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The mass of the electron

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Actually we won't measure the mass of the electron in this experiment. What we measure is the ratio of the charge and mass of the electron (qe / m). If you have done Millikan's oildrop experiment you have a value of the charge you can use to calculate the mass of the electron.

As you might know charged particles are affected by a force when they move in magnetic fields. The force can be calculated with this expression:

F = q·v·B    [1]
where q is the charge, v is the velocity and B is the strength of the magnetic field.

 

In this experiment the electrons are first accelerated by an electric field in the electron canon.

They get a velocity that we can calculate by comparing the kinetic energy Wk = m·v2 / 2, with the electrical energy gain from the electric field, WE = q·U.

We get the speed as:

v = sqrt(2·q·U / m)    [2]
Since the electrons are making a circular motion in the magnetic field we can use the following expression for the force acting on a single electron:
q·v·B = m·v2 / r    [3]
Use your algebraic skills combined with expression [2] for v, and you will find that the ratio q / m can be expressed with just the accelerating voltage U, the magnetic field B and the radius r of the circle. You just have to measure the radius on the screen.

 

Enter the values in your expression for q/m and use the value of q from Millikan's experiment and you will get the mass of the electron.

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15 february 2000 Magnus Karlsson