The historical results of this experiment by determination of the charge to mass ratio of an electron allowed physicist to work out the miniscule mass of an electron through the use of an external magnetic field. Magnetic fields apply a magnetic force on charged particles perpendicular to their direction of motion and to the magnetic field itself. This allows for the magnetic force to act as a centripetal force which then, through analysis, allows for the determination of certain charged particles through the analysis of their curve radius. In lab 15, Measurement of Charge to Mass Ratio for Electrons, the objective was to measure the charge to mass ratio (e/m) of an electron ...view middle of the document...
Bh = (m/e)1/2 x (2V)1/2/r + Be, where m is the mass of an electron, e is the elementary electron charge, V is the voltage applied on the electrons, r is the electron radius curvature, Be is the Earth’s magnetic field, and Bh is the Hemholtz coil magnetic field. This is in the form y = mx +b.
Since slope=m is equal to (m/e)1/2, rearrangement gives e/m = 1/(slope)2, and finally this allows for the experimental calculation of the charge to mass ratio of an electron.
The experimental set up in this experiment involved the use of a mercury vapor chamber in which the Hg atoms became excited when charged particles (i.e. electrons) collide with the Hg atoms to excite them to higher energy levels and when they de-excite they released EMR in the form of visible photon distinguishable with the human eye. Another important machine needed for the extraction of data was a magnetic field to deflect the electrons. In this lab, a Helmholtz coil was used. The way results were conducted in this lab followed a few simple steps. Firstly, a constant voltage was applied for five trials as the radius of the beam was placed at one of the five pre-measured pegs, a change in current allows for the ability to choose the radius in which the electron beam curves. The electrons were fired with a certain amount of kinetic energy, perpendicular to the magnetic field of the coils, this force is perpendicular to the velocity and magnetic field and this allows for the analyzation of the curvature of path an electron takes for various voltage and current values. Once 15 values of curvature radius were determined, slope analysis was carried out by the use of equation (4) to inevitably determine the experimental value for the charge to mass ratio of an electron.
20 Volts 30 Volts 40 Volts
r (m) Current (amps) r (m) Current (amps) r (m) Current (amps)
0.065 2.68 0.065 3.24 0.065 3.66
0.078 2.27 0.078 2.71 0.078 3.13
0.09 1.95 0.09 2.36 0.09 2.71
0.103 1.79 0.103 2.07 0.103 2.37
0.115 1.57 0.115 1.91 0.115 2.08
Uo (4πx10-7 Tm/A) N (number loops) Coefficient (Coil) R (m) E (C) Me (Kg) coefficient 2 Voltage 1 (V) Voltage 2 (V) Voltage 3 (V)
1.25664E-06 72 0.715541753 0.33 1.6E-19 9.11E-31 2 20 30 40
All Data Points:
r (m) I (amps) Bh (T) (2V)1/2/r (V1/2/m) - units
0.065 2.68 0.000526 97.30085108
0.078 2.27 0.000445 81.08404257
0.09 1.95 0.000383 70.27283689
0.103 1.79 0.000351 61.40344971
0.115 1.57 0.000308 54.99613322
0.065 3.24 0.000636 119.1687183
0.078 2.71 0.000532 99.30726529
0.09 2.36 0.000463 86.06629658
0.103 2.07 0.000406 75.20356012
0.115 1.91 0.000375 67.35623211
0.065 3.66 0.000718 137.6041832
0.078 3.13 0.000614 114.6701527
0.09 2.71 0.000532 99.380799
0.103 2.37 0.000465 86.83759136
0.115 2.08 0.000408 77.77627748