Thomson’s experiment with cathode rays.

 The discovery of the electron.

Near the end of the nineteenth century scientists suspected that electrical phenomena were produced by tiny charged particles. J.J.Thomson (1856-1940) proved this fact with an experiment on cathode rays.
Cathode rays had been observed in a glass tube, partially evacuated, with electrodes at each end (see the figure in the textbook on page 347): if electrodes are connected to a source of high potential difference, a glow appears around the cathode (a cathode is the negative electrode). Thomson demonstrated that this glow was produced by a flood of particles, all with identical charges and mass, flowing out of the cathode. He called these particles ELECTRONS and made the first step in determining their physical properties by measuring their charge-mass ratio (q/m). To do this, he built a special and completely evacuated tube like the one below.

A strong potential difference is applied to the electrodes (cathode and anode) inserted in the left side of the tube. Because of this strong voltage, electrons are extracted from the cathode and accelerated towards the positive anode, they overshoot it through the hole in its centre, and bang against the phosphor coated surface at the end of the tube. Because of their collision, the phosphor becomes luminous and a dot-shaped glow appears at the point where the electrons impact, revealing the direction of the whole beam.

The conservation energy principle establishes that the initial potential energy of each electron when at rest on the cathode, equals the total kinetic energy the electron has, when passing through the anode. This statement can be written as

and leads immediately to the charge-mass ratio of the electrons:

                                                                                                      (1)

As you can see, to determine such a ratio, besides the known voltage , the velocity of each electron is needed. What did Thomson do to compute the velocity of the electrons in the beam?
He inserted two charged plates in the middle of the tube, producing an electric field which was downward oriented. Since the electrons of the beam are negatively charged, the beam deviates upward and its deviation is revealed by the displacement of the dot-shaped glow on the phosphor coated screen (see the figure below).

From the physical point of view, the beam deviates because an upward oriented electric force insists on each electron with a magnitude:

.

In order to compute the velocity of the electrons, Thompson took advantage of the Lorentz force: the beam consists of a stream of charged particles, so it can be deflected by a magnetic field too. Hence, in order to restore the initial horizontal direction of the beam, he placed two external current carrying coils, producing a magnetic field perpendicular to the page and outward oriented from it. Such a magnetic field generates a downward oriented magnetic Lorentz force on each electron. Its magnitude is

.

At this point, he balanced the two forces by adjusting the value of both fields and (see the figure below).

He established that the two forces were well-balanced when the glow on the phosphor screen goes back to the original position.

From the physical point of view, the balancing of the previous forces means that the electron beam flows along the original direction and that

.

This relationship let him to compute the velocity of each electron through the ratio of the two balanced fields:

and by inserting the last one in the equation (1) Thomson finally found the value of the charge-mass ratio of the electron:

.

Thomson’s experiment did not produce either the mass or the charge of the electron. It did show that the stream consists of separate and negatively charged particles, all having the same definite mass and charge. As we will see, after Thomson, Millikan used the principle of electrostatic to measure the charge on the electron; it was then a simple matter to find its mass.

The Thomson model of the atom

Thomson’s experiment also demonstrated that atoms contained smaller and negatively charged particles: the electrons were initially thought as being uniformly distributed throughout the volume of the whole atom, like raisins in a panettone. Initially, scientists depicted the structure of the atom like the one represented in the figure above:

In this model, the atom consists of negative particles (electrons) inserted in a sphere of positive charge. Notice that there are NO protons in this primitive model.

Sample problem:

First find the velocity of the particles. Since the beam passes through without deflection, the two force on the particles are equal, and

After the initial acceleration, the potential energy is completely converted to kinetic energy, so

and

.