Determining the Charge-to-Mass Ratio of the Electron

Abstract

The aim of this lab was to determine an experimental value for the charge-to-mass ratio e/me of the electron. In order to do this, an assembly consisting of Helmholtz coils and a helium-filled fine beam tube containing an electron gun was used. Electrons were accelerated from rest by the electron gun at a voltage of 201.3 V kept constant across trials. When the accelerated electrons collided with the helium atoms in the fine beam tube, the helium atoms entered an excited state and released energy as light. Since the Helmholtz coils put the electrons into centripetal motion, this resulted in a circular beam of light, the radius of which was measured by taking a picture and using photo analysis. This procedure was used to test currents through the Helmholtz coils ranging from 1.3 A to 1.7 A in increments of 0.1 A. Using a linearization of these data, the experimental value for the charge-to-mass ratio of the electron was found to be 1.850 × 1011 C/kg, bounded between 1.440 × 1011 C/kg and 2.465 × 1011 C/kg. This range of values includes the accepted value of 1.759 × 1011 C/kg, and yields a percent error of 5.17%. The rather low percent error is a testament to the accuracy of this procedure. During this experiment, the orientation of the ambient magnetic field due to the Earth at the center of the apparatus was not considered. In the future, it would be worthwhile to repeat this procedure, taking care to position the Helmholtz coils in such a way to negate the effects of the Earth’s magnetic field on the centripetal motion of electrons.