Physics Bootcamp

Do atoms have parts? Prior to the work of J.J. Thomson and others 1880's and 1890's it was believed that atoms were the fundamental building blocks of nature. In 1838 Michael Faraday had observed that, when voltage was applied to two plates in a tube which was partially evacuated, a light arc appeared at the cathode (the negative plate) and almost reached the anode (the positive plate).

An improved version of Faraday's tube is a Crooke's tube shown in Figure 55.1.1. With an improved vacuum one can produce a stream of particles that starts from cathode and moves towards the anode by heating the cathode and applying a voltage between the cathode and the anode. If you cut a hole in the anode plate and place a fluorescent plate behind it, then you find that these particles pass through the anode and strike the fluorescent plate making the dye glow. These rays emitted by the cathode were known as cathode rays.

In 1890's J.J. Thomson conducted experiments on cathode rays to characterize the nature of particles that make up the rays. First, he demonstrated that the charge carried by cathode rays could not be separated from the cathode rays themselves. In another experiment he showed that the cathode rays passing through vacuum could be bent in an electric field just as electrically charged particles would.

From these two experiments, J.J. Thomson concluded, “I can see no escape from the conclusion that (cathode rays) are charges of negative electricity carried by particles of matter. ... What are these particles? Are they atoms, or molecules, or matter in a still finer state of subdivision?”

In an ingenious experiment, which is called the \(e/m\) experiment now, he was able to measure the ratio of charge to mass \(e/m\) for the particles of the cathode ray. He found that \(e/m\) of these particles were more than a thousand times larger than that of a charged hydrogen atom, the lightest charged particle known at the time. Either the charged particles of the cathode ray had very small masses or were very highly charged.

In a modern version of the \(e/m\) experiment shown in Figure 55.1.2 electrons from a heated metal filament are boiled off and accelerated to an evacuated chamber where a known electric field \(\vec E\) bends them one way and a known magnetic field \(\vec B\) bends them in the other way. By balancing the electric and magnetic forces we find their speed \(v\) when the ray is not bent when passing through a region of crossed electric and magnetic fields of appropriate magnitudes. Let \(q=-e\) be the charge on an electron, then balancing electric and magnetic forces gives us

The speed of the changed particle can also be obtained from the radius of the circular orbit of the moving the particle in a uniform magnetic field by turning off the deflection voltage \(V_{\textrm{defl}}\) in the apparatus shown in Figure 55.1.2. Assuming cathode rays start out nearly at rest before they are accelerated by the acceleration voltage \(V_{\textrm{acc}}\) the speed with which they enter the evacuated tube will be based on the energy conservation in the acceleration process. Let \(m\) be the mass of an electron. The conservation of energy of the electron gives

which can be solved for \(v\) to yield

From Eqs. (55.1.1) and (55.1.3) we obtain

In the experimental arrangement given in Figure 55.1.2, the magnetic field is related to the number \(N\) of windings in the Helmoholtz coil, the radius \(R\) of the coils, and the current \(I_H\) through the coils by

where

The electric field \(E\) from the deflection voltage \(V_{\textrm{difl}}\) across the plates separated by a distance \(d\) will be

Thus, a measurement of \(d\text{,}\) \(V_{\textrm{difl}}\text{,}\) \(I_H\text{,}\) \(R\text{,}\) \(N\text{,}\) and \(V_{\textrm{acc}}\) yields the experimental value for \(e/m\) from Eq. (55.1.4). The experiment is difficult to do precisely. Despite the impreciseness of the results, there was no doubt in Thomson's mind that cathode rays was made up of entirely new particles as he announced,

“We have in the cathode rays matter in a new state, a state in which the subdivision of matter is carried very much further than in the ordinary gaseous state: a state in which all matter... is of one and the same kind; this matter being the substance from which all the chemical elements are built up.”