This difference in behaviour of the positive and negative ions was investigated in detail by C. T. R. Wilson^[68] in the following way. X rays were made to pass in a narrow beam on either side of a plate AB (Fig. 7) dividing the condensation vessel into two equal parts. The opposite poles of a battery of cells were connected with two parallel plates C and D, placed symmetrically with regard to A. The middle point of the battery and the plate A were connected with earth. If the plate C is positively charged, the ions in the space CA at a short distance from A are all negative in sign. Those to the right are all positive. It was found that condensation occurred only for the negative ions in AC when v₂/v₁ = 1·25 but did not occur in AD for the positive ions until v₂/v₁ = 1·31.

Thus the negative acts more readily than the positive ion as a centre of condensation. The greater effect of the negative ion in causing condensation has been suggested as an explanation of the positive charge always observed in the upper atmosphere. The negative ions under certain conditions become centres for the formation of small drops of water and are removed to the earth by the action of gravity, while the positive ions remain suspended.

With the apparatus described above, it has been shown that the positive and negative ions are equal in number. If the expansion is large enough to ensure condensation on both ions, the drops formed on the right and left of the vessel in Fig. 7 are equal in number and fall at the same rate, i.e. are equal in size.

Since the ions are produced in equal numbers from a gas electrically neutral, this experiment shows that the charges on positive and negative ions are equal in value but opposite in sign.

36. Charge carried by an ion. For a known sudden expansion of a gas saturated with water vapour, the amount of water precipitated on the ions can be calculated readily. The size of the drops can be determined by observing the rate at which the cloud settles under the action of gravity. From Stokes’ equation, the terminal velocity u of a small sphere of radius r and density d falling through a gas of which the coefficient of viscosity is μ is given by

This method has been used by J. J. Thomson^[69] to determine the charge carried by an ion. If the expansion exceeds the value 1·31, both positive and negative ions become centres of condensation. From the rate of fall it can be shown that approximately the drops are all of the same size.

The condensation vessel was similar to that employed by C. T. R. Wilson. Two parallel horizontal plates were fitted in the vessel and the radiation from an X ray tube or radio-active substance ionized the gas between them. A difference of potential V, small compared with that required to saturate the gas, was applied between the parallel plates distant l cms. from each other. The small current i through the gas is given (section 28) by

where

Since the value of N is the same as the number of drops, and the velocity u is known, the value of e can be determined.

In his last determination J. J. Thomson found that

A very concordant value, namely, 3·1 × 10^-10, has been obtained by H. A. Wilson^[70], by using a modified method of counting the drops. A check on the size of the drops, determined by their rate of fall, was made by observing the rate at which the drops moved in a strong electric field, arranged so as to act with or against gravity.

J. J. Thomson found that the charge on the ions produced in hydrogen and oxygen is the same. This shows that the nature of the ionization in gases is distinct from that occurring in the electrolysis of solutions where the oxygen ion always carries twice the charge of the hydrogen ion.

37. Diffusion of the ions. Early experiments with ionized gases showed that the conductivity was removed from the gas by passage through a finely divided substance like cotton-wool, or by bubbling through water. This loss of conductivity is due to the fact that the ions in passing through narrow spaces diffuse to the sides of the boundary, to which they either adhere or give up their charge.

A direct determination of the coefficient of diffusion of the ions produced in gases by Röntgen rays or by the rays from active substances has been made by Townsend^[71]. The general method employed was to pass a stream of ionized gas through a diffusion vessel made up of a number of fine metal tubes arranged in parallel. Some of the ions in their passage through the tubes diffuse to the sides, the proportion being greater the slower the motion of the gas and the narrower the tube. Observations were made of the conductivity of the gas before and after passage through the tubes. In this way, correcting if necessary for the recombination during the time taken to pass through the tubes, the proportion R of either positive or negative ions which are abstracted can be deduced. The value of R can be expressed mathematically by the following equation in terms of K, the coefficient of diffusion of the ions into the gas with which they are mixed^[72],

where

Only the first two terms of the series need be taken into account when narrow tubes are used.

In this equation R, V, and a are determined experimentally, and K can thus be deduced.

The following table shows the results obtained by Townsend when X rays were used. Almost identical results were obtained later, when the radiations from active substances replaced the X rays.

The moist gases were saturated with water vapour at a temperature of 15° C.

It is seen that the negative ion in all cases diffuses faster than the positive. Theory shows that the coefficients of diffusion should be directly proportional to the velocities of the ions, so that this result is in agreement with the observations on the greater velocity of the negative ion.

This difference in the rate of diffusion of the ions at once explains an interesting experimental result. If ionized gases are blown through a metal tube, the tube gains a negative charge while the gas itself retains a positive charge. The number of positive and negative ions present in the gas is originally the same, but, in consequence of the more rapid diffusion of the negative ions, more of the negative ions than of the positive give up their charges to the tube. The tube consequently gains a negative and the gas a positive charge.

38. A very important result can be deduced at once when the velocities and coefficients of diffusion of the ions are known. Townsend (loc. cit.) has shown that the equation of their motion is expressed by the formula

where e is the charge on an ion,

and u is the velocity due to the electric force X in the direction of the axis of x. When a steady state is reached,

Let N be the number of molecules in a cubic centimetre of gas at the pressure P and at the temperature 15° C., for which the values of u and K have been determined. Then N/P may be substituted for n/p, and, since P at atmospheric pressure is 10⁶,

then

where u₁ is the velocity for 1 volt (i.e. ¹⁄₃₀₀ E. S. unit) per cm.

It is known that one absolute electromagnetic unit of electricity in passing through water liberates 1·23 c.c. of hydrogen at a temperature of 15° C. and standard pressure. The number of atoms in this volume is 2·46N, and, if e´ is the charge on the hydrogen atom in the electrolysis of water,

For example, substituting the values of u₁ and K determined in moist air for the positive ion,

Values of this ratio, not very different from unity, are obtained for the positive and negative ions of the gases hydrogen, oxygen, and carbon dioxide. Taking into consideration the uncertainty in the experimental values of u₁ and K, these results indicate that the charge carried by an ion in all gases is the same and is equal to that carried by the hydrogen ion in the electrolysis of liquids.

39. Number of the ions. We have seen that, from experimental data, Townsend has found that N, the number of molecules present in 1 c.c. of gas at 15° C. and standard pressure, is given by

The electron or corpuscle is the body of smallest mass yet known to science. It carries a negative charge of value 3·4 × 10^-10 electrostatic units. Its presence has only been detected when in rapid motion, when, for speeds up to about 10¹⁰ cms. a second, it has an apparent mass m given by e/m = 1·86 × 10⁷ electromagnetic units. This apparent mass increases with the speed as the velocity of light is approached (see section 82).

The ions which are produced in gases at ordinary pressure have an apparent size, as determined from their rates of diffusion, large compared with the molecule of the gas in which they are produced. The negative ion consists of an electron with a cluster of molecules attached to and moving with it; the positive ion consists of a molecule from which an electron has been expelled, with a cluster of molecules attached. At low pressures under the action of an electric field the electron does not form a cluster. The positive ion is always atomic in size, even at low pressures of the gas. Each of the ions carries a charge of value 3·4 × 10^-10 electrostatic units.

41. Ions produced by collision. The greater part of the radiation from the radio-active bodies consists of a stream of charged particles travelling with great velocity. In this radiation, the α particles, which cause most of the ionization observed in the gas, consist of positively charged bodies projected with a velocity about one-tenth the velocity of light. The β rays consist of negatively charged particles, which are identical with the cathode rays generated in a vacuum tube, and travel with a speed about one-half the velocity of light (chapter IV.). Each of these projected particles, in virtue of its great kinetic energy, sets free a large number of ions by collision with the gas molecules in its path. No definite experimental evidence has yet been obtained of the number of ions produced by a single particle, or of the way in which the ionization varies with the speed, but there is no doubt that each projected body gives rise to many thousand ions in its path before its energy of motion is destroyed.

It has already been mentioned (section 29) that at low pressures ions moving under the action of an electric field are able to produce fresh ions by collision with the molecules of the gas. At low pressures the negative ion is identical with the electron set free in a vacuum tube, or emitted by a radio-active substance.

The mean free path of the ion is inversely proportional to the pressure of the gas. Consequently, if an ion moves in an electric field, the velocity acquired between collisions increases with diminution of the pressure. Townsend has shown that fresh ions are occasionally produced by collision when the negative ion moves freely between two points differing in potential by 10 volts. If the difference be about V = 20 volts, fresh ions arise at each collision^[73].

Now the energy W, acquired by an ion of charge e moving freely between two points at a difference of potential V, is given by

Taking V = 20 volts = ²⁰⁄₃₀₀ E. S. units, and e = 3·4 × 10^-10, the energy W required in the case of a negative ion to produce an ion by collision is given by

The velocity u acquired by the ion of mass m just before a collision is given by

and

Now e/m = 1·86 × 10⁷ electromagnetic units for the electron at slow speeds (section 82).

Taking V = 20 volts, we find that

This velocity is very great compared with the velocity of agitation of the molecules of the gas.

In a weak electric field, the negative ions only produce ions by collision. The positive ion, whose mass is at least 1000 times greater than the electron, does not acquire a sufficient velocity to generate ions by collision until an electric field is applied nearly sufficient to cause a spark through the gas.

An estimate of the energy required for the production of an ion by X rays has been made by Rutherford and McClung. The energy of the rays was measured by their heating effect, and the total number of ions produced determined. On the assumption that all the energy of the rays is used up in producing ions, it was found that V = 175 volts—a value considerably greater than that observed by Townsend from data of ionization by collision. The ionization in the two cases, however, is produced under very different conditions, and it is impossible to estimate how much of the energy of the rays is dissipated in the form of heat.

42. Variations are found in the saturation current through gases, exposed to the radiations from active bodies, when the pressure and nature of the gas and the distance between the electrodes are varied. Some cases which are of special importance in measurements will now be considered. With unscreened active material the ionization of the gas is, to a large extent, due to the α rays, which are absorbed in their passage through a few centimetres of air. In consequence of this rapid absorption, the ionization decreases rapidly from the surface of the active body, and this gives rise to conductivity phenomena different in character from those observed with Röntgen rays, where the ionization is in most cases uniform.

43. Variation of the current with distance between the plates. It has been found experimentally^[74] that the intensity of the ionization, due to a large plane surface of active matter, falls off approximately in an exponential law with the distance from the plate. On the assumption that the rate of production of ions at any point is a measure of the intensity I of the radiation, the value of I at that point is given by

where λ is a constant, x the distance from the plate, and I₀ the intensity of the radiation at the surface of the plate.

While the exponential law, in some cases, approximately represents the variation of the ionization with distance, in others the divergence from it is wide. The ionization, due to a plane surface of polonium, for example, falls off more rapidly than the exponential law indicates. The α rays from an active substance like radium are highly complex; the law of variation of the ionization due to them is by no means simple and depends upon a variety of conditions. The distribution of ionization is quite different according as a thick layer or a very thick film of radio-active matter is employed. The question is fully considered at the end of chapter IV., but for simplicity, the exponential law is assumed in the following calculations.

Consider two parallel plates placed as in Fig. 1, one of which is covered with a uniform layer of radio-active matter. If the distance d between the plates is small compared with the dimensions of the plates, the ionization near the centre of the plates will be sensibly uniform over any plane parallel to the plates and lying between them. If q be the rate of production of ions at any distance x and q₀ that at the surface, then q = q₀e^-λx. The saturation current i per unit area is given by

hence, when λd is small, i.e. when the ionization between the plates is nearly constant,

The current is thus proportional to the distance between the plates. When λd is large, the saturation current i₀ is equal to q₀e´/λ, and is independent of further increase in the value of d. In such a case the radiation is completely absorbed in producing ions between the plates, and

For example, in the case of a thin layer of uranium oxide spread over a large plate, the ionization is mostly produced by rays the intensity of which is reduced to half value in passing through 4·3 mms. of air, i.e. the value of λ is 1·6. The following table is an example of the variation of i with the distance between the plates.

Thus the increase of current for equal increments of distance between the plates decreases rapidly with the distance traversed by the radiation.

The distance of 15 mms. was not sufficient to completely absorb all the radiation, so that the current had not reached its limiting value.

When more than one type of radiation is present, the saturation current between parallel plates is given by

where A, A₁ are constants, and λ, λ₁ the absorption constants of the radiations in the gas.

Since the radiations are unequally absorbed in different gases, the variation of current with distance depends on the nature of the gas between the plates.

44. Variation of the current with pressure. The rate of production of ions by the radiations from active substances is directly proportional to the pressure of the gas. The absorption of the radiation in the gas also varies directly as the pressure. The latter result necessarily follows if the energy required to produce an ion is independent of the pressure.

In cases where the ionization is uniform between two parallel plates, the current will vary directly as the pressure; when however the ionization is not uniform, on account of the absorption of the radiation in the gas, the current does not decrease directly as the pressure until the pressure is reduced so far that the ionization is sensibly uniform. Consider the variation with pressure of the saturation current i between two large parallel plates, one of which is covered with a uniform layer of active matter.

Let λ₁ = absorption constant of the radiation in the gas for unit pressure.

For a pressure p, the intensity I at any point x is given by

The saturation current i is thus proportional to

If r be the ratio of the saturation currents for the pressures p₁ and p₂,

The ratio is thus dependent on the distance d between the plates and the absorption of the radiation by the gas.

The difference in the shape of the pressure-current curves^[75] is well illustrated in Fig. 8, where curves are given for hydrogen, air, and carbonic acid for plates 3·5 cms. apart.

For the purpose of comparison, the current at atmospheric pressure and temperature in each case is taken as unity. The actual value of the current was greatest in carbonic acid and least in hydrogen. In hydrogen, where the absorption is small, the current over the whole range is nearly proportional to the pressure. In carbonic acid, where the absorption is large, the current diminishes at first slowly with the pressure, but is nearly proportional to it below the pressure of 235 mms. of mercury. The curve for air occupies an intermediate position.

In cases where the distance between the plates is large, the saturation current will remain constant with diminution of pressure until the absorption is so reduced that the radiation reaches the other plate.

An interesting result follows from the rapid absorption of radiation by the gas. If the current is observed between two fixed parallel plates, distant d₁ and d₂ respectively from a large plane surface of active matter, the current at first increases with diminution of pressure, passes through a maximum value, and then diminishes. In such an experimental case the lower plate through which the radiations pass is made either of open gauze or of thin metal foil to allow the radiation to pass through readily.

The saturation current i is obviously proportional to

This is a function of the pressure, and is a maximum when

For example, if the active matter is uranium, pλ₁ = 1·6 for the α rays at atmospheric pressure. If d₂ = 3, and d₁ = 1, the saturation current reaches a maximum when the pressure is reduced to about ⅓ of an atmosphere. This result has been verified experimentally.

45. Conductivity of different gases when acted on by the rays. For a given intensity of radiation, the rate of production of ions in a gas varies for different gases and increases with the density of the gas. Strutt^[76] has made a very complete examination of the relative conductivity of gases exposed to the different types of rays emitted by active substances. To avoid correction for any difference of absorption of the radiation in the various gases, the pressure of the gas was always reduced until the ionization was directly proportional to the pressure, when, as we have seen above, the ionization must everywhere be uniform throughout the gas. For each type of rays, the ionization of air is taken as unity. The currents through the gases were determined at different pressures, and were reduced to a common pressure by assuming that the ionization was proportional to the pressure.

With unscreened active material, the ionization is almost entirely due to α rays. When the active substance is covered with a layer of aluminium ·01 cm. in thickness, the ionization is mainly due to the β or cathodic rays, and when covered with 1 cm. of lead, the ionization is solely due to the γ or very penetrating rays. Experiments on the γ rays of radium were made by observing the rate of discharge of a special gold-leaf electroscope filled with the gas under examination and exposed to the action of the rays. The following table gives the relative conductivities of gases exposed to various kinds of ionizing radiations.

With the exception of hydrogen, it will be seen that the ionization of gases is approximately proportional to their density for the α, β, γ rays of radium. The results obtained by Strutt for Röntgen rays are quite different; for example, the relative conductivity produced by them in methyl iodide was more than 14 times as great as that due to the rays of radium. The relative conductivities of gases exposed to X rays has been recently re-examined by McClung^[77] and Eve^[78], who have found that the conductivity depends upon the penetrating power of the X rays employed. The results obtained by them will be discussed later (section 107).

This difference of conductivity in gases is due to unequal absorptions of the radiations. The writer has shown^[79] that the total number of ions produced by the α rays for uranium, when completely absorbed by different gases, is not very different. The following results were obtained:

The numbers, though only approximate in character, seem to show that the energy required to produce an ion is probably not very different for the various gases. Assuming that the energy required to produce an ion in different gases is about the same, it follows that the relative conductivities are proportional to the relative absorption of the radiations.

A similar result has been found by McLennan for cathode rays. He proved that the ionization was directly proportional to the absorption of the rays in the gas, thus showing that the same energy is required to produce an ion in all the gases examined.

46. Potential Gradient. The normal potential gradient between two charged electrodes is always disturbed when the gas is ionized in the space between them. If the gas is uniformly ionized between two parallel plates, Child and Zeleny have shown that there is a sudden drop of potential near the surface of both plates, and that the electric field is sensibly uniform for the intermediate space between them. The disturbance of the potential gradient depends upon the difference of potential applied, and is different at the surface of the two plates.

In most measurements of radio-activity the material is spread over one plate only. In such a case the ionization is to a large extent confined to the volume of the air close to the active plate. The potential gradient in such a case is shown in Fig. 9. The dotted line shows the variation of potential at any point between the plates when no ionization is produced between the plates; curve A for weak ionization, such as is produced by uranium, curve B for the intense ionization produced by a very active substance. In both cases the potential gradient is least near the active plate, and greatest near the opposite plate. For very intense ionization it is very small near the active surface. The potential gradient varies slightly according as the active plate is charged positively or negatively.