Radio-activity/Chapter 2
CHAPTER II.
IONIZATION THEORY OF GASES..
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[1] 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[2] 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.
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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[3] 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."[4]
The general shape of the current-voltage curve is shown in Fig. 2, where the ordinates represent current and the abscissae volts.
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Fig. 2.
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[5] 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
Ai² + Bi = V
where A and B are constants for a definite intensity of radiation and a definite distance between the plates.
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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.
Table I.
0·5 cms. apart
Volts Current
·125 18
·25 36
·5 55
1 67
2 72
4 79
8 85
16 88
100 94
335 100
Table II.
2·5 cms. apart
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.
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.
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Saturation Curves for Uranium rays
Fig. 4.
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 q = αN^2, 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
i = NeuV/l,
where u is the sum of the velocity of the ions for unit potential gradient, and e is the charge carried by an ion. uV/l is the velocity of the ions in the electric field of strength V/l.
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 I = q . l . e,
and i/I = NuV/(ql^2) = uV/(l^2[sqrt](qα)).
This equation expresses the fact previously noted that, for small voltages, the current i is proportional to V.
Let i/I = ρ,
then V = ρ . l^2[sqrt](qα)/u.
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 l^2. 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[6] 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[7] 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.
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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.
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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
dn/dt = αn^2,
where α is a constant. Integrating this equation,
1/n - 1/N = αt,
if N is the initial number of ions, and n the number after a time t.
The experimental results obtained[8] 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[9], M^cClung[10] and Langevin[11] 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 1/N = αT, 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 α = Ve/(iT).
The following table shows the value of α obtained for different gases. Value of α.
Gas Townsend M^cClung 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 10^6 ions are present per c.c., half of them recombine in about 0·9 sec. and 99% in 90 secs.
M^cClung (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 M^cClung.
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[12]. 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[13], Zeleny[14], and
Langevin[15] 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[16] 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[17], 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
X = V/(r log_{e}(b/a)).
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 = Xu_{2} dt,
or
dt = (log_{e}(b/a) r dr)/(Vu_{2}).
Let r_{2} 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 t = ((r_{2}^2 - a^2)/(2Vu_{2})) log_{e}(b/a).
If ρ_{2} be the ratio of the number of the negative ions that reach the electrode A to the total number passing by, then
ρ_{2} = (r_{2}^2 - a^2)/(b^2 - a^2).
Therefore
u_{2} = (ρ_{2}(b^2 - a^2) log_{e}(b/a))/(2Vt) (1).
Similarly the ratio ρ_{1} 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
u_{1} = (ρ_{1}(b^2 - a^2) log_{e}(b/a))/(2Vt).
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 ρ_{2} 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 ρ_{2} 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 ρ_{2} 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[18] and
Langevin[19]. Zeleny used a method similar in principle to that
explained above. His results are shown in the following table,
where K_{1} is the mobility of the positive ion and K_{2} that of the
negative ion.
++-+-+-+-+
| Gas |K_{1}|K_{2}|K_{2}/K_{1}|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° |
++-+-+-+-+
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 CO_{2}
/-/\\ /-/\\
K_{1} K_{2} K_{2}/K_{1} K_{1} K_{2} K_{2}/K_{1}
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 CO_{2}, 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[20] for the negative ions produced by ultra-violet light falling on a negatively charged surface, and later by Langevin[21] 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[22] 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[23]. 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 v_{1} = initial volume of the gas in the vessel, v_{2} = volume after expansion.
If v_{2}/v_{1} < 1·25 no condensation is produced in dust-free air. If however v_{2}/v_{1} > 1·25 and < 1·38, a few drops appear. This number is roughly constant until v_{2}/v_{1} = 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 v_{2}/v_{1} < 1·25 no drops are formed, but if v_{2}/v_{1} = 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 v_{2}/v_{1} > 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 218).
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[24] 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.
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Fig. 7.
This difference in behaviour of the positive and negative ions was investigated in detail by C. T. R. Wilson[25] 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 v_{2}/v_{1} = 1·25 but did not occur in AD for the positive ions until v_{2}/v_{1} = 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
u = (2/9)(dgr^2/μ),
where g is the acceleration due to gravity. The radius of the drop and consequently the weight of water in each drop can thus be determined. Since the total weight of water precipitated is known, the number of drops present is obtained at once.
This method has been used by J. J. Thomson[26] 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
i = NuVe/l,
where N = number of ions present in the gas,
e = charge on each ion,
u = sum of the velocities of the positive and negative ions.
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
e = 3·4 × 10^{-10} electrostatic units.
A very concordant value, namely, 3·1 × 10^{-10}, has been obtained by H. A. Wilson[27], 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[28]. 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[29],R = 4(·195e^{-3·66KZ/(a^2V)} + ·0243e^{-22·3KZ/(a^2V)} + &c.),
a = radius of the tube, Z = length of the tube, V = mean velocity of the gas in the tube.
+-++++-+
| |K for |K for |Mean value| Ratio of |
| Gas | + ions | - ions | of K |values of K|
+-++++-+
| Air, dry | ·028 | ·043 | ·0347 | 1·54 |
| " moist | ·032 | ·035 | ·0335 | 1·09 |
| Oxygen, dry | ·025 | ·0396 | ·0323 | 1·58 |
| " moist | ·0288 | ·0358 | ·0323 | 1·24 |
| Carbonic acid, dry | ·023 | ·026 | ·0245 | 1·13 |
| " " moist| ·0245 | ·0255 | ·025 | 1·04 |
| Hydrogen, dry | ·123 | ·190 | ·156 | 1·54 |
| " moist | ·128 | ·142 | ·135 | 1·11 |
+-++++-+
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
(1/K)pu = -dp/dx + nXe,
where e is the charge on an ion,
n = number of ions per c.c.,
p = their partial pressure,
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,
dp/dx = 0 and u = n X e K/p.
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 10^6, Ne = (3 × 10^8u_{1})/K electrostatic units,
where u_{1} 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,
2·46Ne´ = 3 × 10^{10} E. S. units,
Ne´ = 1·22 × 10^{10} E. S. units.
Thus e/e´ = 2·46 × 10^{-2}(u_{1}/K).
For example, substituting the values of u_{1} and K determined in moist air for the positive ion,
e/e´ = (2·46/100) × (1·37/·032) = 1·04.
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 u_{1} 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
Ne = 1·22 × 10^{10}.
Now e, the charge on an ion, is equal to 3·4 × 10^{-10} E. S. units;
thus N = 3·6 × 10^{19}.
If I is the saturation current through a gas, and q the total rate of production of ions in the gas,
q = I/e.
ampères, i.e. 36 E.S. units, for parallel plates 4·5 cms. apart, when ·45 gramme of radium of activity 1000 times that of uranium was spread over an area of 33 sq. cms. of the lower plate. This corresponds to a production of about 10^{11} ions per second. Assuming, for the purpose of illustration, that the ionization was uniform between the plates, the volume of air acted on by the rays was about 148 c.c., and the number of ions produced per c.c. per second about 7 × 10^8. Since N = 3·6 × 10^{19}, we see that, if one molecule produces two ions, the proportion of the gas ionized per second is about 10^{-11} of the whole. For uranium the fraction is about 10^{-14}, and for pure radium, of activity one million times that of uranium, about 10^{-8}. Thus even in the case of pure radium, only about one molecule of gas is acted on per second in every 100 millions.
The electrical methods are so delicate that the production of one ion per cubic centimetre per second can be detected readily. This corresponds to the ionization of about one molecule in every 10^{19} present in the gas.
40. Size and nature of the ions. An approximate estimate
of the mass of an ion, compared with the mass of the molecule of
the gas in which it is produced, can be made from the known data
of the coefficient K of inter-diffusion of the ions into gases. The
value of K for the positive ions in moist carbon dioxide has been
shown to be ·0245, while the value of K for the inter-diffusion of
carbon dioxide with air is ·14. The value of K for different gases
is approximately inversely proportional to the square root of the
products of the masses of the molecules of the two inter-diffusing
gases; thus, the positive ion in carbon dioxide behaves as if its
mass were large compared with that of the molecule. Similar
results hold for the negative as well as for the positive ion, and for
other gases besides carbon dioxide.
This has led to the view that the ion consists of a charged centre surrounded by a cluster of molecules travelling with it, which are kept in position round the charged nucleus by electrical forces. A rough estimate shows that this cluster consists of about 30 molecules of the gas. This idea is supported by the variation in velocity, i.e. the variation of the size of the negative ion, in the presence of water vapour; for the negative ion undoubtedly has a greater mass in moist than in dry gases. At the same time it is possible that the apparently large size of the ion, as determined by diffusion methods, may be in part a result of the charge carried by the ion. The presence of a charge on a moving body would increase the frequency of collision with the molecules of the gas, and consequently diminish the rate of diffusion. The ion on this view may not actually be of greater size than the molecule from which it is produced.
The negative and positive ions certainly differ in size, and this difference becomes very pronounced for low pressures of the gas. At atmospheric pressure, the negative ion, produced by the action of ultra-violet light on a negatively charged body, is of the same size as the ion produced by X rays, but at low pressures J. J. Thomson has shown that it is identical with the corpuscle or electron, which has an apparent mass of about 1/1000 of the mass of the hydrogen atom. A similar result has been shown by Townsend to hold for the negative ion produced by X rays at a low pressure. It appears that the negative ion at low pressure sheds its attendant cluster. The result of Langevin, that the velocity of the negative ion increases more rapidly with the diminution of pressure than that of the positive ion, shows that this process of removal of the cluster is quite appreciable at a pressure of 10 mms. of mercury.
We must suppose that the process of ionization in gases consists in a removal of a negative corpuscle or electron from the molecule of the gas. At atmospheric pressure this corpuscle immediately becomes the centre of an aggregation of molecules which moves with it and is the negative ion. After removal of the negative ion the molecule retains a positive charge, and probably also becomes the centre of a cluster of new molecules.
The terms electron and ion as used in this work may therefore be defined as follows:—
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 10^{10} cms. a second, it has an apparent mass m given by e/m = 1·86 × 10^7 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[30].
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
W = 2·3 × 10^{-11} ergs.
The velocity u acquired by the ion of mass m just before a collision is given by
,
and .
Now e/m = 1·86 × 10^7 electromagnetic units for the electron at slow speeds (section 82).
Taking V = 20 volts, we find that
u = 2·7 × 10^8 cms. per sec.
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 M^cClung. 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[31] 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 I/I_{0} = e^{-λx}, where λ is a
constant, x the distance from the plate, and I_{0} 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 q_{0} that at the surface, then q = q_{0}e^{-λx}. The saturation current i per unit area is given by
i = [integral]_{0}^d q e´ dx, where e´ is the charge on an ion,
= q_{0}e´ [integral]_{0}^d e^{-λx} dx = (q_{0}e´/λ)(1 - e^{-λd});
hence, when λd is small, i.e. when the ionization between the plates is nearly constant,
i = q_{0}e´ d.
The current is thus proportional to the distance between the plates. When λd is large, the saturation current i_{0} is equal to q_{0}e´/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 i/i_{0} = 1 - e^{-λd}.
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.
Distance Saturation Current
2·5 mms. 32
5 " 55
7·5 " 72
10 " 85
12·5 " 96
15 " 100
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
i = A(1 - e^{λd}) + A_{1}(1 - e^{-λ_{1}d}) + &c.
where A, A_{1} are constants, and λ, λ_{1} 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 λ_{1} = 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 I/I_{0} = e^{-pλ_{1}x}. The saturation current i is thus proportional to
[integral]_{0}^d pI dx = [integral]_{0}^d pI_{0}e^{-pλ_{1}x} . dx = (I_{0}/λ_{1}) (1 - e^{pλ_{1}d}).
If r be the ratio of the saturation currents for the pressures p_{1} and p_{2},
r = (1 - e^{-p_{1}λ_{1}d})/(1 - e^{-p_{2}λ_{1}d}).
plates and the absorption of the radiation by the gas.
The difference in the shape of the pressure-current curves[32] is well illustrated in Fig. 8, where curves are given for hydrogen, air, and carbonic acid for plates 3·5 cms. apart.
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Fig. 8.
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 d_{1} and d_{2} 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
[integral]_{d_{1}}^{d_{2}} pI_{0}e^{-pλ_{1}d}, i.e. to (I_{0}/λ_{1})(e^{-pλ_{1}d_{1}} - e^{-pλ_{1}d_{2}}).
This is a function of the pressure, and is a maximum when
log_{e}(d_{1}/d_{2}) = -pλ_1(d_{2} - d_{1}).
For example, if the active matter is uranium, pλ_{1} = 1·6 for the α rays at atmospheric pressure. If d_{2} = 3, and d_{1} = 1, the saturation current reaches a maximum when the pressure is reduced to about 1/3 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[33] 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.
-+-+-+
Gas | | Relative Conductivity |
| Relative +-+++-+
| Density | α rays | β rays | γ rays | Röntgen rays |
-+-+-+++-+
Hydrogen | 0·0693 | 0·226 | 0·157 | 0·169 | 0·114 |
Air | 1·00 | 1·00 | 1·00 | 1·00 | 1·00 |
Oxygen | 1·11 | 1·16 | 1·21 | 1·17 | 1·39 |
Carbon dioxide | 1·53 | 1·54 | 1·57 | 1·53 | 1·60 |
Cyanogen | 1·86 | 1·94 | 1·86 | 1·71 | 1·05 |
Sulphur dioxide | 2·19 | 2·04 | 2·31 | 2·13 | 7·97 |
Chloroform | 4·32 | 4·44 | 4·89 | 4·88 | 31·9 |
Methyl iodide | 5·05 | 3·51 | 5·18 | 4·80 | 72·0 |
Carbon tetrachloride | 5·31 | 5·34 | 5·83 | 5·67 | 45·3 |
-+-+-+++-+
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 M^cClung[34] and Eve[35], 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[36] 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:
Gas Total
Ionization
Air 100
Hydrogen 95
Oxygen 106
Carbonic acid 96
Hydrochloric acid gas 102
Ammonia 101
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 M^cLennan 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.
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Fig. 9.
47. Variation of current with voltage for surface ionization.
Some very interesting results, giving the variation of the
current with voltage, are observed when the ionization is intense,
and confined to the space near the surface of one of two parallel
plates between which the current is measured.
The theory of this subject has been worked out independently by Child[37] and Rutherford[38]. Let V be the potential difference between two parallel plates at a distance d apart. Suppose that the ionization is confined to a thin layer near the surface of the plate A (see Fig. 1) which is charged positively. When the electric field is acting, there is a distribution of positive ions between the plates A and B.
Let n_{1} = number of positive ions per unit volume at a distance
x from the plate A,
K_{1} = mobility of the positive ions,
e = charge on an ion.
The current i_{1} per square centimetre through the gas is constant for all values of x, and is given by
i_{1} = K_{1}n_{1}e(dV/dx).
By Poisson's equation
d^2V/dx^2 = 4πn_{1}e.
Then i_{1} = (K_{1}/(4π))(dV/dx)(d^2V/dx^2).
Integrating (dV/dx)^2 = 8πi_{1}x/K_{1} + A,
where A is a constant. Now A is equal to the value of dV/dx when x = 0. By making the ionization very intense, the value of dV/dx can be made extremely small.
Putting A = 0, we see that
dV/dx = ±[sqrt](8πi_{1}x/K_{1}).
This gives the potential gradient between the plates for different values of x.
Integrating between the limits 0 and d,
V = ±(2/3)[sqrt](8πi_{1}/K_{1})d^{3/2},
or i_{1} = (9V^2/(32πd^3))K_{1}.
reversed, and K_{2} the velocity of the negative ion,
i_{2} = (9V^2/(32πd^3))K_{2},
and i_{1}/i_{2} = K_{1}/K_{2}.
The current in the two directions is thus directly proportional to the velocities of the positive and negative ions. The current should vary directly as the square of the potential difference applied, and inversely as the cube of the distance between the plates.
The theoretical condition of surface ionization cannot be fulfilled by the ionization due to active substances, as the ionization extends some centimetres from the active plate. If, however, the distance between the plates is large compared with the distance over which the ionization extends, the results will be in rough agreement with the theory. Using an active preparation of radium, the writer has made some experiments on the variation of current with voltage between parallel plates distant about 10 cms. from each other[39].
The results showed
(1) That the current through the gas for small voltages increased more rapidly than the potential difference applied, but not as rapidly as the square of that potential difference.
(2) The current through the gas depended on the direction of the electric field; the current was always smaller when the active plate was charged positively on account of the smaller mobility of the positive ion. The difference between i_{1} and i_{2} was greatest when the gas was dry, which is the condition for the greatest difference between the velocities of the ions.
An interesting result follows from the above theory. For given values of V and d, the current cannot exceed a certain definite value, however much the ionization may be increased. In a similar way, when an active preparation of radium is used as a source of surface ionization, it is found that, for a given voltage and distance between the plates, the current does not increase beyond a certain value however much the activity of the material is increased.
48. Magnetic field produced by an ion in motion. It
will be shown later that the two most important kinds of rays
emitted by radio-active substances consist of electrified particles,
spontaneously projected with great velocity. The easily absorbed
rays, known as [Greek: a] rays, are positively electrified atoms of matter;
the penetrating rays, known as [Greek: b] rays, carry a negative charge,
and have been found to be identical with the cathode rays produced
by the electric discharge in a vacuum tube.
The methods adopted to determine the character of these rays are very similar to those first used by J. J. Thomson to show that the cathode rays consisted of a stream of negatively electrified particles projected with great velocity.
The proof that the cathode rays were corpuscular in character, and consisted of charged particles whose mass was very small compared with that of the hydrogen atom, marked an important epoch in physical science: for it not only opened up new and fertile fields of research, but also profoundly modified our previous conceptions of the constitution of matter.
A brief account will accordingly be given of the effects produced by a moving charged body, and also of some of the experimental methods which have been used to determine the mass and velocity of the particles of the cathode stream[40].
Consider an ion of radius α, carrying a charge of electricity e, and moving with a velocity u, small compared with the velocity of light. In consequence of the motion, a magnetic field is set up around the charged ion, which is carried with it. The charged ion in motion constitutes a current element of magnitude eu, and the magnetic field H at any point distant r from the sphere is given by
H = eu sin θ/r^2,
motion. The lines of magnetic force are circles around the axis of motion. When the ion is moving with a velocity small compared with the velocity of light, the lines of electric force are nearly radial, but as the speed of light is approached, they tend to leave the axis of motion and to bend towards the equator. When the speed of the body is very close to that of light, the magnetic and electric field is concentrated to a large extent in the equatorial plane.
The presence of a magnetic field around the moving body implies that magnetic energy is stored up in the medium surrounding it. The amount of this energy can be calculated very simply for slow speeds.
In a magnetic field of strength H, the magnetic energy stored up in unit volume of the medium of unit permeability is given by H^2/(8π). Integrating the value of this expression over the region exterior to a sphere of radius a, the total magnetic energy due to the motion of the charged body is given by [integral]_{a}^[infinity] (H^2/(8π))d(vol) = (e^2u^2/(8π))[integral]_{0}^2π [integral]_{0}^π [integral]_{a}^[infinity] (sin^2 θ)/(r^4)r(sin θ)dφrdθdr
= (e^2u^2)/4[integral]_{0}^π [integral]_{a}^[infinity] ((1 - cos^2 θ)/r^2)(sin θ)dθ.dr
= (e^2 u^2)/3 [integral]_{a}^[infinity] dr/r^2 = e^2 u^2/(3a).
The magnetic energy, due to the motion, is analogous to kinetic energy, for it depends upon the square of the velocity of the body. In consequence of the charge carried by the ion, additional kinetic energy is associated with it. If the velocity of the ion is changed, electric and magnetic forces are set up tending to stop the change of motion, and more work is done during the change than if the ion were uncharged. The ordinary kinetic energy of the body is (1/2)mu^2. In consequence of its charge, the kinetic energy associated with it is increased by (e^2 u^2)/(3a). It thus behaves as if it possessed a mass m + m_{1} where m_{1} is the electrical mass, with the value 2e^2/(3a). We have so far only considered the electrical mass of a charged ion moving with a velocity small compared with that of light. As the speed of light is approached, the magnetic energy can no longer be expressed by the equation already given. The general values of the electrical mass of a charged body for speed were first worked out by J. J. Thomson[41] in 1887. A more complete examination was made in 1889 by Heaviside[42], while Searle[43] worked out the case for a charged ellipsoid. Recently, the question was again attacked by Abraham[44]. Slightly different expressions for the variation of electrical mass with speed have been obtained, depending upon the conditions assumed for the distribution of the electricity on the sphere. The expression found by Abraham, which has been utilized by Kaufmann to show that the mass of the electron is electromagnetic in origin, is given later in section 82.
All the calculations agree in showing that the electrical mass is practically constant for slow speeds, but increases as the speed of light is approached, and is theoretically infinite when the speed of light is reached. The nearer the velocity of light is approached, the greater is the resisting force to a change of motion. An infinite force would be required to make an electron actually attain the velocity of light, so that, according to the present theory, it would be impossible for an electron to move faster than light, i.e. faster than an electromagnetic disturbance travels in the ether.
The importance of these deductions lies in the fact that an electric charge in motion, quite independently of any material nucleus, possesses an apparent mass in virtue of its motion, and that this mass is a function of the speed. Indeed, we shall see later (see section 82) that the apparent mass of the particles constituting the cathode stream can be explained in virtue of their charge, without the necessity of assuming a material body in which the charge is distributed. This has led to the suggestion that all mass may be electrical in origin, and due purely to electricity in motion.
49. Action of a magnetic field on a moving ion. Let us
consider the case of an ion of mass m carrying a charge e and moving freely with a velocity u. If u is small compared with the
velocity of light, the ion in motion corresponds to a current
element of magnitude eu. If the ion moves in an external
magnetic field of strength H, it is acted on by a force at right
angles both to the direction of motion, and to that of the magnetic
force and equal in magnitude to Heu sin [Greek: theta], where [Greek: theta] is the angle
between the direction of the magnetic force and the direction of
motion. Since the force due to the magnetic field is always
perpendicular to the direction of motion, it has no effect upon
the velocity of the particle, but can only alter the direction of its
path.
If [Greek: rho] is the radius of curvature of the path of the ion, the force along the normal is equal to mu^2/ρ, and this is balanced by the force Heu sin [Greek: theta].
If [Greek: theta] = [Greek: pi]/2, i.e. if the ion is moving at right angles to the direction of the magnetic field Heu = mu^2/[Greek: rho] or H[Greek: rho] = (m/e)u. Since u is constant, [Greek: rho] is also constant, i.e. the particle describes a circular orbit of radius [Greek: rho]. The radius of the circular orbit is thus directly proportional to u, and inversely proportional to H.
If the ion is moving at an angle [Greek: theta] with the direction of the magnetic field, it describes a curve which is compounded of a motion of a particle of velocity u sin [Greek: theta] perpendicular to the field and u cos [Greek: theta] in the direction of the field. The former describes a circular orbit of radius [Greek: rho], given by H[Greek: rho] = (m/e)u sin [Greek: theta]; the latter is unaffected by the magnetic field and moves uniformly in the direction of the magnetic field with a velocity u cos [Greek: theta]. The motion of the particle is in consequence a helix, traced on a cylinder of radius [Greek: rho] = mu sin [Greek: theta]/(eH), whose axis is in the direction of the magnetic field. Thus an ion projected obliquely to the direction of a uniform magnetic field always moves in a helix whose axis is parallel to the lines of magnetic force[45]. 50. Determination of e/m for the cathode stream. The cathode rays, first observed by Varley, were investigated in detail by Crookes. These rays are projected from the cathode in a vacuum tube at low pressure. They travel in straight lines, and are readily deflected by a magnet, and produce strong luminosity in a variety of substances placed in their path. The rays are deflected by a magnetic field in the same direction as would be expected for a negatively charged particle projected from the cathode. In order to explain the peculiar properties of these rays Crookes supposed that they consisted of negatively electrified particles, moving with great velocity and constituting, as he appropriately termed it, "a new or fourth state of matter." The nature of these rays was for twenty years a subject of much controversy, for while some upheld their material character, others considered that they were a special form of wave motion in the ether.
Perrin and J. J. Thomson showed that the rays always carried with them a negative charge, while Lenard made the important discovery that the rays passed through thin metal foil and other substances opaque to ordinary light. Using this property, he sent the rays through a thin window and examined the properties of the rays outside the vacuum tube in which they were produced.
The absorption of the rays by matter was shown to be nearly proportional to the density over a very wide range, and to be independent of its chemical constitution.
The nature of these rays was successfully demonstrated by J. J. Thomson[46] in 1897. If the rays consisted of negatively electrified particles, they should be deflected in their passage through an electric as well as through a magnetic field. Such an experiment had been tried by Hertz, but with negative results. J. J. Thomson, however, found that the rays were deflected by an electric field in the direction to be expected for a negatively charged particle, and showed that the failure of Hertz to detect the same was due to the masking of the electric field by the strong ionization produced in the gas by the cathode stream. This effect was got rid of by reducing the pressure of the gas in the tube. The experimental arrangement used for the electric deflection of the rays is shown in Fig. 10.
The cathode rays are generated at the cathode C, and a narrow pencil of rays is obtained by passing the rays through a perforated disc AB. The rays then passed midway between two parallel insulated plates D and E, d centimetres apart, and maintained at a constant difference of potential V. The point of incidence of the pencil of rays was marked by a luminous patch produced on a phosphorescent screen placed at PP´.
The particle carrying a negative charge e in passing between the charged plates, is acted on by a force Xe directed towards the positive plate, where X, the strength of the electric field, is given by V/d.
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Fig. 10.
The application of the electric field thus causes the luminous patch to move in the direction of the positive plate. If now a uniform magnetic field is applied at the plates D and E, perpendicular to the pencil of rays, and parallel to the plane of the plates, and in such a direction that the electric and magnetic forces are opposed to one another, the patch of light can be brought back to its undisturbed position by adjusting the strength of the magnetic field. If H is the strength of the magnetic field, the force on the particle due to the magnetic field is Heu, and when a balance is obtained
Heu = Xe,
or u = X/H (1).
Now if the magnetic field H is acting alone, the curvature ρ of the path of the rays between the plates can be deduced from the deflection of the luminous patch. But we have seen that
Hρ = mu/e (2).
can be determined.
The velocity u is not constant, but depends upon the potential difference between the electrodes, and this in turn depends upon the pressure and nature of the residual gas in the tube.
By altering these factors, the cathode particles may be made to acquire velocities varying between about 10^9 and 10^{10} cms. per second. This velocity is enormous compared with that which can be impressed ordinarily upon matter by mechanical means. On the other hand, the value of e/m for the particles is sensibly constant for different velocities.
As a result of a series of experiments the mean value e/m = 7·7 × 10^6 was obtained. The value of e/m is independent of the nature or pressure of the gas in the vacuum tube and independent of the metal used as cathode. A similar value of e/m was obtained by Lenard[47] and others.
Kaufmann[48] and Simon[49] used a different method to determine the value of e/m. The potential difference V between the terminals of the tube was measured. The work done on the charged particle in moving from one end of the tube to the other is Ve, and this must be equal to the kinetic energy (1/2)mu^2 acquired by the moving particle. Thus
e/m = u^2/(2V) (3).
By combination of this equation with (2) obtained by measurement of the magnetic deflexion, both u and e/m can be determined.
Simon found by this method that
e/m = 1·865 × 10^7.
by Kaufmann for the electrons projected from radium.
These results, which have been based on the effect of a magnetic and electric field on a moving ion, were confirmed by Weichert, who determined by a direct method the time required for the particle to traverse a known distance.
The particles which make up the cathode stream were termed "corpuscles" by J. J. Thomson. The name "electron," first employed by Johnstone Stoney, has also been applied to them and has come into general use[50].
The methods above described do not give the mass of the electron, but only the ratio of the charge to the mass. A direct comparison can, however, be made between the ratio e/m for the electron and the corresponding value for the hydrogen atoms set free in the electrolysis of water. Each of the hydrogen atoms is supposed to carry a charge e, and it is known that 96,000 coulombs of electricity, or, in round numbers, 10^4 electromagnetic units of quantity are required to liberate one gram of hydrogen. If N is the number of atoms in one gram of hydrogen, then Ne = 10^4. But if m is the mass of a hydrogen atom, then Nm = 1. Dividing one by the other e/m = 10^4. We have seen already that a gaseous ion carries the same charge as a hydrogen atom, while indirect evidence shows that the electron carries the same charge as an ion, and consequently the same charge as the atom of hydrogen. Hence we may conclude that the apparent mass of the electron is only about 1/1000 of the mass of the hydrogen atom. The electron thus behaves as the smallest body known to science.
In later experiments J. J. Thomson showed that the negative ions set free at low pressures by an incandescent carbon filament, and also the negative ions liberated from a zinc plate exposed to the action of ultra-violet light, had the same value for e/m as the electrons produced in a vacuum tube. It thus seemed probable that the electron was a constituent of all matter. This view received strong support from measurements of quite a different character. Zeeman in 1897 found that the lines of the spectrum from a source of light exposed in a strong magnetic field were displaced and doubled. Later work has shown that the lines in some cases are trebled, in others sextupled, while, in a few cases, the multiplication is still greater. These results received a general explanation on the radiation theories previously advanced by Lorenz and Larmor. The radiation, emitted from any source, was supposed to result from the orbital or oscillatory motion of the charged parts constituting the atom. Since a moving ion is acted on by an external magnetic field, the motion of the charged ions is disturbed when the source of light is exposed between the poles of a strong magnet. There results a small change in the period of the emitted light, and a bright line in the spectrum is, in consequence, displaced by the action of the magnetic field. According to theory, the small change in the wave-length of the emitted light depends upon the strength of the magnetic field and on the ratio e/m of the charge carried by the ion to its mass. By comparison of the theory with the experimental results, it was deduced that the moving ion carried a negative charge, and that the value of e/m was about 10^7. The charged ion, responsible for the radiation from a luminous body, is thus identical with the electron set free in a vacuum tube.
It thus seems reasonable to suppose that the atoms of all bodies are complex and are built up, in part at least, of electrons, whose apparent mass is very small compared with that of the hydrogen atom. The properties of such disembodied charges has been examined mathematically among others by Larmor, who sees in this conception the ultimate basis of a theory of matter. J. J. Thomson and Lord Kelvin have investigated mathematically certain arrangements of a number of electrons which are stable for small disturbances. This question will be discussed more in detail in section 263. 51. Canal rays. If a discharge is passed through a vacuum tube provided with a perforated cathode, within certain limits of pressure, luminous streams are observed to pass through the holes and to emerge on the side of the cathode remote from the anode. These rays were first observed by Goldstein[51] and were called by him the "Canal-strahlen." These rays travel in straight lines and produce phosphorescence in various substances.
Wien[52] showed that the canal rays were deflected by strong magnetic and electric fields, but the amount of deflection was very small compared with that of the cathode rays under similar conditions. The deflection was found to be opposite in direction to the cathode rays, and this indicates that the canal rays consist of positive ions. Wien determined their velocity and the ratio e/m, by measuring the amount of their magnetic and electric deflection. The value of e/m was found to be variable, depending upon the gas in the tube, but the maximum value observed was 10^4. This shows that the positive ion, in no case, has a mass less than that of the hydrogen atom. It seems probable that the canal rays consist of positive ions, derived either from the gas or the electrodes, which travel towards the cathode, and have sufficient velocity to pass through the holes of the cathode and to appear in the gas beyond.
It is remarkable that, so far, no case has been observed where the carrier of a positive charge has an apparent mass less than that of the hydrogen atom. Positive electricity always appears to be associated with bodies atomic in size. We have seen that the process of ionization in gases is supposed to consist of the expulsion of an electron from the atom. The corresponding positive charge remains behind on the atom and travels with it. This difference between positive and negative electricity appears to be fundamental, and no explanation of it has, as yet, been forthcoming.
52. Radiation of energy. If an electron moves uniformly
in a straight line with constant velocity, the magnetic field, which travels with it, remains constant, and there is no loss of energy
from it by radiation. If, however, its motion is hastened or
retarded, the magnetic field is altered, and there results a loss of
energy from the electron in the form of electromagnetic radiation.
The rate of loss of energy from an accelerated electron was first
calculated by Larmor[53] and shown to be 2e^2/(3V) × (acceleration)^2, where
e is the charge on the electron in electromagnetic units, and V the
velocity of light.
Any alteration in the velocity of a moving charge is thus always accompanied by a radiation of energy from it. Since the electron, set free in a vacuum tube, increases in velocity in passing through the electric field, energy must be radiated from it during its passage from cathode to anode. It can, however, readily be calculated that, in ordinary cases, this loss of energy is small compared with the kinetic energy acquired by the electron in passing through the electric field.
An electron moving in a circular orbit is a powerful radiator of energy, since it is constantly accelerated towards the centre. An electron moving in an orbit of radius equal to the radius of an atom (about 10^{-8} cms.) would lose most of its kinetic energy of motion in a small fraction of a second, even though its velocity was originally nearly equal to the velocity of light. If, however, a number of electrons are arranged at equal angular intervals on the circumference of a circle and move with constant velocity round the ring, the radiation of energy is much less than for a single electron, and rapidly diminishes with an increase in the number of electrons round the ring. This result, obtained by J. J. Thomson, will be discussed in more detail later when the stability of systems composed of rotating electrons is under consideration.
Since the radiation of energy is proportional to the square of the acceleration, the proportion of the total energy radiated depends upon the suddenness with which an electron is started or stopped. Now some of the cathode ray particles are stopped abruptly when they impinge on the metal cathode, and, in consequence, give up a fraction of their kinetic energy in the form of electromagnetic radiation. Stokes and Weichert suggested that this radiation constituted the X rays, which are known to have their origin at the surface on which the cathode rays impinge. The mathematical theory has been worked out by J. J. Thomson[54]. If the motion of an electron is suddenly arrested, a thin spherical pulse in which the magnetic and electric forces are very intense travels out from the point of impact with the velocity of light. The more suddenly the electron is stopped, the thinner and more intense is the pulse. On this view the X rays are not corpuscular like the cathode rays, which produce them, but consist of transverse disturbances in the ether, akin in some respects to light waves of short wave-length. The rays are thus made up of a number of pulses, which are non-*periodic in character, and which follow one another at irregular intervals.
On this theory of the nature of the X rays, the absence of direct deflection, refraction, or polarization is to be expected, if the thickness of the pulse is small compared with the diameter of an atom. It also explains the non-deflection of the path of the rays by a magnetic or electric field. The intensity of the electric and magnetic force in the pulse is so great that it is able to cause a removal of an electron from some of the atoms of the gas, over which the pulse passes, and thus causes the ionization observed.
The cathode rays produce X rays, and these in turn give rise to a secondary radiation whenever they impinge on a solid body. This secondary radiation is emitted equally in all directions, and consists partly of a radiation of the X ray type and also of electrons projected with considerable velocity. This secondary radiation gives rise to a tertiary radiation and so on.
Barkla[55] has shown that the secondary radiation emitted from a gas through which the rays pass consists in part of scattered X rays of about the same penetrating power as the primary rays as well as some easily absorbed rays.
Part of the cathode rays is diffusely reflected on striking the cathode. These scattered rays consist in part of electrons of the same speed as in the primary beam, but also include some others of much less velocity. The amount of diffuse reflection depends upon the nature of the cathode and the angle of incidence of the rays. We shall see later (chapter IV.) that similar effects are produced when the rays from radio-active substances impinge upon solid bodies.
In this chapter an account of the ionization theory of gases has been given to the extent that is necessary for the interpretation of the measurements of radio-activity by the electric method. It would be out of place here to discuss the development of that theory in detail, to explain the passage of electricity through flames and vapours, the discharge of electricity from hot bodies, and the very complicated phenomena observed in the passage of electricity through a vacuum tube.
For further information on this important subject, the reader is referred to J. J. Thomson's Conduction of Electricity through Gases, in which the whole subject is treated in a full and complete manner. A simple account of the effect of moving charges and the electronic theory of matter was given by the same author in the Silliman Lectures of Yale University and published under the title Electricity and Matter (Scribner, New York, 1904).
- ↑ J. J. Thomson and Rutherford, Phil. Mag. Nov. 1896.
- ↑ The word ion has now been generally adopted in the literature of the subject. In using this word, it is not assumed that the ions in gases are the same as the corresponding ions in the electrolysis of solutions.
- ↑ A minute current is observed between the plates even if no radio-active matter be present. This has been found to be due mainly to a slight natural radio-activity of the matter composing them. (See chapter XIV.)
- ↑ This nomenclature has arisen from the similarity of the shape of the current-voltage curves to the magnetization curves for iron. Since, on the ionization theory, the maximum current is a result of the removal of all the ions from the gas, before recombination occurs, the terms are not very suitable. They have however now come into general use and will be retained throughout this work.
- ↑ J. J. Thomson, Phil. Mag. 47, p. 253, 1899; Conduction of Electricity through Gases, p. 73, 1903.
- ↑ Rutherford, Phil. Mag. Jan. 1899.
- ↑ Townsend, Phil. Mag. Feb. 1901.
- ↑ Rutherford, Phil. Mag. Nov. 1897, p. 144, Jan. 1899.
- ↑ Townsend, Phil. Trans. A, p. 157, 1899.
- ↑ M^cClung, Phil. Mag. March, 1902.
- ↑ Langevin, Thèse présentée à la Faculté des Sciences, p. 151, Paris, 1902.
- ↑ Owens, Phil. Mag. Oct. 1899.
- ↑ Rutherford, Phil. Mag. p. 429, Nov. 1897.
- ↑ Zeleny, Phil. Trans. A, p. 193, 1901.
- ↑ Langevin, C. R. 134, p. 646, 1902.
- ↑ Zeleny, Phil. Mag. July, 1898.
- ↑ Rutherford, Phil. Mag. Feb. 1899.
- ↑ Zeleny, Phil. Trans. 195, p. 193, 1900.
- ↑ Langevin, C. R. 134, p. 646, 1902, and Thesis, p. 191, 1902.
- ↑ Rutherford, Proc. Camb. Phil. Soc. 9, p. 410, 1898.
- ↑ Langevin, Thesis, p. 190, 1902.
- ↑ Helmholtz and Richarz, Annal. d. Phys. 40, p. 161, 1890.
- ↑ Wilson, Phil. Trans. p. 265, 1897; p. 403, 1899; p. 289, 1900.
- ↑ Thomson, Phil. Mag. p. 528, Dec. 1898.
- ↑ Wilson, Phil. Trans. A, 193, p. 289, 1899.
- ↑ Thomson, Phil. Mag. p. 528, Dec. 1898, and March, 1903. Conduction of Electricity through Gases, Camb. Univ. Press, 1903, p. 121.
- ↑ Wilson, Phil. Mag. April, 1903.
- ↑ Townsend, Phil. Trans. A, p. 129, 1899.
- ↑ Townsend, loc. cit. p. 139.
- ↑ Some difference of opinion has been expressed as to the value of V required to produce ions at each collision. Townsend considers it to be about 20 volts; Langevin 60 volts and Stark about 50 volts.
- ↑ Rutherford, Phil. Mag. Jan. 1899.
- ↑ Rutherford, Phil. Mag. Jan. 1899.
- ↑ Strutt, Phil. Trans. A, p. 507, 1901 and Proc. Roy. Soc. p. 208, 1903.
- ↑ M^cClung, Phil. Mag. Sept. 1904.
- ↑ Eve, Phil. Mag. Dec. 1904.
- ↑ Rutherford, Phil. Mag. p. 137, Jan. 1899.
- ↑ Child, Phys. Rev. Vol. 12, 1901.
- ↑ Rutherford, Phil. Mag. p. 210, August, 1901; Phys. Rev. Vol. 13, 1901.
- ↑ Rutherford, Phil. Mag. Aug. 1901.
- ↑ A simple and excellent account of the effects produced by the motion of a charged ion and also of the electronic theory of matter was given by Sir Oliver Lodge in 1903 in a paper entitled "Electrons" (Proceedings of the Institution of Electrical Engineers, Part 159, Vol. 32, 1903). See also J. J. Thomson's Electricity and Matter (Scribner, New York, 1904).
- ↑ J. J. Thomson, Phil. Mag. April, 1887.
- ↑ Heaviside, Collected Papers, Vol. II. p. 514.
- ↑ Searle, Phil. Mag. Oct. 1897.
- ↑ Abraham, Phys. Zeit. 4, No. 1 b, p. 57, 1902.
- ↑ A full account of the path described by a moving ion under various conditions is given by J. J. Thomson, Conduction of Electricity in Gases (Camb. Univ. Press, 1903), pp. 79-90.
- ↑ J. J. Thomson, Phil. Mag. p. 293, 1897.
- ↑ Lenard, Annal. d. Phys. 64, p. 279, 1898.
- ↑ Kaufmann, Annal. d. Phys. 61, p. 544; 62, p. 596, 1897; 65, p. 431, 1898.
- ↑ Simon, Annal. d. Phys. 69, p. 589, 1899.
- ↑ A complete discussion of the various methods employed to measure the velocity and mass of electrons and also of the theory on which they are based will be found in J. J. Thomson's Conduction of Electricity through Gases.
- ↑ Goldstein, Berlin Sitzber. 39, p. 691, 1896; Annal. d. Phys. 64, p. 45, 1898.
- ↑ Wien, Annal. d. Phys. 65, p. 440, 1898.
- ↑ Larmor, Phil. Mag. 44, p. 593, 1897.
- ↑ J. J. Thomson, Phil. Mag. Feb. 1897.
- ↑ Barkla, Phil. Mag. June, 1903.