A gas such as air when it is under normal conditions conducts
electricity to a small but only to a very small extent, however small
the electric force acting on the gas may be. The electrical conductivity
of gases not exposed to special conditions is so small that it was only
definitely established in the early years of the 20th century, although
it had engaged the attention of physicists for more than a hundred
years. It had been known for a long time that a body charged with
electricity slowly lost its charge even when insulated with the greatest
care, and though long ago some physicists believed that part of the leak
of electricity took place through the air, the general view seems to
have been that it was due to almost unavoidable defects in the
insulation or to dust in the air, which after striking the charged body
was repelled from it and went off with some of the charge. C. A.
Coulomb, who made some very careful experiments which were published in
1785 (_Mem. de l'Acad. des Sciences_, 1785, p. 612), came to the
conclusion that after allowing for the leakage along the threads which
supported the charged body there was a balance over, which he attributed
to leakage through the air. His view was that when the molecules of air
come into contact with a charged body some of the electricity goes on to
the molecules, which are then repelled from the body carrying their
charge with them. We shall see later that this explanation is not
tenable. C. Matteucci (_Ann. chim. phys._, 1850, 28, p. 390) in 1850
also came to the conclusion that the electricity from a charged body
passes through the air; he was the first to prove that the rate at
which electricity escapes is less when the pressure of the gas is low
than when it is high. He found that the rate was the same whether the
charged body was surrounded by air, carbonic acid or hydrogen.
Subsequent investigations have shown that the rate in hydrogen is in
general much less than in air. Thus in 1872 E. G. Warburg (_Pogg. Ann._,
1872, 145, p. 578) found that the leak through hydrogen was only about
one-half of that through air: he confirmed Matteucci's observations on
the effect of pressure on the rate of leak, and also found that it was
the same whether the gas was dry or damp. He was inclined to attribute
the leak to dust in the air, a view which was strengthened by an
experiment of J. W. Hittorf's (_Wied. Ann._, 1879, 7, p. 595), in which
a small carefully insulated electroscope, placed in a small vessel
filled with carefully filtered gas, retained its charge for several
days; we know now that this was due to the smallness of the vessel and
not to the absence of dust, as it has been proved that the rate of leak
in small vessels is less than in large ones.
Great light was thrown on this subject by some experiments on the rates
of leak from charged bodies in closed vessels made almost simultaneously
by H. Geitel (_Phys. Zeit._, 1900, 2, p. 116) and C. T. R. Wilson
(_Proc. Camb. Phil._ Soc., 1900, 11, p. 32). These observers established
that (1) the rate of escape of electricity in a closed vessel is much
smaller than in the open, and the larger the vessel the greater is the
rate of leak; and (2) the rate of leak does not increase in proportion
to the differences of potential between the charged body and the walls
of the vessel: the rate soon reaches a limit beyond which it does not
increase, however much the potential difference may be increased,
provided, of course, that this is not great enough to cause sparks to
pass from the charged body. On the assumption that the maximum leak is
proportional to the volume, Wilson's experiments, which were made in
vessels less than 1 litre in volume, showed that in dust-free air at
atmospheric pressure the maximum quantity of electricity which can
escape in one second from a charged body in a closed volume of V cubic
centimetres is about 10^-8V electrostatic units. E. Rutherford and S. T.
Allan (_Phys. Zeit._, 1902, 3, p. 225), working in Montreal, obtained
results in close agreement with this. Working between pressures of from
43 to 743 millimetres of mercury, Wilson showed that the maximum rate of
leak is very approximately proportional to the pressure; it is thus
exceedingly small when the pressure is low--a result illustrated in a
striking way by an experiment of Sir W. Crookes (_Proc. Roy. Soc._,
1879, 28, p. 347) in which a pair of gold leaves retained an electric
charge for several months in a very high vacuum. Subsequent experiments
have shown that it is only in very small vessels that the rate of leak
is proportional to the volume and to the pressure; in large vessels the
rate of leak per unit volume is considerably smaller than in small ones.
In small vessels the maximum rate of leak in different gases, is, with
the exception of hydrogen, approximately proportional to the density of
the gas. Wilson's results on this point are shown in the following table
(Proc. Roy. Soc., 1901, 60, p. 277):--
+---------+------------------------+-----------------+
| Gas. | Relative Rate of Leak. | _Rate of Leak._ |
| | | Sp. Gr. |
+---------+------------------------+-----------------+
| Air | 1.00 | 1 |
| H2 | .184 | 2.7 |
| CO2 | 1.69 | 1.10 |
| SO2 | 2.64 | 1.21 |
| CH3Cl | 4.7 | 1.09 |
| Ni(CO)4 | 5.1 | .867 |
+---------+------------------------+-----------------+
The rate of leak of electricity through gas contained in a closed vessel
depends to some extent on the material of which the walls of the vessel
are made; thus it is greater, other circumstances being the same, when
the vessel is made of lead than when it is made of aluminium. It also
varies, as Campbell and Wood (_Phil. Mag._ [6], 13, p. 265) have shown,
with the time of the day, having a well-marked minimum at about 3
o'clock in the morning: it also varies from month to month. Rutherford
(_Phys. Rev._, 1903, 16, p. 183), Cooke (_Phil. Mag._, 1903 [6], 6, p.
403) and M'Clennan and Burton (_Phys. Rev._, 1903, 16, p. 184) have
shown that the leak in a closed vessel can be reduced by about 30% by
surrounding the vessel with sheets of thick lead, but that the reduction
is not increased beyond this amount, however thick the lead sheets may
be. This result indicates that part of the leak is due to a very
penetrating kind of radiation, which can get through the thin walls of
the vessel but is stopped by the thick lead. A large part of the leak we
are describing is due to the presence of radioactive substances such as
radium and thorium in the earth's crust and in the walls of the vessel,
and to the gaseous radioactive emanations which diffuse from them into
the atmosphere. This explains the very interesting effect discovered by
J. Elster and H. Geitel (_Phys. Zeit._, 1901, 2, p. 560), that the rate
of leak in caves and cellars when the air is stagnant and only renewed
slowly is much greater than in the open air. In some cases the
difference is very marked; thus they found that in the cave called the
Baumannshohle in the Harz mountains the electricity escaped at seven
times the rate it did in the air outside. In caves and cellars the
radioactive emanations from the walls can accumulate and are not blown
away as in the open air.
The electrical conductivity of gases in the normal state is, as we have
seen, exceedingly small, so small that the investigation of its
properties is a matter of considerable difficulty; there are, however,
many ways by which the electrical conductivity of a gas can be increased
so greatly that the investigation becomes comparatively easy. Among such
methods are raising the temperature of the gas above a certain point.
Gases drawn from the neighbourhood of flames, electric arcs and sparks,
or glowing pieces of metal or carbon are conductors, as are also gases
through which Rontgen or cathode rays or rays of positive electricity
are passing; the rays from the radioactive metals, radium, thorium,
polonium and actinium, produce the same effect, as does also
ultra-violet light of exceedingly short wave-length. The gas, after
being made a conductor of electricity by any of these means, is found to
possess certain properties; thus it retains its conductivity for some
little time after the agent which made it a conductor has ceased to act,
though the conductivity diminishes very rapidly and finally gets too
small to be appreciable.
[Illustration: FIG. 5.]
This and several other properties of conducting gas may readily be
proved by the aid of the apparatus represented in fig. 5. V is a testing
vessel in which an electroscope is placed. Two tubes A and C are fitted
into the vessel, A being connected with a water pump, while the far end
of C is in the region where the gas is exposed to the agent which makes
it a conductor of electricity. Let us suppose that the gas is made
conducting by Rontgen rays produced by a vacuum tube which is placed in
a box, covered except for a window at B with lead so as to protect the
electroscope from the direct action of the rays. If a slow current of
air is drawn by the water pump through the testing vessel, the charge on
the electroscope will gradually leak away. The leak, however, ceases
when the current of air is stopped. This result shows that the gas
retains its conductivity during the time taken by it to pass from one
end to the other of the tube C.
The gas loses its conductivity when filtered through a plug of
glass-wool, or when it is made to bubble through water. This can readily
be proved by inserting in the tube C a plug of glass-wool or a water
trap; then if by working the pump a little harder the same current of
air is produced as before, it will be found that the electroscope will
now retain its charge, showing that the conductivity can, as it were, be
filtered out of the gas. The conductivity can also be removed from the
gas by making the gas traverse a strong electric field. We can show this
by replacing the tube C by a metal tube with an insulated wire passing
down the axis of the tube. If there is no potential difference between
the wire and the tube then the electroscope will leak when a current of
air is drawn through the vessel, but the leak will stop if a
considerable difference of potential is maintained between the wire and
the tube: this shows that a strong electric field removes the
conductivity from the gas.
The fact that the conductivity of the gas is removed by filtering shows
that it is due to something mixed with the gas which is removed from it
by filtration, and since the conductivity is also removed by an electric
field, the cause of the conductivity must be charged with electricity so
as to be driven to the sides of the tube by the electric force. Since
the gas as a whole is not electrified either positively or negatively,
there must be both negative and positive charges in the gas, the amount
of electricity of one sign being equal to that of the other. We are thus
led to the conclusion that the conductivity of the gas is due to
electrified particles being mixed up with the gas, some of these
particles having charges of positive electricity, others of negative.
These electrified particles are called _ions_, and the process by which
the gas is made a conductor is called the ionization of the gas. We
shall show later that the charges and masses of the ions can be
determined, and that the gaseous ions are not identical with those met
with in the electrolysis of solutions.
[Illustration: FIG. 6.]
One very characteristic property of conduction of electricity through a
gas is the relation between the current through the gas and the electric
force which gave rise to it. This relation is not in general that
expressed by Ohm's law, which always, as far as our present knowledge
extends, expresses the relation for conduction through metals and
electrolytes. With gases, on the other hand, it is only when the current
is very small that Ohm's law is true. If we represent graphically by
means of a curve the relation between the current passing between two
parallel metal plates separated by ionized gas and the difference of
potential between the plates, the curve is of the character shown in
fig. 6 when the ordinates represent the current and the abscissae the
difference of potential between the plates. We see that when the
potential difference is very small, i.e. close to the origin, the curve
is approximately straight, but that soon the current increases much less
rapidly than the potential difference, and that a stage is reached when
no appreciable increase of current is produced when the potential
difference is increased; when this stage is reached the current is
constant, and this value of the current is called the "saturation"
value. When the potential difference approaches the value at which
sparks would pass through the gas, the current again increases with the
potential difference; thus the curve representing the relation between
the current and potential difference over very wide ranges of potential
difference has the shape shown in fig. 7; curves of this kind have been
obtained by von Schweidler (_Wien. Ber._, 1899, 108, p. 273), and J. E.
S. Townsend (_Phil. Mag._, 1901 [6], 1, p. 198). We shall discuss later
the causes of the rise in the current with large potential differences,
when we consider ionization by collision.
The general features of the earlier part of the curve are readily
explained on the ionization hypothesis. On this view the Rontgen rays
or other ionizing agent acting on the gas between the plates, produces
positive and negative ions at a definite rate. Let us suppose that q
positive and q negative ions are by this means produced per second
between the plates; these under the electric force will tend to move,
the positive ones to the negative plate, the negative ones to the
positive. Some of these ions will reach the plate, others before
reaching the plate will get so near one of the opposite sign that the
attraction between them will cause them to unite and form an
electrically neutral system; when they do this they end their
existence as ions. The current between the plates is proportional to
the number of ions which reach the plates per second. Now it is
evident that we cannot go on taking more ions out of the gas than are
produced; thus we cannot, when the current is steady, have more than q
positive ions driven to the negative plate per second, and the same
number of negative ions to the positive. If each of the positive ions
carries a charge of e units of positive electricity, and if there is
an equal and opposite charge on each negative ion, then the maximum
amount of electricity which can be given to the plates per second is
qe, and this is equal to the saturation current. Thus if we measure
the saturation current, we get a direct measure of the ionization, and
this does not require us to know the value of any quantity except the
constant charge on the ion. If we attempted to deduce the amount of
ionization by measurements of the current before it was saturated, we
should require to know in addition the velocity with which the ions
move under a given electric force, the time that elapses between the
liberation of an ion and its combination with one of the opposite
sign, and the potential difference between the plates. Thus if we wish
to measure the amount of ionization in a gas we should be careful to
see that the current is saturated.
[Illustration: FIG. 7.]
The difference between conduction through gases and through metals is
shown in a striking way when we use potential differences large enough
to produce the saturation current. Suppose we have got a potential
difference between the plates more than sufficient to produce the
saturation current, and let us increase the distance between the plates.
If the gas were to act like a metallic conductor this would diminish the
current, because the greater length would involve a greater resistance
in the circuit. In the case we are considering the separation of the
plates will _increase_ the current, because now there is a larger volume
of gas exposed to the rays; there are therefore more ions produced, and
as the saturation current is proportional to the number of ions the
saturation current is increased. If the potential difference between the
plates were much less than that required to saturate the current, then
increasing the distance would diminish the current; the gas for such
potential differences obeys Ohm's law and the behaviour of the gaseous
resistance is therefore similar to that of a metallic one.
In order to produce the saturation current the electric field must be
strong enough to drive each ion to the electrode before it has time to
enter into combination with one of the opposite sign. Thus when the
plates in the preceding example are far apart, it will take a larger
potential difference to produce this current than when the plates are
close together. The potential difference required to saturate the
current will increase as the square of the distance between the plates,
for if the ions are to be delivered in a given time to the plates their
speed must be proportional to the distance between the plates. But the
speed is proportional to the electric force acting on the ion; hence the
electric force must be proportional to the distance between the plates,
and as in a uniform field the potential difference is equal to the
electric force multiplied by the distance between the plates, the
potential difference will vary as the square of this distance.
The potential difference required to produce saturation will, other
circumstances being the same, increase with the amount of ionization,
for when the number of ions is large and they are crowded together, the
time which will elapse before a positive one combines with a negative
will be smaller than when the number of ions is small. The ions have
therefore to be removed more quickly from the gas when the ionization is
great than when it is small; thus they must move at a higher speed and
must therefore be acted upon by a larger force.
When the ions are not removed from the gas, they will increase until the
number of ions of one sign which combine with ions of the opposite sign
in any time is equal to the number produced by the ionizing agent in
that time. We can easily calculate the number of free ions at any time
after the ionizing agent has commenced to act.
Let q be the number of ions (positive or negative) produced in one
cubic centimetre of the gas per second by the ionizing agent, n1, n2,
the number of free positive and negative ions respectively per cubic
centimetre of the gas. The number of collisions between positive and
negative ions per second in one cubic centimetre of the gas is
proportional to n1n2. If a certain fraction of the collisions between
the positive and negative ions result in the formation of an
electrically neutral system, the number of ions which disappear per
second on a cubic centimetre will be equal to [alpha]n1 n2, where
[alpha] is a quantity which is independent of n1, n2; hence if t is
the time since the ionizing agent was applied to the gas, we have
dn1/dt = q - [alpha]n1 n2, dn2/dt = q - [alpha]n1 n2.
Thus n1 - n2 is constant, so if the gas is uncharged to begin with, n1
will always equal n2. Putting n1 = n2 = n we have
dn/dt = q - [alpha]n^2 (1),
the solution of which is, since n = 0 when t = 0,
k([epsilon]^{2k[alpha]t} - 1)
n = ---------------------------- (2)
[epsilon]^{2k[alpha]t} + 1
if k^2 = q/[alpha]. Now the number of ions when the gas has reached a
steady state is got by putting t equal to infinity in the preceding
equation, and is therefore given by the equation
n0 = k = [root](q/[alpha]).
We see from equation (1) that the gas will not approximate to its
steady state until 2k[alpha]t is large, that is until t is large
compared with 1/2k[alpha] or with 1/2[root](q[alpha]). We may thus
take 1/2[root](q[alpha]) as a measure of the time taken by the gas to
reach a steady state when exposed to an ionizing agent; as this time
varies inversely as [root]q we see that when the ionization is feeble
it may take a very considerable time for the gas to reach a steady
state. Thus in the case of our atmosphere where the production of ions
is only at the rate of about 30 per cubic centimetre per second, and
where, as we shall see, [alpha] is about 10^-6, it would take some
minutes for the ionization in the air to get into a steady state if
the ionizing agent were suddenly applied.
We may use equation (1) to determine the rate at which the ions
disappear when the ionizing agent is removed. Putting q=0 in that
equation we get dn/[alpha]t = -[alpha]n^2.
Hence n = n0/(1 + n0[alpha]t) (3),
where n0 is the number of ions when t = 0. Thus the number of ions
falls to one-half its initial value in the time 1/n0[alpha]. The
quantity [alpha] is called the _coefficient of recombination_, and its
value for different gases has been determined by Rutherford (_Phil.
Mag._ 1897 [5], 44, p. 422), Townsend (_Phil. Trans._, 1900, 193, p.
129), McClung (_Phil. Mag._, 1902 [6], 3, p. 283), Langevin (_Ann.
chim. phys._ [7], 28, p. 289), Retschinsky (_Ann. d. Phys._, 1905, 17,
p. 518), Hendred (_Phys. Rev._, 1905, 21, p. 314). The values of
[alpha]/e, e being the charge on an ion in electrostatic measure as
determined by these observers for different gases, is given in the
following table:--
+-----+----------+----------+----------+------------+----------+
| | Townsend.| McClung. | Langevin.|Retschinsky.| Hendred. |
+-----+----------+----------+----------+------------+----------+
| Air | 3420 | 3380 | 3200 | 4140 | 3500 |
| O2 | 3380 | | | | |
| CO2 | 3500 | 3490 | 3400 | | |
| H2 | 3020 | 2940 | | | |
+-----+----------+----------+----------+------------+----------+
The gases in these experiments were carefully dried and free from
dust; the apparent value of [alpha] is much increased when dust or
small drops of water are present in the gas, for then the ions get
caught by the dust particles, the mass of a particle is so great
compared with that of an ion that they are practically immovable under
the action of the electric field, and so the ions clinging to them
escape detection when electrical methods are used. Taking e as 3.5 X
10^-10, we see that [alpha] is about 1.2 X 10^-6, so that the number
of recombinations in unit time between n positive and n negative ions
in unit volume is 1.2 X 10^-6n^2. The kinetic theory of gases shows
that if we have n molecules of air per cubic centimetre, the number of
collisions per second is 1.2 X 10^-10n^2 at a temperature of 0 deg. C.
Thus we see that the number of recombinations between oppositely
charged ions is enormously greater than the number of collisions
between the same number of neutral molecules. We shall see that the
difference in size between the ion and the molecule is not nearly
sufficient to account for the difference between the collisions in the
two cases; the difference is due to the force between the oppositely
charged ions, which drags ions into collisions which but for this
force would have missed each other.
Several methods have been used to measure [alpha]. In one method air,
exposed to some ionizing agent at one end of a long tube, is slowly
sucked through the tube and the saturation current measured at
different points along the tube. These currents are proportional to
the values of n at the place of observation: if we know the distance
of this place from the end of the tube when the gas was ionized and
the velocity of the stream of gas, we can find t in equation (3), and
knowing the value of n we can deduce the value of [alpha] from the
equation
1/n1 - 1/n2 = [alpha](t1 - t2),
where n1, n2 are the values of n at the times t1, t2 respectively. In
this method the tubes ought to be so wide that the loss of ions by
diffusion to the sides of the tube is negligible. There are other
methods which involve the knowledge of the speed with which the ions
move under the action of known electric forces; we shall defer the
consideration of these methods until we have discussed the question of
these speeds.
In measuring the value of [alpha] it should be remembered that the
theory of the methods supposes that the ionization is uniform
throughout the gas. If the total ionization throughout a gas remains
constant, but instead of being uniformly distributed is concentrated
in patches, it is evident that the ions will recombine more quickly in
the second case than in the first, and that the value of [alpha] will
be different in the two cases. This probably explains the large values
of [alpha] obtained by Retschinsky, who ionized the gas by the [alpha]
rays from radium, a method which produces very patchy ionization.
_Variation of [alpha] with the Pressure of the Gas._--All observers
agree that there is little variation in [alpha] with the pressures for
pressures of between 5 and 1 atmospheres; at lower pressures, however,
the value of [alpha] seems to diminish with the pressure: thus
Langevin (_Ann. chim. phys._, 1903, 28, p. 287) found that at a
pressure of 1/5 of an atmosphere the value of [alpha] was about 1/5 of
its value at atmospheric pressure.
_Variation of [alpha] with the Temperature._--Erikson (_Phil. Mag._,
Aug. 1909) has shown that the value of [alpha] for air increases as
the temperature diminishes, and that at the temperature of liquid air
-180 deg. C., it is more than twice as great as at +12 deg. C.
Since, as we have seen, the recombination is due to the coming
together of the positive and negative ions under the influence of the
electrical attraction between them, it follows that a large electric
force sufficient to overcome this attraction would keep the ions apart
and hence diminish the coefficient of recombination. Simple
considerations, however, will show that it would require exceedingly
strong electric fields to produce an appreciable effect. The value of
[alpha] indicates that for two oppositely charged ions to unite they
must come within a distance of about 1.5 X 10^-6 centimetres; at this
distance the attraction between them is e^2 X 10^12/2.25, and if X is
the external electric force, the force tending to pull them apart
cannot be greater than Xe; if this is to be comparable with the
attraction, X must be comparable with e X 10^12/2.25, or putting e = 4
X 10^-10, with 1.8 X 10^2; this is 54,000 volts per centimetre, a
force which could not be applied to gas at atmospheric pressure
without producing a spark.
_Diffusion of the Ions._--The ionized gas acts like a mixture of
gases, the ions corresponding to two different gases, the non-ionized
gas to a third. If the concentration of the ions is not uniform, they
will diffuse through the non-ionized gas in such a way as to produce a
more uniform distribution. A very valuable series of determinations of
the coefficient of diffusion of ions through various gases has been
made by Townsend (_Phil. Trans._, 1900, A, 193, p. 129). The method
used was to suck the ionized gas through narrow tubes; by measuring
the loss of both the positive and negative ions after the gases had
passed through a known length of tube, and allowing for the loss by
recombination, the loss by diffusion and hence the coefficient of
diffusion could be determined. The following tables give the values of
the coefficients of diffusion D on the C.G.S. system of units as
determined by Townsend:--