+-----+------------+------------+----------+------------------+
|Gas. |D for +ions.|D for -ions.|Mean Value| Ratio of D for |
| | | | of D. | - to D for +ions.|
+-----+------------+------------+----------+------------------+
| Air | .028 | .043 | .0347 | 1.54 |
| O2 | .025 | .0396 | .0323 | 1.58 |
| CO2 | .023 | .026 | .0245 | 1.13 |
| H2 | .123 | .190 | .156 | 1.54 |
+-----+------------+------------+----------+------------------+
Table II.--Coefficients of Diffusion in Moist Gases.
+-----+------------+------------+----------+------------------+
|Gas. |D for +ions.|D for -ions.|Mean Value| Ratio of D for |
| | | | of D. | - to D for +ions.|
+-----+------------+------------+----------+------------------+
| Air | .032 | .037 | .0335 | 1.09 |
| O2 | .0288 | .0358 | .0323 | 1.24 |
| CO2 | .0245 | .0255 | .025 | 1.04 |
| H2 | .128 | .142 | .135 | 1.11 |
+-----+------------+------------+----------+------------------+
It is interesting to compare with these coefficients the values of D
when various gases diffuse through each other. D for hydrogen through
air is .634, for oxygen through air .177, for the vapour of isobutyl
amide through air .042. We thus see that the velocity of diffusion of
ions through air is much less than that of the simple gas, but that it
is quite comparable with that of the vapours of some complex organic
compounds.
The preceding tables show that the negative ions diffuse more rapidly
than the positive, especially in dry gases. The superior mobility of
the negative ions was observed first by Zeleny (_Phil. Mag._, 1898
[5], 46, p. 120), who showed that the velocity of the negative ions
under an electric force is greater than that of the positive. It will
be noticed that the difference between the mobility of the negative
and the positive ions is much more pronounced in dry gases than in
moist. The difference in the rates of diffusion of the positive and
negative ions is the reason why ionized gas, in which, to begin with,
the positive and negative charges were of equal amounts, sometimes
becomes electrified even although the gas is not acted upon by
electric forces. Thus, for example, if such gas be blown through
narrow tubes, it will be positively electrified when it comes out, for
since the negative ions diffuse more rapidly than the positive, the
gas in its passage through the tubes will lose by diffusion more
negative than positive ions and hence will emerge positively
electrified. Zeleny snowed that this effect does not occur when, as in
carbonic acid gas, the positive and negative ions diffuse at the same
rates. Townsend (loc. cit.) showed that the coefficient of diffusion
of the ions is the same whether the ionization is produced by Rontgen
rays, radioactive substances, ultra-violet light, or electric sparks.
The ions produced by chemical reactions and in flames are much less
mobile; thus, for example, Bloch (_Ann. chim. phys._, 1905 [8], 4, p.
25) found that for the ions produced by drawing air over phosphorus
the value of [alpha]/e was between 1 and 6 instead of over 3000, the
value when the air was ionized by Rontgen rays.
_Velocity of Ions in an Electric Field._--The velocity of ions in an
electric field, which is of fundamental importance in conduction, is
very closely related to the coefficient of diffusion. Measurements of
this velocity for ions produced by Rontgen rays have been made by
Rutherford (_Phil. Mag._ [5], 44, p. 422), Zeleny (_Phil. Mag._ [5], 46,
p. 120), Langevin (_Ann. Chim. Phys._, 1903, 28, p. 289), Phillips
(_Proc. Roy. Soc._ 78, A, p. 167), and Wellisch (_Phil. Trans._, 1909,
209, p. 249). The ions produced by radioactive substance have been
investigated by Rutherford (_Phil. Mag._ [5], 47, p. 109) and by Franck
and Pohl (_Verh. deutsch. phys. Gesell._, 1907, 9, p. 69), and the
negative ions produced when ultra-violet light falls on a metal plate by
Rutherford (_Proc. Camb. Phil. Soc._ 9, p. 401). H. A. Wilson (_Phil.
Trans._ 192, p. 4O9), Marx (_Ann. de Phys._ 11, p. 765), Moreau (_Journ.
de Phys._ 4, 11, p. 558; _Ann. Chim. Phys._ 7, 30, p. 5) and Gold
(_Proc. Roy. Soc._ 79, p. 43) have investigated the velocities of ions
produced by putting various salts into flames; McClelland (_Phil. Mag._
46, p. 29) the velocity of the ions in gases sucked from the
neighbourhood of flames and arcs; Townsend (_Proc. Camb. Phil. Soc._ 9,
p. 345) and Bloch (_loc. cit._) the velocity of ions produced by
chemical reaction; and Chattock (_Phil. Mag._ [5], 48, p. 401) the
velocity of the ions produced when electricity escapes from a sharp
needle point into a gas.
Several methods have been employed to determine these velocities. The
one most frequently employed is to find the electromotive intensity
required to force an ion against the stream of gas moving with a known
velocity parallel to the lines of electric force. Thus, of two
perforated plane electrodes vertically over each other, suppose the
lower to be positively, the upper negatively electrified, and suppose
that the gas is streaming vertically downwards with the velocity V; then
unless the upward velocity of the positive ion is greater than V, no
positive electricity will reach the upper plate. If we increase the
strength of the field between the plates, and hence the upward velocity
of the positive ion, until the positive ions just begin to reach the
upper plate, we know that with this strength of field the velocity of
the positive ion is equal to V. By this method, which has been used by
Rutherford, Zeleny and H. A. Wilson, the velocity of ions in fields of
various strengths has been determined.
The arrangement used by Zeleny is represented in fig. 8. P and Q are
square brass plates. They are bored through their centres, and to the
openings the tubes R and S are attached, the space between the plates
being covered in so as to form a closed box. K is a piece of wire
gauze completely covering the opening in Q; T is an insulated piece of
wire gauze nearly but not quite filling the opening in the plate P,
and connected with one pair of quadrants of an electrometer E. A plug
of glass wool G filters out the dust from a stream of gas which enters
the vessel by the tube D and leaves it by F; this plug also makes the
velocity of the flow of the gas uniform across the section of the
tube. The Rontgen rays to ionize the gas were produced by a bulb at
O, the bulb and coil being in a lead-covered box, with an aluminium
window through which the rays passed. Q is connected with one pole of
a battery of cells, P and the other pole of the battery are put to
earth. The changes in the potential of T are due to ions giving up
their charges to it. With a given velocity of air-blast the potential
of T was found not to change unless the difference of potential
between P and Q exceeded a critical value. The field corresponding to
this critical value thus made the ions move with the known velocity of
the blast.
[Illustration: FIG. 8.]
[Illustration: FIG. 9.]
Another method which has been employed by Rutherford and McClelland is
based on the action of an electric field in destroying the
conductivity of gas streaming through it. Suppose that BAB, DCD (fig.
9) are a system of parallel plates boxed in so that a stream of gas,
after flowing between BB, passes between DD without any loss of gas in
the interval. Suppose the plates DD are insulated, and connected with
one pair of quadrants of an electrometer, by charging up C to a
sufficiently high potential we can drive all the positive ions which
enter the system DCD against the plates D; this will cause a deflexion
of the electrometer, which in one second will be proportional to the
number of positive ions which have entered the system in that time. If
we charge A up to a high potential, B being put to earth, we shall
find that the deflexion of the electrometer connected with DD is less
than it was when A and B were at the same potential, because some of
the positive ions in their passage through BAB are driven against the
plates B. If u is the velocity along the lines of force in the uniform
electric field between A and B, and t the time it takes for the gas to
pass through BAB, then all the positive ions within a distance ut of
the plates B will be driven up against these plates, and thus if the
positive ions are equally distributed through the gas, the number of
positive ions which emerge from the system when the electric field is
on will bear to the number which emerge when the field is off the
ratio of 1 - ut/l to unity, where l is the distance between A and B.
This ratio is equal to the ratio of the deflexions in one second of
the electrometer attached to D, hence the observations of this
instrument give 1 - ut/l. If we know the velocity of the gas and the
length of the plates A and B, we can determine t, and since l can be
easily measured, we can find u, the velocity of the positive ion in a
field of given strength. By charging A and C negatively instead of
positively we can arrive at the velocity of the negative ion. In
practice it is more convenient to use cylindrical tubes with coaxial
wires instead of the systems of parallel plates, though in this case
the calculation of the velocity of the ions from the observations is a
little more complicated, inasmuch as the electric field is not uniform
between the tubes.
[Illustration: FIG. 10.]
A method which gives very accurate results, though it is only
applicable in certain cases, is the one used by Rutherford to measure
the velocity of the negative ions produced close to a metal plate by
the incidence on the plate of ultra-violet light. The principle of the
method is as follows:--AB (fig. 10) is an insulated horizontal plate
of well-polished zinc, which can be moved vertically up and down by
means of a screw; it is connected with one pair of quadrants of an
electrometer, the other pair of quadrants being put to earth. CD is a
base-plate with a hole EF in it; this hole is covered with fine wire
gauze, through which ultra-violet light passes and falls on the plate
AB. The plate CD is connected with an alternating current dynamo,
which produces a simply-periodic potential difference between AB and
CD, the other pole being put to earth. Suppose that at any instant the
plate CD is at a higher potential than AB, then the negative ions from
AB will move towards CD, and will continue to do so as long as the
potential of CD is higher than that of AB. If, however, the potential
difference changes sign before the negative ions reach CD, these ions
will go back to AB. Thus AB will not lose any negative charge unless
the distance between the plates AB and CD is less than the distance
traversed by the negative ion during the time the potential of CD is
higher than that of AB. By altering the distance between the plates
until CD just begins to lose a negative charge, we find the velocity
of the negative ion under unit electromotive intensity. For suppose
the difference of potential between AB and CD is equal to a sin pt,
then if d is the distance between the plates, the electric intensity
is equal to a sin pt/d; if we suppose the velocity of the ion is
proportional to the electric intensity, and if u is the velocity for
unit electric intensity, the velocity of the negative ion will be ua
sin pt/d. Hence if x represent the distance of the ion from AB
dx ua
--- = --- sin pt
dT d
ua
x = ----(1 - cos pt), if x = 0 when t = 0.
pd
Thus the greatest distance the ion can get from the plate is equal to
2au/pd, and if the distance between the plates is gradually reduced to
this value, the plate AB will begin to lose a negative charge; hence
when this happens
d = 2au/pd, or u = pd^2/2a,
an equation by means of which we can find u.
In this form the method is not applicable when ions of both signs are
present. Franck and Pohl (_Verh. deutsch. physik. Gesell._ 1907, 9, p.
69) have by a slight modification removed this restriction. The
modification consists in confining the ionization to a layer of gas
below the gauze EF. If the velocity of the positive ions is to be
determined, these ions are forced through the gauze by applying to the
ionized gas a small constant electric force acting upwards; if
negative ions are required, the constant force is reversed. After
passing through the gauze the ions are acted upon by alternating
forces as in Rutherford's method.
Langevin (_Ann. chim. phys._, 1903, 28, p. 289) devised a method of
measuring the velocity of the ions which has been extensively used; it
has the advantage of not requiring the rate of ionization to remain
uniform. The general idea is as follows. Suppose that we expose the
gas between two parallel plates A, B to Rontgen rays or some other
ionizing agent, then stop the rays and apply a uniform electric field
to the region between the plates. If the force on the positive ion is
from A to B, the plate B will receive a positive charge of
electricity. After the electric force has acted for a time T reverse
it. B will now begin to receive negative electricity and will go on
doing so until the supply of negative ions is exhausted. Let us
consider how the quantity of positive electricity received by B will
vary with T. To fix our ideas, suppose the positive ions move more
slowly than the negative; let T2 and T1 be respectively the times
taken by the positive and negative ions to move under the electric
field through a distance equal to AB, the distance between the planes.
Then if T is greater than T2 all the ions will have been driven from
between the plates before the field is reversed, and therefore the
positive charge received by B will not depend upon T. Next let T be
less than T2 but greater than T1; then at the time when the field is
reversed all the negative ions will have been driven from between the
plates, so that the positive charge received by B will not be
neutralized by the arrival of fresh ions coming to it after the
reversal of the field. The number of positive ions driven against the
plate B will be proportional to T. Thus if we measure the value of the
positive charge on B for a series of values of T, each value being
less than the preceding, we shall find that until T reaches a certain
value the charge remains constant, but as soon as we reduce the time
below this value the charge diminishes. The value of T when the
diminution in the field begins is T2, the time taken for a positive
ion to cross from A to B under the electric field; thus from T2 we can
calculate the velocity of the positive ion in this field. If we still
further diminish T, we shall find that we reach a value when the
diminution of the positive charge on B with the time suddenly becomes
much more rapid; this change occurs when T falls below T1 the time
taken for the negative ions to go from one plate to the other, for now
when the field is reversed there are still some negative ions left
between the plates, and these will be driven against B and rob it of
some of the positive charge it had acquired before the field was
reversed. By observing the time when the increase in the rate of
diminution of the positive charge with the time suddenly sets in we
can determine T1, and hence the velocity of the negative ions.
The velocity of the ions produced by the discharge of electricity from
a fine point was determined by Chattock by an entirely different
method. In this case the electric field is so strong and the velocity
of the ion so great that the preceding methods are not applicable.
Suppose P represents a vertical needle discharging electricity into
air, consider the force acting on the ions included between two
horizontal planes A, B. If P is the density of the electrification,
and Z the vertical component of the electric intensity, F the
resultant force on the ions between A and B is vertical and equal to
_ _ _
/ / /
| | | Z[rho]dxdydz.
_/_/_/
Let us suppose that the velocity of the ion is proportional to the
electric intensity, so that if w is the vertical velocity of the ions,
which are supposed all to be of one sign, w = RZ.
Substituting this value of Z, the vertical force on the ions between A
and B is equal to
_ _ _
1 / / /
- | | | w[rho]dxdydz.
R _/_/_/
But [integral][integral]w[rho]dxdy = [iota], where [iota] is the
current streaming from the point. This current, which can be easily
measured by putting a galvanometer in series with the discharging
point, is independent of z, the vertical distance of a plane between A
and B below the charging point. Hence we have
_
[iota] / [iota]
F = ------ | dz = ------.z.
R _/ R
This force must be counterbalanced by the difference of gaseous
pressures over the planes A and B; hence if pB and pA denote
respectively the pressures over B and A, we have
[iota]
pB - pA = ------ z.
R
Hence by the measurement of these pressures we can determine R, and
hence the velocity with which an ion moves under a given electric
intensity.
There are other methods of determining the velocities of the ions, but
as these depend on the theory of the conduction of electricity through
a gas containing charged ions, we shall consider them in our
discussion of that theory.
By the use of these methods it has been shown that the velocities of
the ions in a given gas are the same whether the ionization is
produced by Rontgen rays, radioactive substances, ultra-violet light,
or by the discharge of electricity from points. When the ionization is
produced by chemical action the ions are very much less mobile, moving
in the same electric field with a velocity less than one-thousandth
part of the velocity of the first kind of ions. On the other hand, as
we shall see later, the velocity of the negative ions in flames is
enormously greater than that of even the first kind of ion under
similar electric fields and at the same pressure. But when these
negative ions get into the cold part of the flame, they move
sluggishly with velocities of the order of those possessed by the
second kind. The results of the various determinations of the
velocities of the ions are given in the following table. The
velocities are in centimetres per second under an electric force of
one volt per centimetre, the pressure of the gas being 1 atmosphere.
V+ denotes the velocity of the positive ion, V- that of the negative.
V is the mean velocity of the positive and negative ions.
_Velocities of Ions.--Ions produced by Rontgen Rays._
+----------------------+------+------+------+-----------------+
| Gas. | V+. | V-. | V. | Observer. |
+----------------------+------+------+------+-----------------+
| Air | .. | .. | 1.6 | Rutherford |
| Air (dry) | 1.36 | 1.87 | .. | Zeleny |
| " | 1.60 | 1.70 | .. | Langevin |
| " | 1.39 | 1.78 | .. | Phillips |
| " | 1.54 | 1.78 | .. | Wellisch |
| Air (moist) | 1.37 | 1.81 | .. | Zeleny |
| Oxygen (dry) | 1.36 | 1.80 | .. | " |
| Oxygen (moist) | 1.29 | 1.52 | .. | " |
| Carbonic acid (dry) | 0.76 | 0.81 | .. | " |
| " | 0.86 | 0.90 | .. | Langevin |
| " | 0.81 | 0.85 | .. | Wellisch |
| Carbonic acid (moist)| 0.82 | 0.75 | .. | Zeleny |
| Hydrogen (dry) | 6.70 | 7.95 | .. | " |
| Nitrogen | .. | .. | 1.6 | Rutherford |
| Sulphur dioxide | 0.44 | 0.41 | .. | Wellisch |
| Hydrochloric acid | .. | .. | 1.27 | Rutherford |
| Chlorine | .. | .. | 1.0 | " |
| Helium (dry) | 5.09 | 6.31 | .. | Franck and Pohl |
| Carbon monoxide | 1.10 | 1.14 | .. | Wellisch |
| Nitrous oxide | 0.82 | 0.90 | .. | " |
| Ammonia | 0.74 | 0.80 | .. | " |
| Aldehyde | 0.31 | 0.30 | .. | " |
| Ethyl alcohol | 0.34 | 0.27 | .. | " |
| Acetone | 0.31 | 0.29 | .. | " |
| Ethyl chloride | 0.33 | 0.31 | .. | " |
| Pentane | 0.36 | 0.35 | .. | " |
| Methyl acetate | 0.33 | 0.36 | .. | " |
| Ethyl formate | 0.30 | 0.31 | .. | " |
| Ethyl ether | 0.29 | 0.31 | .. | " |
| Ethyl acetate | 0.31 | 0.28 | .. | " |
| Methyl bromide | 0.29 | 0.28 | .. | " |
| Methyl iodide | 0.21 | 0.22 | .. | " |
| Carbon tetrachloride | 0.30 | 0.31 | .. | " |
| Ethyl iodide | 0.17 | 0.16 | .. | " |
+----------------------+------+------+------+-----------------+
_Ions produced by Ultra-Violet Light._
Air 1.4 Rutherford
Hydrogen 3.9 Rutherford
Carbonic acid 0.78 Rutherford
_Ions in Gases sucked from Flames._