Thomson 1904/Chapter 4

Electricity and Matter

Chapter I

Representation of the Electric Field by Lines of Force

Chapter II

Electrical and Bound Mass

Chapter III

Effects Due to the Acceleration of Faraday Tubes

Chapter IV

The Atomic Structure of Electricity

Chapter V

The Constitution of the Atom

Chapter VI

Radio-Activity and Radio-Active Substances

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Chapter IV

The Atomic Structure of Electricity

Hitherto we have been dealing chiefly with the properties of the lines of force, with their tension, the mass of ether they carry along with them, and with the propagation of electric disturbances along them; in this chapter we shall discuss the nature of the charges of electricity which form the beginnings and ends of these lines. We shall show that there are strong reasons for supposing that these changes have what may be called an atomic structure; any charge being built up of a number of finite individual charges, all equal to each other: just as on the atomic theory of matter a quantity of hydrogen is built up of a number of small particles called atoms, all the atoms being equal to each other. If this view of the structure of electricity is correct, each extremity of a Faraday tube will be the place from which a constant fixed number of tubes start or at which they arrive.

Let us first consider the evidence given by the laws of the electrolysis of liquids. Faraday showed that when electricity passes through a liquid electrolyte, the amount of negative electricity given up to the positive electrode, and of positive electricity given to the negative electrode, is proportional to the number of atoms coming up to the electrode. Let us first consider monovalent elements, such as hydrogen, chlorine, sodium, and so on; he showed that when the same number of atoms of these substances deliver up their charges to the electrode, the quantity of electricity communicated is the same whether the carriers are atoms of hydrogen, chlorine, or sodium, indicating that each atom of these elements carries the same charge of electricity. Let us now go to the divalent elements. We find again that the ions of all divalent elements carry the same charge, but that a number of ions of the divalent element carry twice the charge carried by the same number of ions of a univalent element, showing that each ion of a divalent element carries twice as much charge as the univalent ion; again, a trivalent ion carries three times the charge of a univalent ion, and so on. Thus, in the case of the electrolysis of solutions the charges carried by the ions are either the charge on the hydrogen ion or twice that charge, or three times the charge, and so on. The charges we meet with are always an integral multiple of the charge carried by the hydrogen atom; we never meet with fractional parts of this charge. This very remarkable fact shows, as Helmholtz said in the Faraday lecture, that "if we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid the conclusion that electricity, positive as well as negative, is divided into definite elementary portions which behave like atoms of electricity."

When we consider the conduction of electricity through gases, the evidence in favor of the atomic character of electricity is even stronger than it is in the case of conduction through liquids, chiefly because we know more about the passage of electricity through gases than through liquids.

Let us consider for a moment a few of the properties of gaseous conduction. When a gas has been put into the conducting state — say, by exposure to Röntgen rays — it remains in this state for a sufficiently long time after the rays have ceased to enable us to study its properties. We find that we can filter the conductivity out of the gas by sending the gas through a plug of cottonwool, or through a water-trap. Thus, the conductivity is due to something mixed with the gas which can be filtered out of it; again, the conductivity is taken out of the gas when it is sent through a strong electric field. This result shows that the constituent to which the conductivity of the gas is due consists of charged particles, the conductivity arising from the motion of these particles in the electric field. We have at the Cavendish Laboratory measured the charge of electricity carried by those particles.

The principle of the method first used is as follows. If at any time there are in the gas n of these particles charged positively and n charged negatively, and if each of these carries an electric charge e, we can easily by electrical methods determine n e, the quantity of electricity of our sign present in the gas. One method by which this can be done is to enclose the gas between two parallel metal plates, one of which is insulated. Now suppose we suddenly charge up the other plate positively to a very high potential, this plate will now repel the positive particles in the gas, and these before they have time to combine with the negative particles will be driven against the insulated plate. Thus, all the positive charge in the gas will be driven against the insulated plate, where it can be measured by an electrometer. As this charge is equal to n e we can in this way easily determine n e: if then we can devise a means of measuring n we shall be able to find e. The method by which I determined n was founded on the discovery by C. T. R. Wilson that the charged particles act as nuclei round which small drops of water condense, when the particles are surrounded by damp air cooled below the saturation point. In dust-free air, as Aitken showed, it is very difficult to get a fog when damp air is cooled, since there are no nuclei for the drops to condense around; if there are charged particles in the dust-free air, however, a fog will be deposited round these by a supersaturation far less than that required to produce any appreciable effect when no charged particles are present.

Thus, in sufficiently supersaturated damp air a cloud is deposited on these charged particles, and they are thus rendered visible. This is the first step toward counting them. The drops are, however, far too small and too numerous to be counted directly. We can, however, get their number indirectly as follows: suppose we have a number of these particles in dust-free air in a closed vessel, the air being saturated with water vapor, suppose now that we produce a sudden expansion of the air in the vessel; this will cool the air, it will be supersaturated with vapor, and drops will be deposited round the charged particles. Now if we know the amount of expansion produced we can calculate the cooling of the gas, and therefore the amount of water deposited. Thus, we know the volume of water in the form of drops, so that if we know the volume of one drop we can deduce the number of drops. To find the size of a drop we make use of an investigation by Sir George Stokes on the rate at which small spheres fall through the air. In consequence of the viscosity of the air small bodies fall exceedingly slowly, and the smaller they are the slower they fall. Stokes showed that if a is the radius of a drop of water, the velocity v with which it falls through the air is given by the equation

$v=\frac{2}{9}\frac{g{a}^2}{\mu }$ ;

when g is the acceleration due to gravity = 981 and μ the coefficient of viscosity of air = .00018; thus

$v=1.21\times 10^6{a}^2$ ;

hence if we can determine v we can determine the radius and hence the volume of the drop. But v is evidently the velocity with which the cloud round the charged particle settles down, and can easily be measured by observing the movement of the top of the cloud. In this way I found the volume of the drops, and thence n the number of particles. As n e had been determined by electrical measurements, the value of e could be deduced when n was known; in this way I found that its value is

$3.4\times 10^{-10}$ Electrostatic C. G. S. units.

Experiments were made with air, hydrogen, and carbonic acid, and it was found that the ions had the same charge in all these gases; a strong argument in favor of the atomic character of electricity.

We can compare the charge on the gaseous ion with that carried by the hydrogen ion in the electrolysis of solutions in the following way: We know that the passage of one electro-magnetic unit of electric charge, or 3×10^-10 electrostatic units, through acidulated water liberates 1.23 c.c. of hydrogen at the temperature 15°C. and pressure of one atmosphere; if there are N molecules in a c.c. of a gas at this temperature and pressure the number of hydrogen ions in 1.23 c.c. is 2.46 N, so that if E is the charge on the hydrogen ion in the electrolyis of solution,

$2.46NE=3.4\times 10^{-10}$ ,

or $E=1.22\times 10^{10}÷N$ .

Now, e, the charge on the gas ion is 3×10^-10, hence if N=3×10¹⁹ the charge on the gaseous ion will equal the charge on the electrolytic ion. Now, in the kinetic theory of gases methods are investigated for determining this quantity N, or Avogadro's Constant, as it is sometimes called; the values obtained by this theory vary somewhat with the assumptions made as to the nature of the molecule and the nature of the forces which one molecule exerts on another in its near neighborhood. The value 3×10¹⁹ is, however, in good agreement with some of the best of these determinations, and hence we conclude that the charge on the gaseous ion is equal to the charge on the electrolytic ion.

Dr. H. A. Wilson, of the Cavendish Laboratory, by quite a different method, obtained practically the same value for e as that given above. His method was founded on the discovery by C. T. R. Wilson that it requires less supersaturation to deposit clouds from moist air on negative ions than it does on positive. Thus, by suitably choosing the supersaturation, we can get the cloud deposited on the negative ions alone, so that each drop in the cloud is negatively charged ; by observing the rate at which the cloud falls we can, as explained above, determine the weight of each drop. Now, suppose we place above the cloud a positively electrified plate, the plate will attract the cloud, and we can adjust the charge on the plate until the electric attraction just balances the weight of a drop, and the drops, like Mahomet's coffin, hang stationary in the air; if X is the electric force then the electric attraction on the drop is Xe, when e is the charge on the drop. As X e is equal to the weight of the drop which is known, and as we can measure X, e can be at once determined.

Townsend showed that the charge on the gaseous ion is equal to that on the ion of hydrogen in ordinary electrolysis, by measuring the coefficient of diffusion of the gaseous ions and comparing it with the velocity acquired by the ion under a given electric force. Let us consider the case of a volume of ionized gas between two horizontal planes, and suppose that as long as we keep in any horizontal layer the number of ions remains the same, but that the number varies as we pass from one layer to another; let x be the distance of a layer from the lower plane, n the number of ions of one sign in unit volume of this layer, then if D be the coefficient of diffusion of the ions, the number of ions which in one second pass downward through unit area

of the layer is

d n

»ir*'

so that the average velocity of the particles downward is

l)dn

n dx

The force which sets the ions in motion is the variation in the partial pressure due to the ions ; if this pressure is equal top, the force acting on the

ions in a unit volume is T-> and the average force

per ion is -r— . Now we can find the velocity ndx

which an ion acquires when acted upon by a known force by measuring, as Rutherford and Zeleny have done, the velocities acquired by the ions in an electric field. They showed that this velocity is proportional to the force acting on the ion, so that if A. is the velocity when the electric force is JTand when the force acting on the ion is therefore X e, the velocity for unit force will be

-==r-, and the velocity when the force is 1 ^ will .A e n ax

therefore be

i dp ^L.

n dx Xe'

this velocity we have seen, however, to be equal to D dnf n dx' hence we have

dP A --T) dn (l\

~7 ~Tr~ •*/ "7 — • V1/

dx Xe dx

Now if the ions behave like a perfect gas, the pressure p bears a constant ratio to n, the number of ions per unit volume. This ratio is the same for all gases, at the same temperature, so that if jV is Avogadro's constant, i.e., the number of molecules in a cubic centimetre of gas at the atmospheric pressure P

p _ n P~W

and equation (1) gives us PA

Thus, by knowing D and a we can find the value of Ne. In this way Townsend found that Ne was the same in air, hydrogen, oxygen, and carbonic acid, and the mean of his values was N e = 1.24 X 1010. We have seen that if E is the charge on the hydrogen ion

NE = 1.22 X 1010-

Thus, these experiments show that e—E, or that the charge on the gaseous ion is equal to the charge carried by the hydrogen ion in the electrolysis of solutions.

The equality of these charges has also been proved in a very simple way by H. A. Wilson, who introduced per second into a volume of air at a very high temperature, a measured quantity of the vapor of metallic salts. This vapor got ionized and the mixture of air and vapor acquired very considerable conductivity. The current through the vapor increased at first with the electromotive force used to drive it through the gas, but this increase did not go on indefinitely, for after the current had reached a certain value no further increase in the electromotive force produced any change in the current. The current, as in all cases of conduction through gases, attained a maximum value called the " saturation current," which was not exceeded until the electric field applied to the gas approached the intensity at which sparks began to pass through the gas. Wilson found that the saturation current through the salt vapor was just equal to the current which if it passed through an aqueous solution of the salt would electrolyse in one second the same amount of salt as was fed per second into the hot air.

It is worth pointing out that this result gives us a method of determining Avogadro's Constant which is independent of any hypothesis as to the shape or size of molecules, or of the way in which they act upon each other. If .N" is this constant, e the charge on an ion, then JV e — 1.22 X 1010 and we have seen that e = 3.4 X l^10, so that jV= 3.fc X 1019.

Thus, whether we study the conduction of electricity through liquids or through gases, we are led to the conception of a natural unit or atom of electricity of which all charges are integral multiples, just as the mass of a quantity of hydrogen is an integral multiple of the mass of a hydrogen atom.

Mass of the Carriers of Electricity

We must now pass on to consider the nature of the systems which carry the charges, and in order to have the conditions as simple as possible let us begin with the case of a gas at a very low pressure, where the motion of the particles is not impeded by collisions with the molecules of the gas. Let us suppose that we have a particle of mass m, carrying a charge e, moving in the plane of the paper, and that it is acted on by a uniform magnetic field at right angles to this plane. We have seen that under these circumstances the particle will be acted upon by a mechanical force equal to He v, where His the magnetic force and v the velocity of the particle. The direction of this force is in the plane of the paper at right angles to the path of the particle. Since the force is always at right angles to the direction of motion of the particle, the velocity of the particle and therefore the magnitude of the force acting upon it will not alter, so that the path of the particle will be that described by a body acted upon by a constant normal force. It is easy to show that this path is a circle whose radius a is given by the equation

mv ,tv

The velocity v of the particle may be determined by the following method : Suppose the particle is moving horizontally in the plane of the paper, through a uniform magnetic field If, at right angles to this plane, the particle will be acted upon by a vertical force equal to H e v. Now, if in addition to the magnetic force we apply a vertical electric force X, this will exert a vertical mechanical force X e on the moving particle. Let us arrange the direction of JTso that this force is in the opposite direction to that due to the magnet, and adjust the value of X until the two forces are equal. We can tell when this adjustment has been made, since in this case the motion of the particle under the action of the electric and magnetic forces will be the same as when both these forces are absent. When the two forces are equal we have

X e — H e v, or

Hence if we have methods of tracing the motion of the particle, we can measure the radius a of the circle into which it is bent by a constant magnetic force, and determine the value of the electric force required to counteract the effect of the magnetic force. Equations (1) and (2) then give us the

means of finding both v and — •

Values of — for Negatively Electrified Particles in Gases at Low Pressures

The value of e. has been determined in this m

way for the negatively electrified particles which form the cathode rays which are so conspicuous a part of the electric discharge through a gas at low pressures ; and also for the negatively electrified particles emitted by metals, (1) when exposed to ultra-violet light, (2) when raised to the temperature of incandescence. These experiments have led to the very remarkable result that the value of

— is the same whatever the nature of the gas in which the particle may be found, or whatever the nature of the metal from which it may be supposed to have proceeded. In fact, in every case in which the value of — has been determined for m

negatively electrified particles moving with velocities considerably less than the velocity of light, it has been found to have the constant value about 10T, the units being the centimetre, gram, and second, and the charge being measured in electromagnetic units. As the value of — for the hydrogen ion in the electrolysis of liquids is only 104, and as we have seen the charge on the gaseous ion is equal to that on the hydrogen ion in ordinary electrolysis, we see that the mass of a carrier of the negative charge must be only about one thousandth part of the mass of hydrogen atom ; the mass was for a long time regarded as the smallest mass able to have an independent existence.

I have proposed the name corpuscle for these units of negative electricity. These corpuscles are the same however the electrification may have arisen or wherever they may be found. Negative electricity, in a gas at a low pressure, has thus a structure analogous to that of a gas, the corpuscles taking the place of the molecules. The " negative electric fluid," to use the old notation, resembles a gaseous fluid with a corpuscular instead of a molecular structure.

Carriers of Positive Electrification

We can apply the same methods to determine the values of — for the carriers of positive electrify fication. This has been done by Wien for the positive electrification found in certain parts of the discharge in a vacuum tube, and I have

CQ

oo

measured — for the positive electrification given off by a hot wire. The results of these measurements form a great contrast to those for the negative electrification, for — for the positive charge, instead of having, as it has for the negative, the constant high value 107, is found never to have a value greater than 104, the value it would have if the carrier were the atom of hydrogen. In many cases the value of — is very much less than 104, indicating that in these cases the positive charge is carried by atoms having a greater mass than that ^ of the hydrogen atom. The value of — varies with the nature of the electrodes and with the gas in the discharge tube, just as it would if the carriers of the positive charge were the atoms of the elements which happened to be present when the positive electrification was produced.

These results lead us to a view of electrification which has a striking resemblance to that of Franklin's "One Fluid Theory of Electricity." Instead of taking, as Franklin did, the electric fluid to be positive electricity we take it to be negative. The "electric fluid" of Franklin corresponds to an assemblage of corpuscles, negative electrification being a collection of these corpuscles. The transference of electrification from one place to another is effected by the motion of corpuscles from the place where is a gain of positive electrification to the place where there is a gain of negative. A positively electrified body is one that has lost some of its corpuscles. We have seen that the mass and charge of the corpuscles have been determined directly by experiment. We in fact know more about the "electric fluid" than we know about such fluids as air or water.