The e/m Experiment for Electrons and Further Cathode Ray Investigation
- Author: Stephen K. Martinez
- Experimenters: Stephen Martinez, Michael Phillips, Daniel Young
- Laboratory: Junior Lab, Department of Physics and Astronomy, University of New Mexico, Albuquerque NM, 87106
- Contact: firstname.lastname@example.org
AbstractSJK 22:49, 16 December 2008 (EST)
This was an investigation after the method of J.J. Thompson to discover certain characteristics for the material referred to as cathode rays. With the hindsight knowledge of subsequent studies that the substance in question is composed of a beam of electrons, we conducted our experiment to discover the ratio of the electrical charge to mass for the particle. We used the experimental layout suggested in Professor Gold's lab manual to do so. Our procedure created a beam which we manipulated to form a circle by electrodes and Helmholtz coils. We subsequently measured necessary values and solved the Lorentz force law for the value of e/m. Our final accepted measured value for the value of e/m(measured) = 4.7(4) * 10^10 C/kg differing from the accepted value of e/m(accepted) = 1.76 * 10 ^11 C/kg. We believe our great discrepancy from the accepted value is due to two parts: to the systematic error inherent in the setup and the measurement technique (which was by eye). We also investigated a curious phenomenon which occured in the emmission spectra of the helium excited by our electron beam.
IntroductionFor our laboratory investigation of the nature of cathode rays and the particles composing them we followed the experimental guidelines originally conducted by J.J. Thomson. In 1897, Thomson published a paper on the research he had performed to determine the composition of cathode rays, and matter. Thus our reasoning for following in his experimental footsteps is to gain further understanding of the scientific method as it relates to the discovery of atomic structure and cathode ray composition. Our investigation was chiefly to discover the value for the ratio of electric charge to the mass of the particle constituting cathode rays (now identified as electrons after the discovery of the unit of charge of the electron by R. A. Millikan). Thomson used several apparatuses to find useful information regarding this ratio(e/m) and the velocity of the beam, and concluded that information about Q = The quantity of electricity, W = The kinetic energy of the particles, and I = Hρ = The radius of curvature in a uniform magnetic field(H). His procedure J.J. Thomson's experiments with cathode rays(1). The method that Thomson used for his determination of e/m was correcting an electron beam deflected by the electric field by a magnetic one, we avoided this method as the value for the electric field could not be known with much accuracy. Our method was to create an electron beam and then manipulate the path of the beam using a magetic field between Helmholtz coils, this produces spirals, that if you rotate the bulb will terminate at the anode(2). To determine the value of e/m, it is necessary to solve the Lorrentz force equation for the quotient, and resultantly it is necessary to measure the voltage or the accelarating electrodes, current of the Helmholtz coils, and radius of the resulting circle. Another method that closely corresponds to our method is to use a magnetron, which differs in the use of a solenoid, but the data analysis is the same(3). A more advanced approach was found in the magneto-optical investigation by Zeeman, who discovered that using a Faby-Perot interferometer that the frequency of light is affected by a magnetic field. It was discovered in his correspondance with Lorentz, that his method would result in a value for the charge to mass quotient from the magnitude of the effect(5). Finally, I believe the most effective method of measuring the e/m ratio is from the Dunnington's method. This is similar to the procedure of our apparatus, but differs by the complexity of measurement. The quantities measured are, the frequency of an alternating current, the magnetic field at a very specific value that allows for the passage of the beam through a series of slits, and finally the curvature of the apparatus. This method is the most effective because the frequency can be known quite accurately and the apparatus curvature is fixed, so only the magnetic field needs to be varied and the value of interest will correspond to a sequential quenching of current from the incorrect direction of the beam(4).SJK 23:19, 16 December 2008 (EST)
Methods and Materials
Our experiment used a single apparatus: Uchida e/m experimental apparatus, with an extensive electrical set-up requiring a good deal of electrical measuring equipment and power supplies for: the Helmholtz coils(Soar DC Power Supply Model Number PS-3630 - Hemholtz Supply), cathode heater(Soar DC Power Supply Model 7403 UNM 158374 - Heater Supply), and the electrodes(Gelman Instrument Company Delux Regulated Power Supply - Electrodes). We opperated these supplies at the following electrical values for the data aquisition: Helmholtz (under 2.00A, 8.085±.015V), Electrodes (0.04A, between 250-400V), Heater (1.500A, 6.05 +/-.02V). It was also necessary to make sure the values didn't alter, and damage the machinery, therefore we monitored the voltages and currents at all times using: 2 Amprobe 37xR-A,and Fluke 111 True RMS Multimeter. This apparatus is visually imaged in Figues 1-3. Our procedure was to heat a cathode to produce electrons which would then be accelerated into a beam by the electrodes voltage, and arc the resulting beam into a circle using the magnetic Helmholtz coils. The acquisition of data was for the values: r = radius of the circle, I = current powering the Helmholtz coils, and Va = The accelerating potential of the electrodes (related also to the velocity). Our largest source of error in the data collection was that the radius had to be measured using a ruler several inches behind our electrical beam, to correct for this we used the parallax observation of each edge of the ring in order to determine the diameter. The major source of systematic error in this experiment was that the Va voltage was not directly related to the velocity of the beam, and that this value would be reduced because of nonuniform Va and collision with the gas in the bulb. Our experiment follows Professor Gold's lab manual.
We also experimentally investigated with the capabilities of our equipment, following the qualitative section of the lab manual to observe the relative effects of the electric and magnetic fields according to the Lorentz Force: altering the polarity and amplitude of electricity supplied to the deflection plates and Helmholtz coils to respectively measure these effects.
We had some considerable difficulty in our experimental set-up because of some broken equipment. A detailed outline of the set-up procedure can be referrenced in the lab manual entry here.
These photos provided by Professor Koch illustrate the equipment used.
We conducted this experiment in a dark room and have covered the back of the apparatus with a black hood. We turned on the power supplies and allowed 2min for the filament to heat up. Immediately after we observed the characteristic bending into a circle of the electron beam. The beam was not completely accurate in terminated at the cathode it started at, furthermore there was an anomalous color change from teal to violet at the peak for certain low voltages, which will be discussed futher in the results and discussions section (figure 4). We adjusted the accelerating voltage to a level that was enough to change the path to circle and terminate on the back side of the filament, and then were able to lower that voltage again as we had created a new path through the He for the electron beam to follow. There was a significant jump at approximately 230 from this passage to path of lowest resistance. We also adjusted the glass bulb to assure that it terminated on the back side and did not follow a helical path. We proceeded with the experiment by changing both the voltage (from 230-290V), and the current (1-1.6A) randomly for 10 trials. We conducted our measurement by trying to line up each edge of the circle one at a time with the ruler (parallax)(Figure 6). As was expected this measurement process was very inaccurate. To obtain the value for B (magnetic field) from I we used the following equation: B=μ*N*I*R^2/(R^2 + x^2)^5/2
- μ = 4*π*10^-7 (weber/amp-meter)
- x = R/2
- N = 130
- R = .15m
So that our value for B was:
B = (7.8 × 10^−4 weber/amp−meter^2 ) × I.
- m*v^2/r = Q(E+v*B)Lorentz Force law for and acceleration from uniform circular motion.
- (E = 0) Because for data collection the deflection plates were turned off.
- q/m = v/r*B
- v = (2*V*q/m)^2
- q/m = r*B /4*V^2
Figure 4:The cyan colored ring in the glass bulb is the cathode ray or electron beam. This shows the violet band on the peak of the circle, with the cyan below although both of these colors fall within the visible spectrum of helium, we were puzzled that their appearance was so because the color purple would be associated with a higher energy which we suspected should be at the electron gun nozzle.
Figure 6:This shows the schematic of the e/m apparatus: E Envelope to vacuum tube, G Electron Gun, F Focusing element of gun, Z Heater or filament of gun within cathode, A Anode of gun, S Electron Beam, H Helmholtz Coils, B Space of magnetic field, M Mirror scale, W Lamps to measure r, All Others Various connectors as labelled
Qualitative analysis of the experimental equipment.
For the qualitative experiments we first rotated the glass bulb so that the termination of the spiraling electron beam was not on the back end of the cathode. From the Lorentz force we expect the result that under the presence of an electric and magnetic fields an electron will spiral toward the electric force and around the magnetic field lines. F = -q(E + v x B). When we reversed the polarity of the coil leads we found that the electron beam moved downward. We then used the deflector plates that were used in the original experiment to determine e/m. We found that varying the voltage value did not affect the beam deflection as it was indicated to in the lab manual. We could however, tell the polarity of the electric force from the leads and how the beam was affected - namely the beam moved toward the positive plate and away from the negative plate, if we switched the jacks then the plates also switched. When we switched these jacks the beam was deflected downward. Originally the way Thomson set up his apparatus was to correct the deflection of an electric fields influence on the beam with a magnetic field - so we reintroduced our coils. We didn't use this setup because of the inaccuracy of the electric field value but the point at which the magnetic and electric canceled out was at the values - (V = 250.3 +/- 0.1V and I = 1.750A)(Figure 5).
For the qualitative experiments we first rotated the glass bulb so that the termination of the spiraling electron beam was not on the back end of the cathode. From the Lorentz force we expect the result that under the presence of an electric and magnetic fields an electron will spiral toward the electric force and around the magnetic field lines. F = -q(E + v x B). When we reversed the polarity of the coil leads we found that the electron beam moved downward. We then used the deflector plates that were used in the original experiment to determine e/m. We found that varying the voltage value did not affect the beam deflection as it was indicated to in the lab manual. We could however, tell the polarity of the electric force from the leads and how the beam was affected - namely the beam moved toward the positive plate and away from the negative plate, if we switched the jacks then the plates also switched. When we switched these jacks the beam was deflected downward. Originally the way Thomson set up his apparatus was to correct the deflection of an electric fields influence on the beam with a magnetic field - so we reintroduced our coils. We didn't use this setup because of the inaccuracy of the electric field value but the point at which the magnetic and electric canceled out was at the values - (V = 250.3 +/- 0.1V and I = 1.750A).
Geophysical Website from this site we determined the earths magnetic field to account for approx. 5X 10^-5 T which compared to our values for the measured magnetic field of our apparatus was an order of magnitude off and would not really affect our data.
Results and Discussion
The bulb was filled with helium at 10−2mm Hg pressure. The lab manual states "you should be able to see the violet hue of theelectron beam projecting horizontally from the electron gun" on page 16, we did some investigation into this area and found that the measurable range for our experiment was in the cyan wavelength of the arc, but at lower voltage and current we found that the arc created by the electron beam had a different color (purple) at the peak, from the base color (cyan). Furthermore we found that lowering these values more resulted in the disappearance all together of that peak. We postulated the reasons for this at the quantum level and examined helium (the substance in our bulb) under the spectroscope, that substances spectra does in fact have both of these colors within the visible range (and we reasoned that it might have been an ultraviolet wavelength that was the non viewable portion) but we are still inconclusive about why the difference appeared. In Thomson's paper he did give much more attention to the aspect of the substance and pressure of the gas, but did not examine helium, also I would like to note that on page 16 of his paper he noted that different materials for the cathode/anode did result in different appearance of the cathode raySJK 23:46, 16 December 2008 (EST)Helium Spectra
Dr. Koch helped us theorize that the reason for this could be that the beam loses energy from colliding with the helium atoms (which is necessary for the emission of light we see) and that the two colors might correspond to the two colors associated with the ionization of either one or both electrons throughout the path by progressively less energetic electrons. The other theory we considered was that the electric field was significantly important to the experiment and the electrons would be decelerated significantly after departing the cathode and this caused the loss of energy, then they were re-accelerated as they bent around to approach the cathode again.
Some further analysis lead us to some alternate conclusions. Because the violet didn't migrate downward along the circumference when the peak of the beam dissapeared we reasoned that it was not likely ultraviolet light, because that would imply a higher energy for the beam, but the violet line transistion remained unchanged. There was an interesting effect where when increasing the voltage from the violet containing beam to the pure cyan that there was an immediate jump at the value, however when moving down in potential from the pure cyan to the violet containing beam, the process was slower as though a decay effect. Using a green filter we found that the violet region did in fact contain green, and that means that that regions was not monochromatic, an violet was mearly the dominant color. We discovered using diffraction gratings that the cyan color was monochromatic and not a combination of blue and green as we had speculated, and the heated filiment was a blackbody which refers to an equally important alternate experiment concearning the Boltzmann distribution of the energy levels in the material. Finally my hypothesis for the why there is a higher energy light emitted at a certain region at low energy levels is related to Raleigh scattering; the higher energy electrons do not interact with helium atoms as strongly, but when that prominant energy level is scattered only the less prominant violet remains, when the energy is higher the distribution of energy allows for a constant predominant scattering of cyan.
|Accelarating Voltage (V)||Magnetic Field Current (A)||Magnetic Field B = mu*I (Weber/m^2)*10^-4||Diameter 1 (cm)||Diameter 2(cm)||Average (cm)||Error (sum(mean - trials)/2 +/- .3cm line width)||Radius(cm)|
|284.4 +/- .1||1.162||9.063||8||7.5||7.75||0.35||3.875|
We then created an Excel page to analyze the data, we linearly graphed V vs. r^2 to obtain a best fit line for the slope in the graph of e/m vs. 2/B^2. The slope was off by two orders of magnitude for our average calculated value of e/m so we went back and threw out the values that affected our graph. Our Error from the accepted e/m value of 1.756*10^11C/kg was approximately 70% which is terrible. Some possible reasons for our massive error were discussed previously: The systematic error for this experiment is massive, the accelerating voltage is not uniform due to the hole in the anode made to view the arc. The electron beam itself is largely affected in the helium cloud it passes through and loses energy to ionize them. The beam is also decelerated the farther from the potential it travels. The curvature of the glass bulb may have affected our view at larger diameters, and the beam itself had a width. For random error we expect that our eyes would be extremely inaccurate tools to determine the diameter, but we were mostly confident with our electric data recordings. Image:EM.xls
Accepted value for e/m: 1.76×10^11 C/kg For our data we got the value of:
- 4.7(4) * 10^10 C/kg
which is the mean and the standard deviation of 4.0 * 10^9 C/kg within 68% accuracy which is approximately half the accepted value of this quantity. Our experiment had a lot of possible errors which could account for our large error from the accepted, notably systematic errors that occurred because of the non uniformity of the electric field and the decrease in energy of our field away from the electron gun.
Our experimentally measured value for the quantity e/m is well deviated from the accepted. I conclude that this experimental apparatus is not an effective measurement technique for the e/m value. There is large systematic error of the equipment as well as the error inherit in the measurement process. If the measurements could have been taken entirely electronically, then only the error of the equipment would be necessary to account for. There is an alternate apparatus analagous to ours, where the electon beam is projected upward through a hole and then when the beam is curved by the magnetic field the beam is projected upon a radial ruler. To attain an even more accurate measurement of the quotient it would be most usefull to reproduce Dunnington's method.
I would like to acknowledge my lab partner Michael R. Phillips for his experimental assistance, as well as Dan Young, my Professor Steve Koch for his experience and guidance, as well as Lab T.A. Aram Gragossian for his experience and guidance, and finally The UNM Physics and Astronomy Department for their equipment and lab time.
(1)Thomson, J.J., Cathode Rays, Philosophical Magazine, 44, 293 Cambridge Aug. 7, 1897. [facsimile from Stephen Wright, Classical Scientific Papers, Physics (Mills and Boon, 1964).]
(2)Gold, Michael, PHYSICS 307L: Junior Laboratory, University of New Mexico Dept. Physics and Astronomy (pgs. 15-20), Fall 2006
(3)Azooz A A, "The Magneton Method for the Determination of e/m for Electrons: Revisited", Euorpean Journal of Physics, 28, 1-7 (2007)
(4)Whyte, T. D., Rymillis, P. J., and Willis J. S., "Meausrement of e/m0 using Dunnington's Method - An Experiment for Advanced Undergraduates", American Journal of Physics 52(8) August 1984
(5)Zeeman P. " The Effects of Magnetisation on the Nature of Light Emitted by a Substance", Nature, vol. 55, pg. 347 February 11, 1897