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1911 Encyclopedia Britannica

Electrical Properties of Gases

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"ELECTRICAL PROPERTIES OF GASES 6.864 for Electric Conduction Through Gases). - The electrical properties of gases vary greatly with the conditions to which the gas is exposed.

A gas in its normal condition is a non-conductor of electricity even though it is the vapour of a good conductor like mercury. On the other hand, when it is exposed to such influences as Röntgen rays, intense electrical forces or the radiation from radioactive substances, it becomes a conductor of electricity. Radioactive radiations are so wide-spread and so difficult to eliminate that it has not been found possible to obtain gases which do not show traces of conductivity under tests as delicate as some of those now at our command. This residual conductivity is, however, so small that we may here leave it out of account. The most important electrical property of a gas in a normal state is its specific inductive capacity. The significance of this property is best illustrated from the relation K-1/47r= NM, between the specific inductive capacity K, N the number of molecules per unit volume, and M the electrostatic moment which a molecule acquires under unit electric force. As we know N, we can if we know the value of K deduce the value of M, and this will tell us a good deal about the shape and size of the molecule. For example, if we regard the molecules as solid conducting spheres, M = r 3 where r is the radius of the sphere. Thus, on this hypothesis we can find the radius of the molecule, if we know the value of K, and though the hypothesis itself does not throw much light on the structure of the atom, it is probable that the radius of a conducting sphere which would produce the same electrical moment would be of the same order of magnitude as the linear dimensions of the molecule: the radii of metallic spheres which would give the specific inductive capacities possessed by hydrogen, nitrogen, oxygen and chlorine, are respectively 1.19 X 10-8, 1.60 X i 08, 1.48 X 10 -8, 2 04 X i 08 centimetres. On the more probable hypothesis that the atoms and molecules consist of electrons arranged in equilibrium round centres of positive electricity, the electric force will displace the electrons relatively to the positive centres and thus cause the molecule to have a finite electrical moment. The more rigidly the electrons are connected to the positive charge, the smaller will be this moment and the smaller the specific inductive capacity of the gas.

The values of K - I for the elements belonging to the same family are connected by a remarkably simple and interesting relation, which was discovered by Mr. Cuthbertson (Phil. Trans.

N

0

F

297

270

192

P

S

CI

1197

II 0 I

768

=299X4 As 1J50 =258 X6

=275X4 Se =261 X6 Te 2495 =249 X10

=192X4 Br 1125 =187X6

1920

= 192 X 10

A.207, p. 1 35). It is shown in the following table, where the numbers under the symbols denoting the elements are the values of - ( K - i) X 106: - Thus the values of K - i for successive elements of the same family - (N.P.As): (O,S ,Se,Te): (F.C1.Br.I): (Ne,Ar,Kr,X) - are in all cases very nearly in the proportion i, 4, 6, io. In the simple theory, where the molecules are regarded as conductors, this would indicate that the volumes of the molecules of the successive elements in the same family are in the proportion i, 4, 6, io, for each of these types of elements. On the theory which regards the atom as built up of electrons arranged round positive centres, the configuration of the outer layer of electrons for different members of the same family would be similar, and it is easy to show that for similar configurations of electrons the value of K - i would be proportional to the cube of the linear dimensions, i.e. to the volume enclosed by the outer layer of electrons; so that again on this theory Cuthbertson's result shows that volumes of successive elements in the same family are in the same ratio whether the family be that of the inert gases, the halogens, or the oxygen or nitrogen groups.

Another example of the information as to the nature of the molecule afforded by determinations of the specific inductive capacity is that, while the specific inductive capacity of many gases, e.g. H2, N 2, 02, CO, C02, C12, is equal (as Maxwell's Electromagnetic Theory of Light suggests) to the square of the refractive index, there are, as Badeker ( Zeitschrift Physik. Chem. 3 6, p. 305) has shown, others, such as NH 3, HC1, S02, the vapours of water and the alcohols, whose specific inductive capacity is far in excess of the value given by this rule, and moreover the specific inductive capacity of these gases diminishes much more rapidly as the temperature increases than that of gases of the first type. The difference can be accounted for by supposing that the molecules of gases of the first type have no electrical moment when they are free from the action of an external electrical force, while those of the second type have an intrinsic electrical moment apart from that which may be produced by the external force. When there is no electrical field, the collisions between the molecules will cause the axes of electrical moments of the different molecules to be uniformly distributed, so that the average effect will be zero. An electric force will tend to drag the axes of the different molecules into alignment, and the assemblage of molecules will have a finite electrical moment which will be a measure of the specific inductive capacity. Inasmuch as the collisions between the molecules tend to knock their axes out of line and diminish the specific inductive capacity, the latter will diminish as the temperature and with it the vigour of the encounters increases. The substances which have an intrinsic electrical moment have exceptionally active chemical properties and are good solvents, dissociating the salts dissolved in them.

Argon .

Hydrogen

Nitrogen

Air .

Oxygen

Carbon dioxide .

Nitrous oxide .

0.46%

3.83%

4.06%

5.00%

9.40%

11.70%

15.40%

If the distribution of electrons in a molecule were not symmetrical about three axes at right angles to each other, the specific inductive capacity of a single molecule would vary with the direction of the electric force, but as the molecules in a gas are orientated in equal numbers in all directions we should not detect this by direct measurements of the specific inductive capacity. We can however detect this effect in another way; for if the molecules have different specific inductive capacities in different directions the light scattered by the molecules at right angles to the incident unpolarized light will not be plane polarized as it would be if the molecule were symmetrical (J. J. Thomson, Phil. Mag. 40, p. 393), and if the incident light is plane polarized the scattered light will not vanish in any direction. Strutt ( Proc. Roy. Soc. 98A. 57) has measured the departure from plane polarization for different gases with the result shown in the following table: This shows that the molecule of argon is very symmetrical, while the nitrogen molecule is more symmetrical than the oxygen, and this again more symmetrical than that of C02.

1 Ionized Gases

2 The Nature of the Ions

3 Recombination of the Ions

4 Large Ions

5 Relation between the Potential Difference and the Current through an Ionized Gas

6 Current from Hot Wires

7 Ionization by Collision

8 Ionization by Moving Ions

9 Electrical Wind

10 Relation between Potential Difference and Current

11 Structure of the Discharge

12 Distribution of the Electric Force along the Discharge

13 Cathode Fall of Potential

14 Striated Discharge

15 Cathode Rays

16 Positive Rays as a Method of Chemical Analysis

17 Use of Positive Rays to Determine Atomic Weight

18 The Charge of Electricity Carried by Gaseous Ions and Electrons

Ionized Gases

Gases may in various ways be put into a state in which they conduct electricity on an altogether different scale from the normal gas. They acquire this conductivity when Röntgen rays or the rays from radioactive substances pass through them, or when they are traversed by cathode or positive rays. Ultra-violet light of very short wave length can impart this property to a gas, while gases recently driven from flames or from near arcs or sparks or bubbled through certain liquids or passed slowly over phosphorus also possess this property.

The conductivity of gases possesses interesting characteristics. In the first place it persists for some time after the agent which made the gas a conductor has ceased to act; it always however diminishes after the agent is removed, in some cases very rapidly, and finally disappears. The conducting gas loses its conductivity if it is sucked through glass-wool, or made to bubble through water. The conductivity may also be removed by making the gas traverse a strong electric field so that a current of electricity passes through it. The removal of the conductivity by filtering the gas through glass-wool or water shows that the conductivity is due to something mixed with the gas which can be removed by filtration, while the removal of the conductivity by the electrical field shows that this something is charged with electricity and moves under the action of the electric force. Since the gas when in the conducting state shows as a whole no charge of electricity, the charges mixed with the gas must be both positive and negative. We conclude that the conductivity of the gas is due to the presence of electrified particles; some of these particles are positively, others negatively, electrified. These electrified particles are called ions, and the process ionization.

The passage of electricity through a conducting gas does not follow the same laws as the flow through metals and liquid electrolytes; in these the current is proportional to the electromotive force, while for gases the relation is represented by a graph like fig. r, where the ordinates are proportional to the current and 20 ' '10. 100. Z00.300.400.500.600700.800.9001000.1100.1200.1300.1400 1500 Volts FIG.1 the abscissa to the electromotive forces. We see that when the electromotive force is small, the current is proportional to the electromotive force, as in the case of metallic conduction; as the electromotive force increases, the current after a time does not increase nearly so rapidly, and a stage is reached where the current remains constant in spite of the increase in the electromotive force. There is a further stage, which we shall consider later, where the current again increases with the electromotive force, and does so much more rapidly than at any previous stage. The He 14 137 Ar.

568 =142X4 Kr.

850 =142X6 X 1 37 8 =138X10 50 current in the stage when it does not depend upon the electromotive force is said to be saturated. The reason for this saturation is that the passage of a current of electricity through the gas involves the removal of a number of ions proportional to the quantity of electricity passing through the gas. Thus the gas is losing ions at a rate proportional to the current; it cannot go on losing more ions than are produced, so that the current cannot increase beyond a critical value which is proportional to the rate of production of ions. This sometimes produces a state of things which seems anomalous to those accustomed to look at conduction of electricity exclusively from the point of Ohm's law. For example, when gases are exposed to Röntgen rays, the number of ions produced per second is proportional to the volume of the gas, so that, if two parallel plates are immersed in such a gas and a current sent from one to the other, when the distance between the plates is increased the number of ions available for carrying the current and therefore the saturation current will be increased also. Thus apparent " resistance " will diminish as the length of 'the gaseous conductor is increased.

The Nature of the Ions

The question arises, what is the nature of the particles which carry the charges of electricity? Are they the atoms or molecules of the gas, or, for the negative charges, electrons? Information on these points is afforded by measuring the velocity of the ions under given electric forces.

It follows from the kinetic theory of gases that the velocity V of an ion due to an electric force X is given by the equation :- e X V=X

(i) - v Here X is the mean free path of the ion through the surrounding molecules, v the average velocity of the ion due to its thermal agitation, this velocity depending only on the mass of the ion and the temperature of the gas, and m is the mass of the ion and e the electric charge carried by it. If we calculate by this formula the velocity of an ion in hydrogen, assuming that the mass of the ion and its free path are the same as those for a molecule of hydrogen, we find that it would be 26 cm/sec. for an electric force of a volt per cm.; the value found by experiment is 6.7 cm/sec. for the positive and 7.9 cm/sec. for the negative ion. The assumption that both X and m are the same for the ion as for the molecule is therefore wrong. It is clear that if, as we have every reason to believe, the normal hydrogen molecule is made up of positively and negatively electrified parts, the ion in virtue of its charge, even if its mass is the same as that of the hydrogen molecule, will exert a greater force upon a neighbouring molecule than would an uncharged molecule, and this increase in the force implies a diminution in the free path, and therefore by equation (i) a diminution in V. That a part of the discrepancy between the results given by the equation and those found by experiment is due to this cause cannot be questioned; the point which is still doubtful is whether the attraction due to the charge on the ion may not cause some of the hydrogen molecules to cling to it, forming a cluster of molecules with a greater mass and smaller free path than a single molecule. It would follow from the general principles of thermodynamics that, if the work required to separate a neutral molecule of hydrogen from a positive charge in its near neighbourhood were comparable with the average energy of translation of the molecules at the temperature of the gas, some such clusters would be formed, and that, if the work of separation were large compared with the energy of agitation, practically all the ions would consist of such clusters. This work would be greater for molecules which, like those of ammonia, or the vapours of water and alcohol, have a finite electrical moment, than for those which, like the molecules of hydrogen, oxygen and nitrogen, have no such moment, so that it is quite possible that, though there may be no clustering with these very permanent gases, there may be some when gases of the other type are present. This differentiation seems borne out by experiment, for no clear indications of clustering seem to have been found for the permanent gases. Since clustering is analogous to chemical combination, we should expect the mobilities, if they depended upon clusters, to have very large temperature coefficients. The mobilities of some of the permanent gases at constant density have been measured by Erikson over a considerable range of temperature, and though there is a considerable temperature effect it is not nearly so large as we should expect if it depended on chemical combination. Again, since clustering is a process of condensation, it would be favoured by an increase in pressure; thus a decrease in pressure would be accompanied by a simplification of the ion, and would increase its mean free path beyond the natural increase due to the diminution in the number of molecules with which the ion comes into collision. If there were no change in the character of the ion with the pressure, the mobility would vary inversely as the pressure; if the character of the ion changes, the mobility at low pressures will be greater than that given by this law. Now experiments show that for the positive ion the mobility is, very accurately, inversely proportional to the pressure over a wide range of pressures; this again is inconsistent with the existence of clusters. On the other hand, it is found that the addition of small quantities of gases which, like the vapours of water and alcohol, have a finite electrical moment produce a marked diminution in the mobility; this effect is more pronounced for the negative than for the positive ion, but as Zeleny has shown it exists for both ions. This effect is readily explained by supposing the water molecules to cluster round the ion. It would seem in accordance with the evidence to conclude that, though there is no evidence of clustering for the permanent gases, it does occur when certain easily condensible gases are present.

The behaviour of negative ions is in many respects quite different from that of the positive ones. In the first place the mobility of the negative ions is for the permanent gases greater than that of the positive; thus, for example, in dry hydrogen the velocities of the negative and positive ions, when the electric force is one volt per cm., are 7:95 and 6.7 respectively, and for air 1.87 and 1.36. The difference is less for moist gases than for dry, while for complex vapours which have comparatively small mobilities Wellisch found that there was very little difference between the mobilities of the positive and negative ions.

For the permanent gases the ratio of the mobilities of the negative and positive ions varies but little with the pressure, until the pressure is reduced below that represented by about 10 cm. of mercury. For lower pressures than this, the mobility of the negative ion increases, as Langevin showed, more rapidly than that of the positive; at the pressure of a mm. or so the mobility of the negative ion in air may be three or four times that of the positive.

An even more interesting result was discovered by Franck and Hertz, who, when they experimented with very carefully purified nitrogen or argon, found that the mobility of the negative ion was more than 100 times that of the positive. The mobilities in these gases are extremely sensitive to traces of oxygen, and a fraction of 1% of oxygen added to the pure gas will reduce the mobility of the negative ion to less than one-tenth of its maximum value. The enormous mobility of the negative ion in nitrogen and argon as compared with that of the positive shows that in them the negative electricity must be carried by electrons and not by atoms or molecules, while the effect of introducing traces of oxygen shows that these electrons readily attach themselves to the molecules of oxygen though they are unable to adhere to molecules of nitrogen or argon. The same effect has also been observed in helium and hydrogen.

These properties of the negative ion are of great importance in connexion with the mechanism of ionization in gases and the structure of atoms and molecules. In the first place, they furnish strong evidence in support of the view that the first stage in the ionization of a gas is the ejection of an electron from the molecule of the gas rather than the separation of the molecule into atoms of which some are charged with positive and others with negative electricity. On this view the negative ion begins its career as an electron and not as an atom, while the positive ion from the beginning is of molecular dimensions. As an electron has much greater mobility than a molecule the mobility of the negative ion will at first be much greater than that of the positive. In some gases, such as oxygen, the electron soon gets attached to a molecule, and its mass and mobility become comparable with those of the positive one. The mobility we measure is the average mobility of the negative ion during its life; part of the time its mobility, being that of an electron, is very much larger than that of the positive ion, while in the other part the two mobilities will be much the same. The excess of mobility of the negative over the positive ion will depend upon the fraction of its life which the negative ion spends as a free electron - a fraction which would tend to increase as the pressure of the gas diminished.

To calculate the mobility of an electron as compared with that of a molecule, we must make some assumption as to the effect of the charge on the mean free path of an electron. We saw that there were some grounds for supposing that, in the case of the positive ions, the mean free path was determined rather by the charge of the ion than by the dimensions of the molecule carrying the charge. Since the magnitude of the charge on the electron is the same as that on the positive ion, we might expect, if this were the case, that the mean free path of an electron would be much the same as that of an ion, so that in equation (i) it would be the factor my which would differentiate the mobility of the ion from that of the electron. If the electron is in thermal equilibrium with the surrounding gas, m y 2 will be the same for the ion and the electron, and thus the mobility will be inversely proportional to the square root of the mass; as the mass of the hydrogen molecule is 3.6 X io 3 times that of the electron, the mobility of the electron in hydrogen should be 60 times that of the positive ion; in nitrogen the mobility of the electron would be about 220 times that of the positive ion. If the positive ion were a cluster of molecules instead of a single molecule, the mobility of the electron as compared with that of the positive electron would be much larger than the preceding figures would indicate.

The difference between the behaviour of the electron in nitrogen or argon and in oxygen is of great importance in connexion with the structure of the atom and molecule, for it indicates that, while a molecule of oxygen can accommodate another electron in addition to those already present, the molecules of nitrogen and argon are unable to do so. It is instructive therefore to consider the results in connexion with the power of the atoms and molecules of the different elements to acquire a negative charge obtained by the study of the positive rays. These show that, while the atoms of hydrogen, carbon, oxygen, fluorine or chlorine readily acquire a negative charge, those of helium, nitrogen, neon, and argon do not; and again that, while it is very exceptional for a molecule whether of a compound or an elementary gas to acquire a negative charge, the molecule of oxygen is able to do so. We see that this result is in accordance with the behaviour of the carrier of the negative charge in an ionized gas. Since the atoms in the positive rays show so much greater affinity for the electrons than the molecules, it follows that if the agent producing ionization were to dissociate some of the molecules of the gas into neutral atoms (and to do this would require the expenditure of much less energy than to ionize the gas), these atoms would be much more effective traps for the electrons than the undissociated molecules. Loeb has shown that even in oxygen an electron collides on the average with about 50,000 molecules of oxygen before it is captured; thus if the oxygen atom could capture an electron at the first encounter, if only one molecule in 50,000 were dissociated into atoms, the effect of the atoms would be as efficacious as that of the molecules in capturing the electrons. When this dissociation takes place the abnormal velocity of the negative ion will only occur in gases like nitrogen and the inert gases whose atoms cannot receive an electron.

Recombination of the Ions

Even when the ions are not removed from a gas by sending a current of electricity through it, their number will not increase indefinitely with the time of exposure of the gas to the ionizing agent. This is due to the recombination which takes place between the positive and negative ions; these ions as they move about in the gas sometimes come into collision with each other, and by forming electrically neutral systems cease to act as ions. The gas will reach a steady state with regard to ionization when the number of ions which disappear in one second as the result of the collisions is equal to the number produced in the same time by the ionizing agent.

If there are n ions of either kind per cub. cm., the number of collisions between the positive and negative ions in one second in a cub. cm. of the gas will be proportional to n 2; hence the number of ions of either sign which are lost by recombination in one second will be represented by an t when a is called the coefficient of recombination. If the ionizing agent produces q ions per cub. cm. per second, then dn _ dt = q - ant.

The solution of this equation, if we reckon t from the instant the ionizing agent begins to act, so that n =o when 1=0, and where K 2 =q/a, is - / n =K(E2Ka1 - I)/(€2hal+I) We see that, when the gas reaches a steady state, n = K = .1 q/a, and that the gas will not approximate to this state until t is large compared with 1Ka, i.e. to Znoa where no is the value of n in the steady state. Thus when the ionization is very weak it may take a considerable time for the gas to reach a steady state.

Town-

send

Mc-

Clung

Lan-

gevin

Thir-

kill

Hen-

dren

Ret-

schin-

sky

Rume-

lin

Riint-

Ront-

Ront-

Ront-

Gas

gen

rays

gen

rays

gen

rays

gen

rays

a rays

a rays

a. rays 0 rays

Air

3420

3380

3200

3580

3300

4200

4240 5820

CO 2

35 20

349 0

34 00

35 00

..

..

H 2 3020

2940

..

..

..

..

..

2

3380

. .

..

..

..

..

SO

..

..

..

3000

..

..

N 2 0.

..

..

2960

..

..

C

..

..

1780

..

..

When the ionizing agent is removed, the ions do not disappear at once, but decay at the rate given by the equation dn dt = q - an2. - ant. The solution of this, where t is the time which has elapsed since the removal of the ionizing agents, and no the number of ions when t=o, is The results as ascribed to Thirkill were obtained by extrapolation from experiment made at lower pressures. Since e, in electrostatic measure, is 4.8 X I o 10, the value of a for air is about I. 6 X to °, so that, when there are n positive and n negative ions per cub. cm., the number of ions which recombine per second is I. 6X Io °n2.

This shows very markedly the influence of the electric charge in increasing the number of collisions between the particles, for the number of collisions in a second between 2n, uncharged molecules in a cub. cm. of air is only - which is only about I/4,000 of 4 th X e io num 1°n2, ber of recombinations between the same number of ions.

It is a very remarkable fact, and one which has not yet received a satisfactory explanation, that the values of a for gases of such different molecular weights as H2, 02, C02, S02 should be so nearly equal, while the value of a for CO is only about one-half of that for the other gases.

For pressures less than one atmosphere Thirkill has shown that a diminishes as the pressure p diminishes, and that the relation between a and p is a linear one. Langevin showed that a for air attained a maximum value at a pressure about two atmospheres, and that at higher pressures it diminished somewhat rapidly as the pressure increased.

When the density is constant the value of a diminishes as the temperature increases. The connexion between a and the absolute temperature T seems to be expressed with fair accuracy by the equation a = cT -n.

According to Erikson, n is equal to 2.3, 2.42, 2.35 for hydrogen, air and CO 2 respectively, while Phillips' experiments gave n = 2.

Large Ions

The ions we have been considering are those produced in dust-free gases by Röntgen or cathode rays. In some cases, however, ions with very much lower mobilities are to be found in gases. Thus Langevin found in air from the top of the Eiffel Tower two types of ions, one consisting of ions of the kind we have been considering, with a mobility of about i

5 cm/sec., the other of ions with a mobility of 1/3,000 cm/sec. Ions with mobilities of the same order as this second type may be produced by bubbling air through water, by passing air over phosphorus, or by drawing air from the neighbourhood of flames. They are probably charged particles of dust of various kinds, held in suspension in gas which is exposed to some kind of ionizing agent which gives a supply of ions of the first type; these settle on the particles of dust and form the slow ions. The number of these slow ions when the gas is in a steady state will only depend on the number of dust particles in the gas, and will not be affected by the strength of the ionizing agent. This follows from the principle that in the steady state the number of dust particles which acquire a positive charge must equal the number which lose such a charge. A positively electrified dust particle might lose its charge by meeting and coalescing with a negative small ion or by coalescing with a negatively electrified dust particle. These dust particles are, however, so sluggish in their movements that, unless the dust particles are enormously more numerous than the small ions, we may neglect the second source of loss in comparison with the first.

Thus if U is the number of uncharged dust particles in a cub. cm. of the gas, P and N the number of those with positive and negative charges respectively, and p, n the number of positive and negative small ions, the number of dust particles which acquire per second a positive charge will be aUp and the number losing such a charge by coalescing with a negative ion 13Pn, where a and (3 are constants; hence for equilibrium aUp = 13Pn.

Similarly by considering the negatively charged particles we geta'Un = R'Np. Hence we see that the proportion between the charged and uncharged particles of dust depends only upon the ratio of p to n, and not upon the absolute magnitude of either of these quantities. Thus, though it would take much longer to reach the steady state with a feeble source of ionization than with a strong one, when that state was reached there would be as much dust electrified in one case as in the other. De Broglie estimates that in this state about one-tenth of the particles would be electrified.

Relation between the Potential Difference and the Current through an Ionized Gas

We shall take the case of two infinite parallel metal plates maintained at different potentials and immersed in an ionized gas; the line at right angles to these plates we shall take as the axis of x, it being evidently parallel to the direction of the electric force X. Let ni, n 2 be respectively the number of positive and negative n = no/ (I +mat). Thus the number of ions will be reduced to one-half their initial value after a time I/ano. We may therefore take I/an as the measure of the life of an ion when there are n ions per cub. centimetre. The values of a/e, where e is the charge on an ion, have been measured by various experimenters, and for different methods of ionization the results are given in the following table: - Values of ale for various gases at atmospheric pressure and ordinary temperature. ions at the place fixed by the coordinate x; u l and u 2 the velocities of these ions. The volume density of the electrification in the gas, if it is entirely due to the ions, is ( n i - n 2)e when e is the charge on an ion, hence where q is the number of ions produced per second in a cub. cm. of gas, and a is the coefficient of recombination; if K 1 , ate the mobilities of the positive and negative ions respectively, then u 1 =K 1 X, u2=K2X.

From equations (I), (5) and (6) we get - 2 2 x = 87re(g - an,n 2 ) C KI + K2, d and, substituting the values of n 1 and n 2, we ge(t - l d2X dx' = 87re (k i -IK2/ q e 2 X 2 (K 1 a +K2) 2 + 8 2 d d 2 / C K1 dX2 / 87r No general solution of this equation has been obtained, but when e is small compared with the saturation current qle, an approximate solution is represented by the graph in fig. 2.

If, as is more convenient in this case, x is the distance from the cathode instead of from the anode, as we have hitherto assumed, the solution of this equation is - 2= 6`2 +C e -87re2K2Qx gg_e2 (9)

as The second term on the right-hand side diminishes very rapidly as x increases and soon gets negligible, so that we see that the electric force will be constant except in the immediate neighbourhood of the cathode. To find the value close to the cathode we must find the value of C in equation (9). We have from equation (7) - [87re I dX 2 K,K2 l xi_ xI (q - an, n 2) dx (IO). dx (Kid]-K2)io - The right-hand side of this equation is the excess of ionization over recombination in the region between the cathode and x; it must therefore be equal to the excess of number of the negative ions passing through the gas at x; it must therefore be equal to ( t - to)/e where co is the amount of negative electricity emitted by unit area of the cathode in unit time. Putting this value for the right-hand side of equation (Io) we find approximately, since K 1 is small compared with K2, - C _ at ( t - to) K 1 -f-K 2_ at (c - co). gK1 K ( "Kt K2 Substituting this value for C, we find - 2_ a C 1 - to - 8 7re2K2gx () X gKZe? I +KI c ac I I .

This distribution of force is represented by the graph in fig. 4; the force at some distance from the cathode is equal tot a 1 Kek q and is thus proportional to the current; the force at the cathode itself is { K2(t - to)/ K i t } I times greater than this. The fall of potential be tween the electrodes is made up of two parts, one arising from the constant force; as this force is proportional to t, this part of the potential fall will be proportional to it when 1 is the distance between the electrodes, and may be represented by Ail when A is a constant; the other part of the potential fall is that which occurs close to the cathode. We find from equation (I I) that this is proportional to t2 dX - dx = 47r(nl - n2)e (I). If c is the current through unit area of the gas c = e (n i u l - -n 2 u 2) (2). Hence from (I) and (2) we have - I u2 dX nle + 47r + u dx t I u 1 dX nee =

(3),

(4).

47r u l +u2 dx When things are in a steady state, neglecting any loss of ions by diffusion we have - x(nlw2) =q - anin2 - dx(n 2 u 2) = q - anin2 FIG.

'FIG. 2 The force is practically constant, and equal to - C 'a';: q / 'e( K I f K2)' except close to the electrode, where it increases; and as the mobil ity of the negative ion is greater than that of the positive the increase in the force will be greater at the cathode than at the anode. As the potential difference between the electrodes increases, and the current approaches more nearly the saturation value, the flat part of the graph diminishes, and the graph for X takes the form given in fig. 3. When the potential difference is so large that the current is FIG. 3 nearly saturated, X is very approximately constant from one electrode to another.

In one extremely important case, that in which the negative ions are electrons and have a mobility which may be regarded as infinite in comparison with that of the positive ions, equation (7) admits of integration: for by putting K l /K 2 = o in equation (8) it becomes dX 2 8re 2 K 2 gX 2 _ 87rt dx at Distance from Cathode and does not depend upon 1. Thus, if V is the potential difference between the electrodes when A and B are constants V =Atl+Br. 2 (12).

H. A. Wilson has shown that an equation of this type represents the relation between the current and potential difference for conduction through flames. In many cases the drop of potential at the cathode is much greater than the fall in the rest of the circuit; when this is so we see that the current is proportional to the square root of the potential difference. The value of B increases with the pressure and decreases with the amount of the ionization.

Current from Hot Wires

A case of great importance from its industrial application in hot wire valves is one where all the ions are negative and are emitted from the cathode. Metal wires raised to incandescence emit electrons, and if they are used as cathodes can transmit across a vacuum or gas at a low pressure very considerable currents. No currents will pass if they are used as anodes.

Take the hot cathode as the origin from which x is measured; let V be the potential at the point x, n the density of the negative ions at this point, and c the current through unit area. If a is the velocity of the negative ion, we have 2 nue = c and dx2 There are two cases to be considered; the first is when the hot wire is surrounded by gas of sufficient density to make the velocity

(7)

(8).

of the ions proportional to the electric force; the second is when the hot wire is surrounded by a vacuum, and the motion of the ions is not affected by the gas.

In the first case u =K 2 d x , when K2 is the mobility of the nega tive ion, and the equation nue =1 is equivalent to - K2 dV d2V 47r dx dx 2 - The solution of this is - 87rc + C dx) K2 Therefore if V is the difference of potential between the anode and cathode, and 1 the distance between them, - V ' =' r 87rc1 +C _01 127ra K If uo is the velocity of the negative ions at the cathode, a=neuo; hence _ 1167ruo

-  c (15).  I So that, unless  c is small compared with I,  uo will be comparable with  c; in this case, however, the velocity of the ion is no longer proportional to the electric force so that equation (13) no longer holds. Again, when the current approaches saturation,  t/(I  - c ) is large, and therefore by (15) uo will be large compared with c. For the negative ion to acquire a velocity of this magnitude the electric field would have to be so strong that sparks would pass through the gas unless the pressure were very low. Thus saturation currents from hot bodies are only obtainable at very low pressures.

Since uo = K J, c2 C = 67rK 2 (I - c)2 Comparing this with the value of 87rc1/K we find, by substituting the values of K and c, that if the current is far from saturation, C will be negligible compared with 87rcl/K, unless 11, when 1 is measured in centimetres and i in milliamperes, is small compared with unity. When C can be neglected, equation 02) gives q V2 - 327r l3 (r6).

Thus the current is proportional to the square of the potential difference. A remarkable thing about this expression is that for these very small currents the intensity of the current is independent of the temperature of the wire, although, of course, the range of currents over which this formula is applicable is wider the higher the temperature of the wire.

When the hot body is in a vacuum, we have, if the ions have no initial velocity, - 3mu2 =Ve, where m is the mass and e the charge on an ion; hence the equation nue = c is equivalent to d 2V dx2 V3 = 47rcy 1 a solution of which is V = (97rc)3 ( m/2e)ixi (18). Hence, if V is the potential difference and l the distance between the electrodes 1 = 97 r 12 yn) V? We see from this equation that the electric force vanishes at the cathode, and that the density of the negative electrification is proportional to x-1; thus it is infinite close to the cathode and diminishes as the distance from the anode diminishes. The total quantity of electricity between the anode and cathode is proportional to 1c2. We see again that for a given potential difference the current does not depend on the temperature of the hot wire; this law only holds when the currents are less than the maximum currents which can pass between the electrodes. When the current approaches this value, the current instead of increasing as VI becomes independent of V and the negative electricity between the electrodes diminishes as V increases. Langmuir, who has made a very complete investigation of the currents from hot wires, finds that the expression (7) represents, with considerable accuracy, the relation between the current and potential over a wide range in the values of the currents. The curves in fig. 5 given by him represent the relation between the current and potential for wires at different temperatures. They illustrate the point that a colder wire, until it is approaching the stage of saturation, gives as large a current as a hotter one, though the hotter one, of course, has a wider range of currents.

Ionization by Collision

The curve representing the relation between the currents through a gas ionized (say) by Röntgen rays and the difference of potential between the electrodes is found to be of the form already shown in fig. r, where the ordinates represent the currents and the abscissae the potential difference. The fiat part represents the state of saturation when the potential difference is large enough to send all the ions produced by the rays to the electrode before they can recombine. When the potential difference is still further increased we see that a stage is

005 004 1500 1800 2000 2200 Temperature reached when the current begins to increase with great rapidity with the potential difference, and reaches values much greater than could be attained by the ions produced by the Röntgen rays. Thus in addition to the ions produced by the rays there must be other ions, and some other source of ionization associated with the strong electric fields. Now the processes going on in a gas while it is conveying an electric current are: - (I) the ionization of the gas by the external agent - in this an electron is liberated from the molecule and the residue forms a positive ion; (2) the electron and the positive ion acquire energy under the action of the electric forces; (3) in many gases the electron finally unites with an uncharged molecule to form a negative ion. As the most noticeable change in the conditions when the intensity of the electric field increases is in the energy of the electrons and ions, it is natural to look to these as the source of the additional ionization. We have moreover direct experimental evidence that rapidly moving electrons and ions are able to ionize a gas through which they are passing. Hot wires and metals exposed to ultraviolet light yield a supply of electrons which when they leave the metal have very little energy; by applying suitable electric fields these electrons can be endowed with definite amounts of energy and can then be sent through a gas from which all extraneous ionizing agencies are shielded off. When this is done it is found that, when the energy of the electrons exceeds a certain critical value, depending upon the nature of the gas, the gas is ionized by the electrons, but no ionization occurs when the energy of the electron falls below this limit. It is convenient to measure the energy of the electron in terms of the difference of electrical potential through which the electron has to fall in order to acquire this energy. The potential difference which would give to the electron the energy at which it begins to ionize the gas is called the ionizing potential. The values of the ionizing potential have been found for several gases, as will be seen from the following table. There is, however, considerable discrepancy between the results obtained by different observers.

Gas

Stead &

Gosling

Franck

& Hertz

ii

Davis &

Goucher

I I and 15

Horton

& Davis

Tate &

Foote

Hughes

& Dixon

10.2

He

0 2

20.8

20.5

9

25.6

9.2

N

17.2

7'5

17

7.7

CO

Arg.

15

12.5

12

7.2

15

Ne

16.7& 20

& 22.8

Hg

10.8

10.2

Cd

8.9

Na

5. I

K

4

I

Zn

9'5

.003 240 Volts 120 lofts 60 Volts 2400 2600

(13).

(14). The most obvious view to take of this ionization by moving electrons is that the moving electron comes so near to an electron in a molecule of the gas that the latter receives from the collision enough energy to enable it to escape from the molecule and start as a free electron. If the electrons repel each other with forces varying inversely as the square of the distance between them, and if T is the energy of the moving electron, and d the length of the perpendicular from the electron in the molecule on the initial direction of motion of the moving electron, then the energy communicated to the electron in the molecule by its collision with the moving electron is T equal to d where e is the charge of electricity on an elec I-}-e4 T2 tron. This is on the supposition that the electron is moving so rapidly that the time while it is in close proximity to the electron in the molecule is small compared with the time of vibration of that electron; if this time is comparable with the duration of the collision, the energy taken from the moving electron will be considerably less, and it will become vanishingly small when the duration of the collision is large compared with the time of vibration. The energy given to the electron in the molecule does not increase indefinitely with that of the moving molecule, for it vanishes when T is infinite as well as when T is zero; it has the maximum value when T =e 2 /d. In order that the electron in the molecule should receive an amount of energy Q, - T, or d 2= e4(T/Q - I) d2 T2

d4 T2 e If Q is the ionizing potential, d 2 must be less than the value given by this expression. If n is the number of electrons in unit volume of the gas, and if the spheres with radius d described round the different electrons do not overlap, the probability that the moving electrons should come within this distance of one of them, when moving through a distance Ax, is n-ird 2 :zx, or n-rre4(T/Q - I) T2 The coefficient of Ax is the number of ions made per unit path by a moving electron with energy T. The maximum is when T =2Q.

Experiments on ionization by moving electrons have been made by KSssel (Ann. der Phys. 37, p. 406) and by Mayer 45, p. 1), who found that the maximum ionization per unit path occurred when the energy of the moving electron was in the neighbourhood of 200 volts. Mayer's results are 125 for hydrogen, 130 for air, and 140 for carbon dioxide. These numbers are much greater than twice the potential at which the ionization begins, as this potential is of the order of II volts. It must be remembered, however, that, though there may be some electrons in the atom which can be ejected by II volt electrons, there may be other electrons of different types which require more energy for their expulsion, so that, as the energy of the moving electrons increases beyond the energy required to liberate these electrons, fresh sources of detachable electrons will be trapped, and these may more than counterbalance the falling off in the ionization of the more easily detached electrons. Again, some of the electrons ejected by the primary electrons may have enough energy to ionize on their own account; the total ionization may thus be increased by ionization due to the secondary electrons, and also by radiation excited by the impact of the primary electrons against the molecules of the gas.

When, as in the case of cathode rays in highly exhausted tubes or in that of the R rays from radioactive substances, T is very large compared with Q, the number of ions produced per unit path is nae 4 /QT, and so varies inversely as the energy of the moving electrons. The experiments of Glasson on ionization by cathode rays, and of Durack on that by J3 particles, seem to be in accordance with this result. If we measure the number of ions produced per centimetre in a gas at known pressure, for which we know the value of Q, we could determine n, the number of electrons in unit volume; as the pressure gives us the number of molecules, we could deduce in this way the number of electrons in each molecule.

Ionization by Moving Ions

When the moving systems are ions instead of electrons, the collision between them and the electrons are collisions between masses of very different magnitudes, and in consequence a very much smaller fraction of the energy of the moving body is transferred to the electron than when the colliding bodies have equal masses.

The amount of energy transferred to the electron when the moving body has a mass M is equal to: - // 4141142 T (M 1+ M 2) 2= 4d 2 T 2 M2 2' 1 I e2E2 (M1+M2) when is the mass of the electron and E the charge on the moving body. When, as in the case of the collision between an ion and an electron, M 2 is very small compared with M 1, this becomes 4M 2 T m 1 +4 d2T2 M e 2 E 2 M 12 Thus, if Q is the ionizing potential, the minimum value of T, which will communicate this energy to the electron is 4 - ' Q, For the smallest possible ion, an atom of hydrogen, 114 1 /M 2 =1,700, so that the minimum energy that will enable an ion to ionize a gas by knocking out an electron from a molecule is equal to 425Q. Q for many gases is about Io volts; thus a positive ion must have at least energy represented by 4,250 volts to ionize the gas. With more massive ions the energy required for ionization would be still greater.

An ion with a mass equal to that of a molecule of oxygen would not ionize unless its energy were greater than 136,000 volts. Thus if any ionization by ions takes place in discharge tubes it must be due to ions of the lighter elements hydrogen or helium.

If the ion came into collision with the ion of the atom instead of with one of its electrons, it could, since its mass is comparable with that of the ion, give up to this a large fraction of its energy, a very much larger fraction than it is able to give to an electron. Inasmuch as it requires less work to dissociate a molecule into neutral atoms than to dissociate it into positively and negatively electrified ions, the result of such a collision is more likely to be the production of neutral atoms than of electrified ions.

An ion is, however, a much more complex thing than the simple charge of electricity which has in the preceding considerations been taken to represent the forces it exerts; and it may be that some strongly electronegative ions have such a strong attraction for an electron that when they pass through the molecule of a more electropositive element they are able to capture one of its electrons and carry it away with them. This type of ionization would differ from the ordinary type, inasmuch as in it the electron is never free; it produces negative ions, the other negative electrons.

It is evident from the preceding considerations that except in very intense fields it must be the electrons and not the ions which produce ionization by collision. Let us consider what are the chances of an electron acquiring sufficient energy in a uniform electric field; if the electron moved freely under the electric force X for a distance 1 it would acquire Xel units of energy. The electron in its course through the gas will come into collision with other bodies; its path will be deflected, possibly reversed, and in moving against the electric field it may lose all the energy it had previously acquired. Thus a collision of this type will destroy any ionizing power given to the electron by the electric force before the collision.

Let X be the average distance passed over by an electron between two collisions; then the chance of an electron moving through a distance 1 without a collision --1; but if it moves through a distance 1 it will acquire energy =T = hence the chance of an T electron acquiring energy equal or greater than T is e ?' CA, and the chance that it should acquire energy between T and T+dT is I Y) dT. If it possess this amount of energy the chance 4 that it makes one ion per centimetre of path is n14 22 (T/Q - I); hence the chance that an electron should make one pair of ions per centimetre of path is: - T n?re4J o dT E eA) (T/Q - I)dl, - r.

_ Q n7re 4 E `'ex /Q F(- o eA), co XeX -x

x

where F = X eA dx.

+ 0 Thus if a is the chance that an electron may produce one electron per unit path, since X for the same gas is inversely proportioned to the pressure p, a will be of the form of (p): and since n is proportional to the number of molecules per unit volume, a may be written as pf (p). When the spheres described round the electrons with radius d do not overlap, n will also be proportional to the number of electrons in the molecule. The greatest value of d is e /2Q; hence if D, the distance between two electrons, is greater than e /2Q, there can be no overlapping; if D is less than this quantity there may be overlapping; since the value of d diminishes as the kinetic energy of the electron increases, n for very fast electrons will be proportional to the number of electrons in the molecule.

Some of the electrons will by adhesion to a neutral molecule become negative ions. Let the chance of an electron doing so while passing over i centimetre be -yp. If N be the number of electrons per c.c. at a place fixed by the coordinate x, then +d x (NU) =rate of increase of number of ions per c.c., where U is the velocity of the electron parallel to x.

X =volts per

CM.

Pressure (mm.)

20

17

24

.38

..

1.10

2.1

4.1,

40

65

'34

..

80

1'35

1'3

'45

'13

120

1.8

2.0

1

1

-42

13

160

2

I

2.8

2.0

9

-28

20

..

3.4

2.8

1.6

5

240

2-45

3'8

4.0

2.35

'99

320

2.7

4.5

5.5

4.0

2

1

400

..

50

6.8


Copyright Statement
These files are public domain.

Bibliography Information
Chisholm, Hugh, General Editor. Entry for 'Electrical Properties of Gases'. 1911 Encyclopedia Britanica. https://www.studylight.org/encyclopedias/bri/e/electrical-properties-of-gases.html. 1910.

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