How is the mass of the electron calculated?

It was historically done in two steps. JJ Thomson calculated the mass-tocharge ratio in 1897. He was able to measure the effect of an electric field on electrons fired from a cathode guns at a given velocity and observe the amount that the beam is deflected by the field. This allowed him to calculate the mass-to charge ratio. me/Q

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More details: J. J. Thomson 1897

Harvey Fletcher and Robert Millikan determined the charge in 1897. The electric field was then populated with fine oil droplets. A few electrons would be picked up by the droplets, so they adjusted the field strength to balance the gravitational force against the droplet. They were able to determine the size of each droplet and the gravity force. Because the forces were balanced, they could determine the size of electric force and the charge of electrons.

One interesting thing about this experiment is the discrete values you get for the force. The droplet will absorb 1, 2, 3 or another integer number of electrons. You’ll notice that the force needed to balance the droplet is an exact multiple of some base number, and not a continuous range. This shows that the electric charge comes as quanta of fixed Q.

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