never good, but it isn't as bad as some chemistry errors I've accumulated over the years (Steve Koch:Ha!), so I'm not WHOLLY displeased. My errors correlate with others' from this lab as well. I suspect that making the entire path interact with He in order to fluoresce is a large source of error in this experiment. Perhaps repeating the experiment in a vacuum with a fluorescing target at fixed position and angle from the electron gun would yield better results. In regards to this apparatus, I think optical analysis with software tools has potential. One might be able to better analyze the path of electrons by isolating different saturations of color in the photo of the path, assuming more light comes from more heavily traveled electron routes through the He over time.