Thomson's third contribution to our understanding of the atom (after the discovery of the electron and the Plum Pudding Model of the atom) was to determine the charge to mass ratio (e/m) for the electron.
The currently accepted value for this ratio is 1.7588 x 108 coulombs/g. (coulombs is the standard metric unit of charge.
Thomson was able to use a magnet with a known magnetic field strength to bend the path of the electron beam as it traveled across the tube. He then was able to straighten the beam by applying an opposing electric field. By measuring the amount of the deflection and the strengths of the magnetic and electric fields, he was able to derive the ratio between the charge of the electron and its mass.
The math is beyond the scope of this text.
Unfortunately, neither of the individual values (charge or mass of the electron) was yet known. This is similar to knowing the density of something, but not knowing the mass or volume. IF you knew one, you could find the other.
Similarly, when either the mass or the charge of an electron was independenlty measured, the other could be found using thomson's ratio.
It would take the work of Robert Millikan to move these numbers forward.
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