MEASUREMENT OF THE ELECTRON CHARGE TO MASS RATIO The above measuring instrument is a large glass bulb containing low‐pressure (about 10‐5 bar) hydrogen. Inside the bulb a current heats up a filament, which upon reaching incandescence, emits electrons due to the thermoelectric effect. The electrons produced are then accelerated by a potential difference (max. 300 V) between the filament and the anode, which is located immediately above it. The cone like shape anode has a small hole on the tip, thus allowing the electrons to exit the cone forming a collimated beam. The energy of the electrons is sufficient to excite, by collision, the hydrogen atoms present in the bulb. Such atoms then quickly return the ground state and in doing so emit photons of wavelengths of around 450 nm. Therefore the trajectory of the electrons, which is a vertical straight line, can be seen as a pale blue trail. The bulb is placed in the centre of a pair of Helmholtz coils where a current flows producing a uniform magnetic field, of intensity equal to: 4
5
Here N is the number of turns of the coil (for our device N = 130), Rb is the radius of the coils (Rb = 15.5 cm) and μ0 is the permeability of free space (μ0 = 4π 10‐7 N/A2). An electron moving at velocity v perpendicular to a uniform magnetic field B is subject to the Lorentz force: (e being the electron charge). This force, which is perpendicular to the velocity and to the magnetic field, is a centripetal force that modifies the trajectory of the electrons inside the bulb. The force accelerates the electrons in a circular orbit, whose radius r can be determined by the relationship: m being the mass of the electron. If the accelerating potential V is known, the velocity of the electrons can be simply obtained from the equation: 1
2
(the initial velocity of electrons, after their emission, is negligible). The charge‐to‐mass ratio of the electron is therefore given by: 2
2
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The experimental apparatus consists of: • a large, hydrogen‐filled bulb, used to produce and display the electron beam, placed in the centre of the Helmholtz coils; • the voltage generators to create the needed voltages: ƒ 6 V for the filament ƒ 0 ‐ 300 V to extract the electron beam ƒ 0‐12 V to generate the current in the coils; • a voltage meter to measure the accelerating voltage and a current meter to determine the current inside the coils. Once the voltages have been switched on, the circular path of the electrons inside the bulb can be seen. If the direction of the beam leaving the anode is not perpendicular to the magnetic field, electrons will move along a cylindrical helix. In this occurrence slightly rotate the bulb: the trajectory of electrons should be a circle located on the symmetry plane of the coils. Then you can measure the diameter of the circle formed by the electrons. Measurements should be repeated in different conditions of accelerating high voltage and current of the coils. Because of the influence of the terrestrial magnetism, the symmetry axis of the coils should be set in a horizontal plane and perpendicular to the direction of Earth’s magnetic field, which can be found using a compass. We suggest to compare the magnetic field expected for a given current, according to eq. (1), with the field really produced, as measured by the gaussmeter supplied for the experiment. By means of the gaussmeter you can also verify that the field is uniform in the radial direction up to distances of a few cm away from the centre of the coils.