Physics 342 LaboratoryThe Determination of e/m for ElectronsRR 7/00SS 12/01 Physics 342 LaboratoryThe Determination of e/m for ElectronsObjective: To determine the charge to mass ratio of electrons. Apparatus: Vacuum tube (Bainbridge); Helmholtz coil pair; calibrated meters to measurecurrent and voltage; 300 V power supply; 6.3V ac power supply; Sargent-Welch interfacebox.References: 1. J.J. Thomson, Phil. Mag. 44, 295 (1897). 2. K. T. Bainbridge, The American Physics Teacher 6, 3 (1938). 3. Common Apparatus AAPT Novel Experiments in Physics (Am. Inst. of Physics 1964)pp. 237-41. 4. J.R. Reitz and F.J. Milford, Foundations of Electromagnetic Theory, (Addison Wesley;Reading, Massachusetts; 1969), pgs. 156-57. IntroductionThe first experimental evidence for the granular nature of electricity can be found inMichael Faraday’s work on electrochemical processes in 1839. Prior to Faraday’s work,electricity was considered a ‘fluid’ that could be added or subtracted in a continuousfashion from objects. It was subsequently discovered that metals emitted negativeelectrical current when heated, illuminated by light, or subjected to a strong electric field.It was shown that the negative current was comprised of particles carrying a negativecharge of 1.610-19 C. These negative particles were found to be universally detectedwhenever a negative current was emitted from an electrode. Surprisingly, they were notrelated to the particular metal from which the emitting electrode was fabricated, thusproviding strong evidence for their fundamental nature. In 1874, C. Johnstone Stoneydubbed these particles electrons.Early attempts to measure the mass of electrons proved futile. To address this issue,various direct experiments were devised. For instance, if a metal sphere of 1 meter radiusis charged to a potential of -1106 V, you can quickly estimate that about 71014 electronsmust be added. Yet attempts to directly measure the mass increase of such an electrifiedsphere from the added electrons yielded no conclusive results. As a consequence, it was1argued that the mass of an electron must be very, very small compared to any atomicmasses that were known in the late 1800’s.Indirect methods were therefore sought to measure the mass of these negatively chargedparticles. J. J. Thomson in 1897 was the first to succeed in this endeavor. Since theamount of charge carried by each electron was known independently, the mass of anindividual electron could be inferred if the charge to mass ratio was known. Thomson’sexperiments combined both ingenious insight and the use of recent advances in vacuumpumps and charge measuring devices (electrometers). Using clever calorimetrictechniques, he measured the temperature rise of thin metal targets inserted into a glowdischarge (first produced by Faraday, when two metal plates were inserted inside anevacuated glass tube and raised to a high electrostatic potential). This strategy enabledThomson to calculate the energy imparted to the metal targets by the invisible particlesresponsible for producing the glow. By assuming the invisible particles followed Newton’slaws of motion (at the time, there was no reason to suspect that this might be the case), hewas able to estimate the velocity of the particles responsible for the glow discharge. Healso used crossed electric and magnetic fields to further study the motion of these invisibleparticles. As a result, Thomson concluded (within the accuracy of his measurements) that anegatively charged particle with a mass to charge ratio of 1.30.210-11 kg/C wasresponsible for producing the glow discharge. This mass to charge ratio was roughly 103times smaller than any ratio previously recorded for atoms or molecules. For this reason,he was forced to postulate the presence of a new particle now called the electron. Themodern, accepted value for the mass to charge ratio of an electron is0.5685680.00000110-11 kg/C.The importance of Thomson’s work was recognized by the Noble Prize in physics in 1906.In this experiment, you will perform a modification of Thomson’s original work. Bymeasuring the deflection that a magnetic field produces on a beam of electrons having aknown energy, you will deduce a value for the charge to mass ratio of electrons.Theory A charged particle moving in a magnetic field experiences a force F given byBvqF(1)where q is the charge of the particle, vis the particle’ s velocity, and B is the magneticfield. If v is perpendicular to B, the resultant trajectory is circular. Using Newton’slaws of motion, the radius of curvature is given byqBmvR (2)2where m is the mass of the charged particle. Although R and B in Eq. 2 can be measured experimentally, determining the velocity v ismore problematic. Progress can be made by using conservation of energy considerations.If a charged particle is initially at rest and is accelerated through an electric potentialdifference V, then the kinetic energy after acceleration is equal to the the change of thepotential energy qV. From the conservation of energy principle we know thatqVmv22(3)Eliminating the velocity v from Eqs. (2) and (3), we obtain 222RBVmq(4)Since the charge of an electron is particularly important, we often use its special symbol einstead of q. To calculate the e/m ratio for an electron we need to know the accelerating potential V, thevalue of the magnetic field B and the radius R of the circular path of the electron beam.Since it is hard to detect a single electron, we will use a beam of electrons in which allhave approximately the same kinetic energy. Experimental Method In this experiment, a beam of electrons is produced by an electron gun composed of afilament surrounded by a coaxial anode (i.e., electrode with a positive charge) as shown inFig. 1. Electrons thermally emitted from the heated filament are accelerated by a knownpotential difference V between the filament and the anode. The source of electrons in thisexperiment is a metal plate called the cathode. The cathode is often coated with achemical slurry comprised of metal carbonates having a low work function. Thisenhances electron emission from a material in which