In 1897 J.J. Thomson discovered the electron. While he could notfind all the separate properties of the electron, he veryaccurately found the charge to mass ratio, Q/m, using a fairlysimple set up, and the same physics we have learned in class.Thomson knew electric and magnetic fields could deflect chargedparticles, and used these concepts to prove that cathode rays wereactually negatively charged particles which were later namedelectrons. There are several set ups which can mimic Thomsonâsdiscovery, and you will be working out the details of two of them.Note that you will not be solving for a number for the charge tomass ratio, but rather a formula that could be experimentallytested. Your equations will have a few parameters anexperimentalist could tweak to get results. With the charge to massratio known, 1.758820150*1011 C/kg, find some values for yourparameters that would produce the correct results.
The first experiment involves a vacuum tube with a cathode andanode at one end, and a phosphor plate at the other (the theelectrons strike the phosphor it glows, signifying where theelectron hit). The cathode/anode pair provides an initial voltagessource to accelerate the electrons. The electrons then pass througha small slit in order to focus them into a thin beam. This beanthen passes through two parallel plates (creating an electricfield), and past the midpoint of two Helmholtz coils (two largecurrent carrying coils of radius R, separated by a distance R). Ifthe voltage across the plates and the current across the Helmholtzcoil are tuned just right, there should be no deflection of theelectron beam, and the phosphor plate should simple glow at itscenter. Using the concepts and equations discussed in class, findan expression for the charge to mass ratio, Q/m.
The second experiment is similar to the mass spectrometer wediscussed in class. An electron beam is first accelerated by avoltage source, and then passes into a region of uniform magneticfield. The experiment is performed in a vacuum tube which is filledwith a small amount of phosphor gas so the arc of the electron beancan be seen and measured. Find a new expression for the charge tomass ratio, which this time will also include the radius of the arcthe electron beam would make.
Hint: Your final expressions should not contain the velocity of thebeam, as it cannot be directly measured. Think about work andenergy to find a way to remove velocity from the equations.
Now pretend you are giving your equations to an experimentalist.Provide some voltages, currents, magnetic fields, etc. for each ofyour equations to give no deflection, and hence the proper chargeto mass ratio.
Please show all of your work. After you have derived yourexpressions, briefly explain in a paragraph or two what conceptsyou used and why you chose the formulas used. After J.J. Thompsonfound the charge to mass ratio, he concluded the electron must havean extremely small mass. Based on the charge to mass ratio given(pretend for this part you do not know the charge and mass of anelectron separately), try to give some reasons why Thompson madehis assumptions.
In 1897 J.J. Thomson discovered the electron. While he could notfind all the separate properties of the electron, he veryaccurately found the charge to mass ratio, Q/m, using a fairlysimple set up, and the same physics we have learned in class.Thomson knew electric and magnetic fields could deflect chargedparticles, and used these concepts to prove that cathode rays wereactually negatively charged particles which were later namedelectrons. There are several set ups which can mimic Thomsonâsdiscovery, and you will be working out the details of two of them.Note that you will not be solving for a number for the charge tomass ratio, but rather a formula that could be experimentallytested. Your equations will have a few parameters anexperimentalist could tweak to get results. With the charge to massratio known, 1.758820150*1011 C/kg, find some values for yourparameters that would produce the correct results.
The first experiment involves a vacuum tube with a cathode andanode at one end, and a phosphor plate at the other (the theelectrons strike the phosphor it glows, signifying where theelectron hit). The cathode/anode pair provides an initial voltagessource to accelerate the electrons. The electrons then pass througha small slit in order to focus them into a thin beam. This beanthen passes through two parallel plates (creating an electricfield), and past the midpoint of two Helmholtz coils (two largecurrent carrying coils of radius R, separated by a distance R). Ifthe voltage across the plates and the current across the Helmholtzcoil are tuned just right, there should be no deflection of theelectron beam, and the phosphor plate should simple glow at itscenter. Using the concepts and equations discussed in class, findan expression for the charge to mass ratio, Q/m.
The second experiment is similar to the mass spectrometer wediscussed in class. An electron beam is first accelerated by avoltage source, and then passes into a region of uniform magneticfield. The experiment is performed in a vacuum tube which is filledwith a small amount of phosphor gas so the arc of the electron beancan be seen and measured. Find a new expression for the charge tomass ratio, which this time will also include the radius of the arcthe electron beam would make.
Hint: Your final expressions should not contain the velocity of thebeam, as it cannot be directly measured. Think about work andenergy to find a way to remove velocity from the equations.
Now pretend you are giving your equations to an experimentalist.Provide some voltages, currents, magnetic fields, etc. for each ofyour equations to give no deflection, and hence the proper chargeto mass ratio.
Please show all of your work. After you have derived yourexpressions, briefly explain in a paragraph or two what conceptsyou used and why you chose the formulas used. After J.J. Thompsonfound the charge to mass ratio, he concluded the electron must havean extremely small mass. Based on the charge to mass ratio given(pretend for this part you do not know the charge and mass of anelectron separately), try to give some reasons why Thompson madehis assumptions.
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