25. Ionization of gases by radiation. The most important property possessed by the radiations from radio-active bodies is their power of discharging bodies whether positively or negatively electrified. As this property has been made the basis of a method for an accurate quantitative analysis and comparison of the radiations, the variation of the rate of discharge under different conditions and the processes underlying it will be considered in some detail.
In order to explain the similar discharging power of Röntgen rays, the theory[44] has been put forward that the rays produce positively and negatively charged carriers throughout the volume of the gas surrounding the charged body, and that the rate of production is proportional to the intensity of the radiation. These carriers, or ions[45] as they have been termed, move with a uniform velocity through the gas under a constant electric field, and their velocity varies directly as the strength of the field.
Fig. 1.
Suppose we have a gas between two metal plates A and B (Fig. 1) exposed to the radiation, and that the plates are kept at a constant difference of potential. A definite number of ions will be produced per second by the radiation, and the number produced will depend in general upon the nature and pressure of the gas. In the electric field the positive ions travel towards the negative plate, and the negative ions towards the positive, and consequently a current will pass through the gas. Some of the ions will also recombine, the rate of recombination being proportional to the square of the number present. For a given intensity of radiation, the current passing through the gas will increase at first with the potential difference between the plates, but it will reach a limit when all the ions are removed by the electric field before any recombination occurs.
This theory accounts also for all the characteristic properties of gases made conducting by the rays from active substances, though there are certain differences observed between the conductivity phenomena produced by active substances and by X rays. These differences are for the most part the result of unequal absorption of the two types of rays. Unlike Röntgen rays, a large proportion of the radiation from active bodies consists of rays which are absorbed in their passage through a few centimetres of air. The ionization of the gas is thus not uniform, but falls off rapidly with increase of distance from the active substance.
26. Variation of the current with voltage. Suppose that a layer of radio-active matter is spread uniformly on the lower of two horizontal plates A and B (Fig. 1). The lower plate A is connected with one pole of a battery of cells the other pole of which is connected with earth. The plate B is connected with one pair of quadrants of an electrometer, the other pair being connected with earth.
The current[46] between the plates, determined by the rate of movement of the electrometer needle, is observed at first to increase rapidly with the voltage, then more slowly, finally reaching a value which increases very slightly with a large increase in the voltage. This, as we have indicated, is simply explained on the ionization theory.
The radiation produces ions at a constant rate, and, before the electric field is applied, the number per unit volume increases until the rate of production of fresh ions is exactly balanced by the recombination of the ions already produced. On application of a small electric field, the positive ions travel to the negative electrode and the negative to the positive.
Since the velocity of the ions between the plates is directly proportional to the strength of the electric field, in a weak field the ions take so long to travel between the electrodes that most of them recombine on the way.
The current observed is consequently small. With increase of the voltage there is an increase of speed of the ions and a smaller number recombine. The current consequently increases, and will reach a maximum value when the electric field is sufficiently strong to remove all the ions before appreciable recombination has occurred. The value of the current will then remain constant even though the voltage is largely increased.
This maximum current will be called the “saturation” current, and the value of the potential difference required to give this maximum current, the “saturation P.D.”[47]
The general shape of the current-voltage curve is shown in Fig. 2, where the ordinates represent current and the abscissae volts.
Fig. 2.
Although the variation of the current with voltage depends only on the velocity of the ions and their rate of recombination, the full mathematical analysis is intricate, and the equations, expressing the relation between current and voltage, are only integrable for the case of uniform ionization. The question is complicated by the inequality in the velocity of the ions and by the disturbance of the potential gradient between the plates by the movement of the ions. J. J. Thomson[48] has worked out the case for uniform production of ions between two parallel plates, and has found that the relation between the current i and the potential difference V applied is expressed by
where A and B are constants for a definite intensity of radiation and a definite distance between the plates.
Fig. 3.
In certain cases of unsymmetrical ionization, which arise in the study of the radiations from active bodies, the relation between current and voltage is very different from that expressed by the above equation. Some of these cases will be considered in section 47.
27. The general shape of the current-voltage curves for gases exposed to the radiations from active bodies is shown in Fig. 3.
This curve was obtained for ·45 grams of impure radium chloride, of activity 1000 times that of uranium, spread over an area of 33 sq. cms. on the lower of two large parallel plates, 4·5 cms. apart. The maximum value of the current observed, which is taken as 100, was 1·2 × 10-8 amperes, the current for low voltages was nearly proportional to the voltage, and about 600 volts between the plates was required to ensure approximate saturation.
In dealing with slightly active bodies like uranium or thorium, approximate saturation is obtained for much lower voltages. Tables I. and II. show the results for the current between two parallel plates distant 0·5 cms. and 2·5 cms. apart respectively, when one plate was covered with a thin uniform layer of uranium oxide.
| Volts | Current |
|---|---|
| ·125 | 18 |
| ·25 | 36 |
| ·5 | 55 |
| 1 | 67 |
| 2 | 72 |
| 4 | 79 |
| 8 | 85 |
| 16 | 88 |
| 100 | 94 |
| 335 | 100 |
| Volts | Current |
|---|---|
| ·5 | 7·3 |
| 1 | 14 |
| 2 | 27 |
| 4 | 47 |
| 8 | 64 |
| 16 | 73 |
| 37·5 | 81 |
| 112 | 90 |
| 375 | 97 |
| 800 | 100 |
The results are shown graphically in Fig. 4.
Fig. 4.
From the above tables it is seen that the current at first increases nearly in proportion to the voltage. There is no evidence of complete saturation, although the current increases very slowly for large increases of voltage. For example, in Table I. a change of voltage from ·125 to ·25 volts increases the current from 18 to 36% of the maximum, while a change of voltage from 100 to 335 volts increases the current only 6%. The variation of the current per volt (assumed uniform between the range of voltages considered) is thus about 5000 times greater for the former change.
Taking into consideration the early part of the curves, the current does not reach a practical maximum as soon as would be expected on the simple ionization theory. It seems probable that the slow increase with the large voltages is due either to an action of the electric field on the rate of production of ions, or to the difficulty of removing the ions produced near the surface of the uranium before recombination. It is possible that the presence of a strong electric field may assist in the separation of ions which otherwise would not initially escape from the sphere of one another’s attraction. From the data obtained by Townsend for the conditions of production of fresh ions at low pressures by the movement of ions through the gas, it seems that the increase of current cannot be ascribed to an action of the moving ions in the further ionization of the gas.
28. The equation expressing the relation between the current and the voltage is very complicated even in the case of a uniform rate of production of ions between the plates. An approximate theory, which is of utility in interpreting the experimental results, can however be simply deduced if the disturbance of the potential gradient is disregarded, and the ionization assumed uniform between the plates.
Suppose that the ions are produced at a constant rate q per cubic centimetre per second in the gas between parallel plates distant l cms. from each other. When no electric field is applied, the number N present per c.c., when there is equilibrium between the rates of production and recombination, is given by
where α is a constant.
If a small potential difference V is applied, which gives only a small fraction of the maximum current, and consequently has not much effect on the value of N, the current i per sq. cm. of the plate, is given by
where u is the sum of the velocity of the ions for unit potential gradient, and e is the charge carried by an ion.
is the velocity of the ions in the electric field of strength
The number of ions produced per second in a prism of length l and unit area of cross-section is ql. The maximum or saturation current I per sq. cm. of the plate is obtained when all of these ions are removed to the electrodes before any recombination has occurred.
Thus
and
This equation expresses the fact previously noted that, for small voltages, the current i is proportional to V.
Let
then
Now the greater the value of V required to obtain a given value of ρ (supposed small compared with unity), the greater the potential required to produce saturation.
It thus follows from the equation that:
(1) For a given intensity of radiation, the saturation P.D. increases with the distance between the plates. In the equation, for small values of ρ, V varies as l2. This is found to be the case for uniform ionization, but it only holds approximately for non-uniform ionization.
(2) For a given distance between the plates, the saturation P.D. is greater, the greater the intensity of ionization between the plates. This is found to be the case for the ionization produced by radio-active substances. With a very active substance like radium, the ionization produced is so intense that very large voltages are required to produce approximate saturation. On the other hand, only a fraction of a volt per cm. is necessary to produce saturation in a gas where the ionization is very slight, for example, in the case of the natural ionization observed in a closed vessel, where no radio-active substances are present.
For a given intensity of radiation, the saturation P.D. decreases rapidly with the lowering of the pressure of the gas. This is due to two causes operating in the same direction, viz. a decrease in the intensity of the ionization and an increase in the velocity of the ions. The ionization varies directly as the pressure, while the velocity varies inversely as the pressure. This will obviously have the effect of causing more rapid saturation, since the rate of recombination is slower and the time taken for the ions to travel between the electrodes is less.
The saturation curves observed for the gases hydrogen and carbon dioxide[49] are very similar in shape to those obtained for air. For a given intensity of radiation, saturation is more readily obtained in hydrogen than in air, since the ionization is less than in air while the velocity of the ions is greater. Carbon dioxide on the other hand requires a greater P.D. to produce saturation than does air, since the ionization is more intense and the velocity of the ions less than in air.
29. Townsend[50] has shown that, for low pressures, the variation of the current with the voltage is very different from that observed at atmospheric pressure. If the increase of current with the voltage is determined for gases, exposed to Röntgen rays, at a pressure of about 1 mm. of mercury, it is found that for small voltages the ordinary saturation curve is obtained; but when the voltage applied increases beyond a certain value, depending on the pressure and nature of the gas and the distance between the electrodes, the current commences to increase slowly at first but very rapidly as the voltage is raised to the sparking value. The general shape of the current curve is shown in Fig. 5.
Fig. 5.
The portion OAB of the curve corresponds to the ordinary saturation curve. At the point B the current commences to increase. This increase of current has been shown to be due to the action of the negative ions at low pressures in producing fresh ions by collision with the molecules in their path. The increase of current is not observed in air at a pressure above 30 mms. until the P.D. is increased nearly to the value required to produce a spark. This production of ions by collision is considered in more detail in section 41.
30. Rate of recombination of the ions. A gas ionized by the radiation preserves its conducting power for some time after it is removed from the presence of the active body. A current of air blown over an active body will thus discharge an electrified body some distance away. The duration of this after conductivity can be examined very conveniently in an apparatus similar to that shown in Fig. 6.
Fig. 6.
A dry current of air or any other gas is passed at a constant rate through a long metal tube TL. After passing through a quantity of cotton-wool to remove dust particles, the current of air passes over a vessel T containing a radio-active body such as uranium, which does not give off a radio-active emanation. By means of insulated electrodes A and B, charged to a suitable potential, the current between the tube and one of these electrodes can be tested at various points along the tube.
A gauze screen, placed over the cross-section of the tube at D, serves to prevent any direct action of the electric field in abstracting ions from the neighbourhood of T.
If the electric field is sufficiently strong, all the ions travel in to the electrodes at A, and no current is observed at the electrode B. If the current is observed successively at different distances along the tube, all the electrodes except the one under consideration being connected to earth, it is found that the current diminishes with the distance from the active body. If the tube is of fairly wide bore, the loss of the ions due to diffusion is small, and the decrease in conductivity of the gas is due to recombination of the ions alone.
On the ionization theory, the number dn of ions per unit volume which recombine in the time dt is proportional to the square of the number present. Thus
where α is a constant.
Integrating this equation,
if N is the initial number of ions, and n the number after a time t.
The experimental results obtained[51] have been shown to agree very well with this equation.
In an experiment similar to that illustrated in Fig. 6, using uranium oxide as a source of ionization, it was found that half the number of ions present in the gas recombined in 2·4 seconds, and that at the end of 8 seconds one-fourth of the ions were still uncombined.
Since the rate of recombination is proportional to the square of the number present, the time taken for half of the ions present in the gas to recombine decreases very rapidly with the intensity of the ionization. If radium is used, the ionization is so intense that the rate of recombination is extremely rapid. It is on account of this rapidity of recombination that large voltages are necessary to produce saturation in the gases exposed to very active preparations of radium.
The value of α, which may be termed the coefficient of recombination, has been determined in absolute measure by Townsend[52], McClung[53] and Langevin[54] by different experimental methods but with very concordant results. Suppose, for example, with the apparatus of Fig. 6, the time T, taken for half the ions to recombine after passing by the electrode A, has been determined experimentally. Then
where N is the number of ions per c.c. present at A. If the saturation current i is determined at the electrode A, i = NVe, where e is the charge on an ion and V is the volume of uniformly ionized gas carried by the electrode A per second. Then
The following table shows the value of α obtained for different gases.
| Gas | Townsend | McClung | Langevin |
|---|---|---|---|
| Air | 3420 × e | 3384 × e | 3200 × e |
| Carbon Dioxide | 3500 × e | 3492 × e | 3400 × e |
| Hydrogen | 3020 × e |
The latest determination of the value of e (see section 36) is 3·4 × 10-10 E.S. units; thus α = 1·1 × 10-6.
Using this value, it can readily be shown from the equation of recombination that, if 106 ions are present per c.c., half of them recombine in about 0·9 sec. and 99% in 90 secs.
McClung (loc. cit.) showed that the value of α was approximately independent of the pressure between ·125 and three atmospheres. In later observations, Langevin has found that the value of α decreases rapidly when the pressure is lowered below the limits used by McClung.
31. In experiments on recombination it is essential that the gas should be free from dust or other suspended particles. In dusty air, the rate of recombination is much more rapid than in dust-free air, as the ions diffuse rapidly to the comparatively large dust particles distributed throughout the gas. The effect of the suspension of small particles in a conducting gas is very well illustrated by an experiment of Owens[55]. If tobacco smoke is blown between two parallel plates as in Fig. 1, the current at once diminishes to a small fraction of its former value, although a P.D. is applied sufficient to produce saturation under ordinary conditions. A much larger voltage is then necessary to produce saturation. If the smoke particles are removed by a stream of air, the current returns at once to its original value.
32. Mobility of the ions. Determinations of the mobility of the ions, i.e. the velocity of the ions under a potential gradient of 1 volt per cm., have been made by Rutherford[56], Zeleny[57], and Langevin[58] for gases exposed to Röntgen rays. Although widely different methods have been employed, the results have been very concordant, and fully support the view that the ions move with a velocity proportional to the strength of the field. On the application of an electric field, the ions almost instantly attain the velocity corresponding to the field and then move with a uniform speed.
Zeleny[59] first drew attention to the fact that the positive and negative ions had different velocities. The velocity of the negative ion is always greater than that of the positive, and varies with the amount of water vapour present in the gas.
The results, previously discussed, of the variation of the current with voltage and of the rate of recombination of the ions do not of themselves imply that the ions produced in gases by the radiations from active bodies are of the same size as those produced by Röntgen rays under similar conditions. They merely show that the conductivity under various conditions can be satisfactorily explained by the view that charged ions are produced throughout the volume of the gas. The same general relations would be observed if the ions differed considerably in size and velocity from those produced by Röntgen rays. The most satisfactory method of determining whether the ions are identical in the two cases is to determine the velocity of the ions under similar conditions.
In order to compare the velocity of the ions[60], the writer has used an apparatus similar to that shown in Fig. 6 on p. 40.
The ions were carried with a rapid constant stream of air past the charged electrode A, and the conductivity of the gas tested immediately afterwards at an electrode B, which was placed close to A. The insulated electrodes A and B were fixed centrally in the metal tube L, which was connected with earth.
For convenience of calculation, it is assumed that the electric field between the cylinders is the same as if the cylinders were infinitely long.
Let a and b be the radii of the electrode A, and of the tube L respectively, and let V = potential of A.
The electromotive intensity X (without regard to sign) at a distance r from the centre of the tube is given by
Let u1 and u2 be the velocities of the positive and negative ions for a potential gradient of 1 volt per cm. If the velocity is proportional to the electric force at any point, the distance dr traversed by the negative ion in the time dt is given by
dr = Xu2 dt,
or
Let r2 be the greatest distance measured from the axis of the tube from which the negative ion can just reach the electrode A in the time t taken for the air to pass along the electrode.
Then
If ρ2 be the ratio of the number of the negative ions that reach the electrode A to the total number passing by, then
Therefore
Equation 1.
Similarly the ratio ρ1 of the number of positive ions that give up their charge to the external cylinder to the total number of positive ions is given by
In the above equations it is assumed that the current of air is uniform over the cross-section of the tube, and that the ions are uniformly distributed over the cross-section; also, that the movement of the ions does not appreciably disturb the electric field. Since the value of t can be calculated from the velocity of the current of air and the length of the electrode, the values of the velocities of the ions under unit potential gradient can at once be determined.
The equation (1) shows that ρ2 is proportional to V,—i.e. that the rate of discharge of the electrode A varies directly as the potential of A, provided that the value of V is not large enough to remove all the ions from the gas as it passes by the electrode. This was found experimentally to be the case.
In the comparison of the velocities, the potential V was adjusted to such a value that ρ2 was about one half, when uranium oxide was placed in the tube at L. The active substance was then removed, and an aluminium cylinder substituted for the brass tube. X rays were allowed to fall on the centre of this aluminium cylinder, and the strength of the rays adjusted to give about the same conductivity to the gas as the uranium had done. Under these conditions the value of ρ2 was found to be the same as for the first experiment.
This experiment shows conclusively that the ions produced by Röntgen rays and by uranium move with the same velocity and are probably identical in all respects. The method described above is not very suitable for an accurate determination of the velocities, but gave values for the positive ions of about 1·4 cms. per second per volt per centimetre, and slightly greater values for the negative ions.
33. The most accurate determinations of the mobility of the ions produced by Röntgen rays have been made by Zeleny[61] and Langevin[62]. Zeleny used a method similar in principle to that explained above. His results are shown in the following table, where K1 is the mobility of the positive ion and K2 that of the negative ion.
| Gas | K1 | K2 | K2/K1 | Temperature |
|---|---|---|---|---|
| Air, dry | 1·36 | 1·87 | 1·375 | 13°·5 C. |
| „ moist | 1·37 | 1·51 | 1·10 | 14° |
| Oxygen, dry | 1·36 | 1·80 | 1·32 | 17° |
| „ moist | 1·29 | 1·52 | 1·18 | 16° |
| Carbon dioxide, dry | 0·76 | 0·81 | 1·07 | 17°·5 |
| „ „ moist | 0·81 | 0·75 | 0·915 | 17° |
| Hydrogen, dry | 6·70 | 7·95 | 1·15 | 20° |
| „ moist | 5·30 | 5·60 | 1·05 | 20° |
Langevin determined the velocity of the ions by a direct method in which the time taken for the ion to travel over a known distance was observed.
The following table shows the comparative values obtained for air and carbon dioxide.
| Air K1 | Air K2 | Air K2/K1 | CO2 K1 | CO2 K2 | CO2 K2/K1 | |
|---|---|---|---|---|---|---|
| Direct method (Langevin) | 1·40 | 1·70 | 1·22 | 0·86 | 0·90 | 1·05 |
| Current of gas (Zeleny) | 1·36 | 1·87 | 1·375 | 0·76 | 0·81 | 1·07 |
These results show that for all gases except CO2, there is a marked increase in the velocity of the negative ion with the dryness of the gas, and that, even in moist gases, the velocity of the negative ions is always greater than that of the positive ions. The velocity of the positive ion is not much affected by the presence of moisture in the gas.
The velocity of the ions varies inversely as the pressure of the gas. This has been shown by Rutherford[63] for the negative ions produced by ultra-violet light falling on a negatively charged surface, and later by Langevin[64] for both the positive and negative ions produced by Röntgen rays. Langevin has shown that the velocity of the positive ion increases more slowly with the diminution of pressure than that of the negative ion. It appears as if the negative ion, especially at pressures of about 10 mm. of mercury, begins to diminish in size.
34. Condensation experiments. Some experiments will now be described which have verified in a direct way the theory that the conductivity produced in gases by the various types of radiation is due to the production of charged ions throughout the volume of the gas. Under certain conditions, the ions form nuclei for the condensation of water, and this property allows us to show the presence of the individual ions in the gas, and also to count the number present.
It has long been known that, if air saturated with water-vapour be suddenly expanded, a cloud of small globules of water is formed. These drops are formed round the dust particles present in the gas, which act as nuclei for the condensation of water around them. The experiments of R. von Helmholtz and Richarz[65] had shown that chemical reactions, for example the combustion of flames, taking place in the neighbourhood, affected the condensation of a steam-jet. Lenard showed that a similar action was produced when ultra-violet light fell on a negatively charged zinc surface placed near the steam-jet. These results suggested that the presence of electric charges in the gas facilitated condensation.
A very complete study of the conditions of condensation of water on nuclei has been made by C. T. R. Wilson[66]. An apparatus was constructed which allowed a very sudden expansion of the air over a wide range of pressure. The amount of condensation was observed in a small glass vessel. A beam of light was passed into the apparatus which allowed the drops formed to be readily observed by the eye.
Preliminary small expansions caused a condensation of the water round the dust nuclei present in the air. These dust nuclei were removed by allowing the drops to settle. After a number of successive small expansions, the air was completely freed from dust, so that no condensation was produced.
Let v1 = initial volume of the gas in the vessel, v2 = volume after expansion.
If v2/v1 < 1·25 no condensation is produced in dust-free air. If however v2/v1 > 1·25 and < 1·38, a few drops appear. This number is roughly constant until v2/v1 = 1·38, when the number suddenly increases and a very dense cloud of fine drops is produced.
If the radiation from an X ray tube or a radio-active substance is now passed into the condensation vessel, a new series of phenomena is observed. As before, if v2/v1 < 1·25 no drops are formed, but if v2/v1 = 1·25 there is a sudden production of a cloud. The water drops of which this cloud is formed are finer and more numerous the greater the intensity of the rays. The point at which condensation begins is very marked, and a slight variation of the amount of expansion causes either a dense cloud or no cloud at all.
It now remains to be shown that the formation of a cloud by the action of the rays is due to the productions of ions in the gas. If the expansion vessel is provided with two parallel plates between which an electric field can be applied, it is seen that the number of drops, formed by the expansion with the rays acting, decreases with increase of the electric field. The stronger the field the smaller the number of drops formed. This result is to be expected if the ions are the centres of condensation; for in a strong electric field the ions are carried at once to the electrodes, and thus disappear from the gas. If no electric field is acting, a cloud can be produced some time after the rays have been cut off; but if a strong electric field is applied, under the same conditions, no cloud is formed. This is in agreement with experiments showing the time required for the ions to disappear by recombination. In addition it can be shown that each one of the fine drops carries an electric charge and can be made to move in a strong uniform electric field.
The small number of drops produced without the action of the rays when v2/v1 > 1·25 is due to a very slight natural ionization of the gas. That this ionization exists has been clearly shown by electrical methods (section 284).
The evidence is thus complete that the ions themselves serve as centres for the condensation of water around them. These experiments show conclusively that the passage of electricity through a gas is due to the presence of charged ions distributed throughout the volume of the gas, and verify in a remarkable way the hypothesis of the discontinuous structure of the electric charges carried by matter.
This property of the ions of acting as nuclei of condensation gives a very delicate method of detecting the presence of ions in the gas. If only an ion or two is present per c.c., their presence after expansion is at once observed by the drops formed. In this way the ionization due to a small quantity of uranium held a yard away from the condensation vessel is at once made manifest.
35. Difference between the positive and negative ions. In the course of experiments to determine the charge carried by an ion, J. J. Thomson[67] observed that the cloud formed under the influence of X rays increased in density when the expansion was about 1·31, and suggested in explanation that the positive and negative ions had different condensation points.