The mean of the values of Ne in the preceding table is 1.24 X 10^10.
Hence we may conclude that the charge of electricity carried by a
gaseous ion is equal to the charge carried by the hydrogen atom in the
electrolysis of solutions. The values of Ne for the different gases
differ more than we should have expected from the probable accuracy of
the determination of D and the velocity of the ions: Townsend (_Proc.
Roy. Soc._ 80, p. 207) has shown that when the ionization is produced
by Rontgen rays some of the positive ions carry a double charge and
that this accounts for the values of Ne being greater for the positive
than for the negative ions. Since we know the value of e, viz. 3.5 X
10^-10, and, also Ne, = 1.24 X 10^10, we find N the number of
molecules in a cubic centimetre of gas at standard temperature and
pressure to be equal to 3.5 X 10^19. This method of obtaining N is the
only one which does not involve any assumption as to the shape of the
molecules and the forces acting between them.
Another method of determining the charge carried by an ion has been
employed by Rutherford (_Proc. Roy. Soc._ 81, pp. 141, 162), in which
the positively electrified particles emitted by radium are made use
of. The method consists of: (1) Counting the number of [alpha]
particles emitted by a given quantity of radium in a known time. (2)
Measuring the electric charge emitted by this quantity in the same
time. To count the number of the [alpha] particles the radium was so
arranged that it shot into an ionization chamber a small number of
[alpha] particles per minute; the interval between the emission of
individual particles was several seconds. When an [alpha] particle
passed into the vessel it ionized the gas inside and so greatly
increased its conductivity; thus, if the gas were kept exposed to an
electric field, the current through the gas would suddenly increase
when an [alpha] particle passed into the vessel. Although each [alpha]
particle produces about thirty thousand ions, this is hardly large
enough to produce the conductivity appreciable without the use of very
delicate apparatus; to increase the conductivity Rutherford took
advantage of the fact that ions, especially negative ones, when
exposed to a strong electric field, produce other ions by collision
against the molecules of the gas through which they are moving. By
suitably choosing the electric field and the pressure in the
ionization chamber, the 30,000 ions produced by each [alpha] particle
can be multiplied to such an extent that an appreciable current passes
through the ionization chamber on the arrival of each [alpha]
particle. An electrometer placed in series with this vessel will show
by its deflection when an [alpha] particle enters the chamber, and by
counting the number of deflections per minute we can determine the
number of [alpha] particles given out by the radium in that time.
Another method of counting this number is to let the particles fall on
a phosphorescent screen, and count the number of scintillations on the
screen in a certain time. Rutherford has shown that these two methods
give concordant results.
The charge of positive electricity given out by the radium was
measured by catching the [alpha] particles in a Faraday cylinder
placed in a very highly exhausted vessel, and measuring the charge per
minute received by this cylinder. In this way Rutherford showed that
the charge on the [alpha] particle was 9.4 X 10^-10 electrostatic
units. Now e/m for the [alpha] particle = 5 X 10^3, and there is
evidence that the [alpha] particle is a charged atom of helium; since
the atomic weight of helium is 4 and e/m for hydrogen is 10^4, it
follows that the charge on the helium atom is twice that on the
hydrogen, so that the charge on the hydrogen atom is 4.7 X 10^-10
electrostatic units.
_Calculation of the Mass of the Ions at Low Pressures._--Although at
ordinary pressures the ion seems to have a very complex structure and to
be the aggregate of many molecules, yet we have evidence that at very
low pressures the structure of the ion, and especially of the negative
one, becomes very much simpler. This evidence is afforded by
determination of the mass of the atom. We can measure the ratio of the
mass of an ion to the charge on the ion by observing the deflections
produced by magnetic and electric forces on a moving ion. If an ion
carrying a charge e is moving with a velocity v, at a point where the
magnetic force is H, a mechanical force acts on the ion, whose direction
is at right angles both to the direction of motion of the ion and to the
magnetic force, and whose magnitude is evH sin [theta], where [theta] is
the angle between v and H. Suppose then that we have an ion moving
through a gas whose pressure is so low that the free path of the ion is
long compared with the distance through which it moves whilst we are
experimenting upon it; in this case the motion of the ion will be free,
and will not be affected by the presence of the gas.
Since the force is always at right angles to the direction of motion
of the ion, the speed of the ion will not be altered by the action of
this force; and if the ion is projected with a velocity v in a
direction at right angles to the magnetic force, and if the magnetic
force is constant in magnitude and direction, the ion will describe a
curve in a plane at right angles to the magnetic force. If [rho] is
the radius of curvature of this curve, m the mass of the ion,
mv^2/[rho] must equal the normal force acting on the ion, i.e. it must
be equal to Hev, or [rho] = mv/He. Thus the radius of curvature is
constant; the path is therefore a circle, and if we can measure the
radius of this circle we know the value of mv/He. In the case of the
rapidly moving negative ions projected from the cathode in a highly
exhausted tube, which are known as _cathode rays_, the path of the
ions can be readily determined since they make many substances
luminous when they impinge against them. Thus by putting a screen of
such a substance in the path of the rays the shape of the path will be
determined. Let us now suppose that the ion is acted upon by a
vertical electric force X and is free from magnetic force, if it be
projected with a horizontal velocity v, the vertical deflection y
after a time t is 1/2 X et^2/m, or if l is the horizontal distance
travelled over by the ion in this time we have since l = vt,
Xe l^2
y = 1/2 -- ---.
m v^2
Thus if we measure y and l we can deduce e/mv^2. From the effect of the
magnetic force we know e/mv. Combining these results we can find both
e/m and v.
[Illustration: FIG. 13.]
The method by which this determination is carried out in practice is
illustrated in fig. 13. The cathode rays start from the electrode C in
a highly exhausted tube, pass through two small holes in the plugs A
and B, the holes being in the same horizontal line. Thus a pencil of
rays emerging from B is horizontal and produces a bright spot at the
far end of the tube. In the course of their journey to the end of the
tube they pass between the horizontal plates E and D, by connecting
these plates with an electric battery a vertical electric field is
produced between E and D and the phosphorescent spot is deflected. By
measuring this deflection we determine e/mv^2. The tube is now placed
in a uniform magnetic field, the lines of magnetic force being
horizontal and at right angles to the plane of the paper. The magnetic
force makes the rays describe a circle in the plane of the paper, and
by measuring the vertical deflection of the phosphorescent patch at
the end of the tube we can determine the radius of this circle, and
hence the value of e/mv. From the two observations the value of e/m
and v can be calculated.
Another method of finding e/m for the negative ion which is applicable
in many cases to which the preceding one is not suitable, is as
follows: Let us suppose that the ion starts from rest and moves in a
field where the electric and magnetic forces are both uniform, the
electric force X being parallel to the axis of x, and the magnetic
force Z parallel to the axis of z; then if x, y, are the co-ordinates
of the ion at the time t, the equations of motion of the ion are--
d^2x dy
m ---- = Xe - He --,
dt^2 dt
d^2y dx
m ---- = He --.
dt^2 dt
The solution of these equations, if x, y, dx/dt, dy/dt all vanish when
t = 0, is
Xm / / e \ \
x = ---- {1 - cos( -- Ht ) }
eH^2 \ \ m / /
Xm /e / e \ \
y = ---- {-- Ht - sin( -- Ht ) }.
eH^2 \m \ m / /
These equations show that the path of the ion is a cycloid, the
generating circle of which has a diameter equal to 2Xm/eH^2, and rolls
on the line x = 0.
Suppose now that we have a number of ions starting from the plane x =
0, and moving towards the plane x = a. The particles starting from x =
0 describe cycloids, and the greatest distance they can get from the
plane is equal to the diameter of the generating circle of the
cycloid, i.e. to 2Xm/eH^2. (After reaching this distance they begin to
approach the plane.) Hence if a is less than the diameter of the
generating circle, all the particles starting from x = 0 will reach
the plane x = a, if this is unlimited in extent; while if a is greater
than the diameter of the generating circle none of the particles which
start from x = 0 will reach the plane x = a. Thus, if x = 0 is a plane
illuminated by ultra-violet light, and consequently the seat of a
supply of negative ions, and x = a a plane connected with an
electrometer, then if a definite electric intensity is established
between the planes, i.e. if X be fixed, so that the rate of emission
of negative ions from the illuminated plate is given, and if a is less
than 2Xm/eH^2, all the ions which start from x = 0 will reach x = a.
That is, the rate at which this plane receives an electric charge
will be the same whether there is a magnetic field between the plate
or not, but if a is greater than 2Xm/eH^2, then no particle which
starts from the plate x = 0 will reach the plate x = a, and this plate
will receive no charge. Thus the supply of electricity to the plate
has been entirely stopped by the magnetic field. Thus, on this theory,
if the distance between the plates is less than a certain value, the
magnetic force should produce no effect on the rate at which the
electrometer plate receives a charge, while if the distance is greater
than this value the magnetic force would completely stop the supply of
electricity to the plate. The actual phenomena are not so abrupt as
this theory indicates. We find that when the plates are very near
together the magnetic force produces a very slight effect, and this an
increase in the rate of charging of the plate. On increasing the
distance we come to a stage where the magnetic force produces a great
diminution in the rate of charging. It does not, however, stop it
abruptly, there being a considerable range of distance, in which the
magnetic force diminishes but does not destroy the current. At still
greater distances the current to the plate under the magnetic force is
quite inappreciable compared with that when there is no magnetic
force. We should get this gradual instead of abrupt decay of the
current if some of the particles, instead of all starting from rest,
started with a finite velocity; in that case the first particles
stopped would be those which started from rest. This would be when a =
2Xm/eH^2. Thus if we measure the value of a when the magnetic force
first begins to affect the leak to the electrometer we determine
2Xm/eH^2, and as we can easily measure X and H, we can deduce the value
of m/e.
By these methods Thomson determined the value of e/m for the negative
ions produced when ultra-violet light falls on a metal plate, as well as
for the negative ions produced by an incandescent carbon filament in an
atmosphere of hydrogen (_Phil. Mag._ [5], 48, p. 547) as well as for the
cathode rays. It was found that the value of e/m for the negative ions
was the same in all these cases, and that it was a constant quantity
independent of the nature of the gas from which the ions are produced
and the means used to produce them. It was found, too, that this value
was more than a thousand times the value of e/M, where e is the charge
carried by an atom of hydrogen in the electrolysis of solutions, and M
the mass of an atom of hydrogen. We have seen that this charge is the
same as that carried by the negative ion in gases; thus since e/m is
more than a thousand times e/M, it follows that M must be more than a
thousand times m. Thus the mass of the negative ion is exceedingly small
compared with the mass of the atom of hydrogen, the smallest mass
recognized in chemistry. The production of negative ions thus involves
the splitting up of the atom, as from a collection of atoms something is
detached whose mass is less than that of a single atom. It is important
to notice in connexion with this subject that an entirely different line
of argument, based on the Zeeman effect (see MAGNETO-OPTICS), leads to
the recognition of negatively electrified particles for which e/m is of
the same order as that deduced from the consideration of purely
electrical phenomena. These small negatively electrified particles are
called corpuscles. The latest determinations of e/m for corpuscles
available are the following:--
Observer. e/m.
Classen (_Ber. deut. phys. Ges._ 6, p. 700) 1.7728 X 10^7
Bucherer (_Ann. der Phys._, 28, p. 513) 1.763 X 10^7
It follows from electrical theory that when the corpuscles are moving
with a velocity comparable with that of light their masses increase
rapidly with their velocity. This effect has been detected by Kauffmann
(_Gott. Nach._, Nov. 8, 1901), who used the corpuscles shot out from
radium, some of which move with velocities only a few per cent less than
that of light. Other experiments on this point have been made by
Bucherer (_Ann. der Phys._ 28, p. 513).
_Conductivity Produced by Ultra-Violet Light._--So much use has been
made in recent times of ultra-violet light for producing ions that it is
desirable to give some account of the electrical effects produced by
light. The discovery by Hertz (_Wied. Ann._ 31, p. 983) in 1887, that
the incidence of ultra-violet light on a spark gap facilitates the
passage of a spark, led to a series of investigations by Hallwachs,
Hoor, Righi and Stoletow, on the effect of ultra-violet light on
electrified bodies. These researches have shown that a freshly cleaned
metal surface, charged with negative electricity, rapidly loses its
charge, however small, when exposed to ultra-violet light, and that if
the surface is insulated and without charge initially, it acquires a
positive charge under the influence of the light. The magnitude of this
positive charge may be very much increased by directing a blast of air
on the plate. This, as Zeleny (_Phil. Mag._ [5], 45, p. 272) showed, has
the effect of blowing from the neighbourhood of the plate negatively
electrified gas, which has similar properties to the charged gas
obtained by the separation of ions from a gas exposed to Rontgen rays or
uranium radiation. If the metal plate is positively electrified, there
is no loss of electrification caused by ultra-violet light. This has
been questioned, but a very careful examination of the question by
Elster and Geitel (_Wied. Ann._ 57, p. 24) has shown that the apparent
exceptions are due to the accidental exposure to reflected ultra-violet
light of metal surfaces in the neighbourhood of the plate negatively
electrified by induction, so that the apparent loss of charge is due to
negative electricity coming up to the plate, and not to positive
electricity going away from it. The ultra-violet light may be obtained
from an arc-lamp, the effectiveness of which is increased if one of the
terminals is made of zinc or aluminium, the light from these substances
being very rich in ultra-violet rays; it may also be got very
conveniently by sparking with an induction coil between zinc or cadmium
terminals. Sunlight is not rich in ultra-violet light, and does not
produce anything like so great an effect as the arc light. Elster and
Geitel, who have investigated with great success the effects of light on
electrified bodies, have shown that the more electro-positive metals
lose negative charges when exposed to ordinary light, and do not need
the presence of the ultra-violet rays. Thus they found that amalgams of
sodium or potassium enclosed in a glass vessel lose a negative charge
when exposed to daylight, though the glass stops the small amount of
ultra-violet light left in sunlight after its passage through the
atmosphere. If sodium or potassium be employed, or, what is more
convenient, the mercury-like liquid obtained by mixing sodium and
potassium in the proportion of their combining weights, they found that
negative electricity was discharged by an ordinary petroleum lamp. If
the still more electro-positive metal rubidium is used, the discharge
can be produced by the light from a glass rod just heated to redness;
but there is no discharge till the glass is luminous. Elster and Geitel
arrange the metals in the following order for the facility with which
negative electrification is discharged by light: rubidium, potassium,
alloy of sodium and potassium, sodium, lithium, magnesium, thallium,
zinc. With copper, platinum, lead, iron, cadmium, carbon and mercury the
effects with ordinary light are too small to be appreciable. The order
is the same as that in Volta's electro-chemical series. With
ultra-violet light the different metals show much smaller differences in
their power of discharging negative electricity than they do with
ordinary light. Elster and Geitel found that the ratio of the
photo-electric effects of two metals exposed to approximately
monochromatic light depended upon the wave-length of the light,
different metals showing a maximum sensitiveness in different parts of
the spectrum. This is shown by the following table for the alkaline
metals. The numbers in the table are the rates of emission of negative
electricity under similar circumstances. The rate of emission under the
light from a petroleum lamp was taken as unity:--
Blue. Yellow. Orange. Red.
Rb .16 .64 .33 .039
Na .37 .36 .14 .009
K .57 .07 .04 .002
The table shows that the absorption of light by the metal has great
influence on the photo-electric effect, for while potassium is more
sensitive in blue light than sodium, the strong absorption of yellow
light by sodium makes it more than five times more sensitive to this
light than potassium. Stoletow, at an early period, called attention to
the connexion between strong absorption and photo-electric effects. He
showed that water, which does not absorb to any great extent either the
ultra-violet or visible rays, does not show any photo-electric effect,
while strongly coloured solutions, and especially solutions of
fluorescent substances such as methyl green or methyl violet, do so to a
very considerable extent; indeed, a solution of methyl green is more
sensitive than zinc. Hallwachs (_Wied. Ann._ 37, p. 666) proved that in
liquids showing photo-electric effects there is always strong
absorption; we may, however, have absorption without these effects.
Phosphorescent substances, such as calcium sulphide show this effect, as
also do various specimens of fluor-spar. As phosphorescence and
fluorescence are probably accompanied by a very intense absorption by
the surface layers, the evidence is strong that to get the
photo-electric effects we must have strong absorption of some kind of
light, either visible or ultra-violet.
[Illustration: FIG. 14.]
If a conductor A is placed near a conductor B exposed to ultra-violet
light, and if B is made the negative electrode and a difference of
potential established between A and B, a current of electricity will
flow between the conductors. The relation between the magnitude of the
current and the difference of potential when A and B are parallel plates
has been investigated by Stoletow (_Journal de physique_, 1890, 11, p.
469), von Schweidler (_Wien. Ber._, 1899, 108, p. 273) and Varley
(_Phil. Trans. A._, 1904, 202, p. 439). The results of some of Varley's
experiments are represented in the curves shown in fig. 14, in which the
ordinates are the currents and the abscissae the potentials. It will be
seen that when the pressure is exceedingly low the current is
independent of the potential difference and is equal to the negative
charge carried off in unit time by the corpuscles emitted from the
surface exposed to the light. At higher pressures the current rises far
above these values and increases rapidly with the potential difference.
This is due to the corpuscles emitted by the illuminated surface
acquiring under the electric field such high velocities that when they
strike against the molecules of the gas through which they are passing
they ionize them, producing fresh ions which can carry on additional
current. The relation between the current and the potential difference
in this case is in accordance with the results of the theory of
ionization by collision. The corpuscles emitted from a body under the
action of ultra-violet light start from the surface with a finite
velocity. The velocity is not the same for all the corpuscles, nor
indeed could we expect that it should be: for as Ladenburg has shown
(_Ann. der Phys._, 1903, 12, p. 558) the seat of their emission is not
confined to the surface layer of the illuminated metal but extends to a
layer of finite, though small, thickness. Thus the particles which start
deep down will have to force their way through a layer of metal before
they reach the surface, and in doing so will have their velocities
retarded by an amount depending on the thickness of this layer. The
variation in the velocity of the corpuscles is shown in the following
table, due to Lenard (_Ann. der Phys._, 1902, 8, p. 149).
+------------------------------------+--------+----------+-----------+
| | Carbon.| Platinum.| Aluminium.|
+------------------------------------+--------+----------+-----------+
| Corpuscles emitted with velocities | | | |
| between 12 and 8 X 10^7 cm sec. | 0.000 | 0.000 | 0.004 |
| between 8 and 4 X 10^7 cm sec. | 0.049 | 0.155 | 0.151 |
| between 4 and 0 X 10^7 cm sec. | 0.67 | 0.65 | 0.49 |
| | | | |
| Corpuscles only emitted with the | | | |
| help of an external electric | 0.28 | 0.21 | 0.35 |
| field. +--------+----------+-----------|
| | 1.00 | 1.00 | 1.00 |
+------------------------------------+--------+----------+-----------+
If the illuminated surface is completely surrounded by an envelope of
the same metal insulated from and completely shielded from the light,
the emission of the negative corpuscles from the illuminated surface
would go on until the potential difference V between this surface and
the envelope became so great that the corpuscles with the greatest
velocity lost their energy before reaching the envelope, i.e. if m is
the mass, e the charge on a corpuscle, v the greatest velocity of
projection, until Ve = 1/2mv^2. The values found for V by different
observers are not very consistent. Lenard found that V for aluminium was
about 3 volts and for platinum 2. Millikan and Winchester (_Phil. Mag._,
July 1907) found for aluminium V = .738. The apparatus used by them was
so complex that the interpretation of their results is difficult.
An extremely interesting fact discovered by Lenard is that the velocity
with which the corpuscles are emitted from the metal is independent of
the intensity of the incident light. The quantity of corpuscles
increases with the intensity, but the velocity of the individual
corpuscles does not. It is worthy of notice that in other cases when
negative corpuscles are emitted from metals, as for example when the
metals are exposed to cathode rays, Canal-strahlen, or Rontgen rays, the
velocity of the emitted corpuscles is independent of the intensity of
the primary radiation which excites them. The velocity is not, however,
independent of the nature of the primary rays. Thus when light is used
to produce the emission of corpuscles the velocity, as Ladenburg has
shown, depends on the wave length of the light, increasing as the wave
length diminishes. The velocity of corpuscles emitted under the action
of cathode rays is greater than that of those ejected by light, while
the incidence of Rontgen rays produces the emission of corpuscles moving
much more rapidly than those in the cases already mentioned, and the
harder the primary rays the greater is the velocity of the corpuscles.
The importance of the fact that the velocity and therefore the energy of
the corpuscles emitted from the metal is independent of the intensity of
the incident light can hardly be overestimated. It raises the most
fundamental questions as to the nature of light and the constitution of
the molecules. What is the source of the energy possessed by these
corpuscles? Is it the light, or in the stores of internal energy
possessed by the molecule? Let us follow the consequences of supposing
that the energy comes from the light. Then, since the energy is
independent of the intensity of the light, the electric forces which
liberate the corpuscles must also be independent of that intensity. But
this cannot be the case if, as is usually assumed in the electromagnetic
theory, the wave front consists of a uniform distribution of electric
force without structure, for in this case the magnitude of the electric
force is proportional to the square root of the intensity. On the
emission theory of light a difficulty of this kind would not arise, for
on that theory the energy in a luminiferous particle remains constant as
the particle pursues its flight through space. Thus any process which a
single particle is able to effect by virtue of its energy will be done
just as well a thousand miles away from the source of light as at the
source itself, though of course in a given space there will not be
nearly so many particles to do this process far from the source as there
are close in. Thus, if one of the particles when it struck against a
piece of metal caused the ejection of a corpuscle with a given velocity,
the velocity of emission would not depend on the intensity of the light.
There does not seem any reason for believing that the electromagnetic
theory is inconsistent with the idea that on this theory, as on the
emission theory, the energy in the light wave may instead of being
uniformly distributed through space be concentrated in bundles which
occupy only a small fraction of the volume traversed by the light, and
that as the wave travels out the bundles get farther apart, the energy
in each remaining undiminished. Some such view of the structure of light
seems to be required to account for the fact that when a plate of metal
is struck by a wave of ultra-violet light, it would take years before
the corpuscles emitted from the metal would equal in number the
molecules on the surface of the metal plate, and yet on the ordinary
theory of light each one of these is without interruption exposed to the
action of the light. The fact discovered by E. Ladenburg (_Verh. d.
deutsch. physik. Ges._ 9, p. 504) that the velocity with which the
corpuscles are emitted depends on the wave length of the light suggests
that the energy in each bundle depends upon the wave length and
increases as the wave length diminishes.
These considerations illustrate the evidence afforded by photo-electric
effects on the nature of light; these effects may also have a deep
significance with regard to the structure of matter. The fact that the
energy of the individual corpuscles is independent of the intensity of
the light might be explained by the hypothesis that the energy of the
corpuscles does not come from the light but from the energy stored up in
the molecules of the metal exposed to the light. We may suppose that
under the action of the light some of the molecules are thrown into an
unstable state and explode, ejecting corpuscles; the light in this case
acts only as a trigger to liberate the energy in the atom, and it is
this energy and not that of the light which goes into the corpuscles. In
this way the velocity of the corpuscles would be independent of the
intensity of the light. But it may be asked, is this view consistent
with the result obtained by Ladenburg that the velocity of the
corpuscles depends upon the nature of the light? If light of a definite
wave length expelled corpuscles with a definite and uniform velocity, it
would be very improbable that the emission of the corpuscles is due to
an explosion of the atoms. The experimental facts as far as they are
known at present do not allow us to say that the connexion between the
velocity of the corpuscles and the wave length of the light is of this
definite character, and a connexion such as a gradual increase of
average velocity as the wave length of the light diminishes, would be
quite consistent with the view that the corpuscles are ejected by the
explosion of the atom. For in a complex thing like an atom there may be
more than one system which becomes unstable when exposed to light. Let
us suppose that there are two such systems, A and B, of which B ejects
the corpuscles with the greater velocity. If B is more sensitive to the
short waves, and A to the long ones, then as the wave length of the
light diminishes the proportion of the corpuscles which come from B will
increase, and as these are the faster, the average velocity of the
corpuscles emitted will also increase. And although the potential
acquired by a perfectly insulated piece of metal when exposed to
ultra-violet light would depend only on the velocity of the fastest
corpuscles and not upon their number, in practice perfect insulation is
unattainable, and the potential actually acquired is determined by the
condition that the gain of negative electricity by the metal through
lack of insulation, is equal to the loss by the emission of negatively
electrified corpuscles. The potential acquired will fall below that
corresponding to perfect insulation by an amount depending on the number
of the faster corpuscles emitted, and the potential will rise if the
proportion of the rapidly moving corpuscles is increased, even though
there is no increase in their velocity. It is interesting to compare
other cases in which corpuscles are emitted with the case of
ultra-violet light. When a metal or gas is bombarded by cathode rays it
emits corpuscles and the velocity of these is found to be independent of
the velocity of the cathode rays which excite them; the velocity is
greater than for corpuscles emitted under ultra-violet light. Again,
when bodies are exposed to Rontgen rays they emit corpuscles moving with
a much greater velocity than those excited by cathode rays, but again
the velocity does not depend upon the intensity of the rays although it
does to some extent on their hardness. In the case of cathode and
Rontgen rays, the velocity with which the corpuscles are emitted seems,
as far as we know at present, to vary slightly, but only slightly, with
the nature of the substance on which the rays fall. May not this
indicate that the first effect of the primary rays is to detach a
neutral doublet, consisting of a positive and negative charge, this
doublet being the same from whatever system it is detached? And that the
doublet is unstable and explodes, expelling the negative charge with a
high velocity, and the positive one, having a much larger charge, with a
much smaller velocity, the momentum of the negative charge being equal
to that of the positive.
Up to now we have been considering the effects produced when light is
incident on metals. Lenard found (and the result has been confirmed by
the experiments of J. J. Thomson and Lyman) that certain kinds of
ultra-violet light ionize a gas when they pass through. The type of
ultra-violet light which produces this effect is so easily absorbed that
it is stopped by a layer a few millimetres thick of air at atmospheric
pressure.
_Ionization by Collision._--When the ionization of the gas is produced
by external agents such as Rontgen rays or ultra-violet light, the
electric field produces a current by setting the positive ions moving in
one direction, and the negative ones in the opposite; it makes use of
ions already made and does not itself give rise to ionization. In many
cases, however, such as in electric sparks, there are no external agents
to produce ionization and the electric field has to produce the ions as
well as set them in motion. When the ionization is produced by external
means the smallest electric field is able to produce a current through
the gas; when, however, these external means are absent no current is
produced unless the strength of the electric field exceeds a certain
critical value, which depends not merely upon the nature of the gas but
also upon the pressure and the dimensions of the vessel in which it is
contained. The variation of the electric field required to produce
discharge can be completely explained if we suppose that the ionization
of the gas is produced by the impact with its molecules of corpuscles,
and in certain cases of positive ions, which under the influence of the
electric field have acquired considerable kinetic energy. We have direct
evidence that rapidly moving corpuscles are able to ionize molecules
against which they strike, for the cathode rays consist of such
corpuscles, and these when they pass through a gas produce large amounts
of ionization. Suppose then that we have in a gas exposed to an electric
field a few corpuscles. These will be set in motion by the field and
will acquire an amount of energy in proportion to the product of the
electric force, their charge, and the distance travelled in the
direction of the electric field between two collisions with the
molecules of the gas. If this energy is sufficient to give them the
ionizing property possessed by cathode rays, then when a corpuscle
strikes against a molecule it will detach another corpuscle; this under
the action of the electric field will acquire enough energy to produce
corpuscles on its own account, and so as the corpuscles move through the
gas their number will increase in geometrical progression. Thus, though
there were but few corpuscles to begin with, there may be great
ionization after these have been driven some distance through the gas by
the electric field.
The number of ions produced by collisions can be calculated by the
following method. Let the electric force be parallel to the axis of x,
and let n be the number of corpuscles per unit volume at a place fixed
by the co-ordinate x; then in unit time these corpuscles will make
nu/[lambda] collisions with the molecules, if u is the velocity of a
corpuscle and [lambda] the mean free path of a corpuscle. When the
corpuscles are moving fast enough to produce ions by collision their
velocities are very much greater than those they would possess at the
same temperature if they were not acted on by electrical force, and so
we may regard the velocities as being parallel to the axis of x and
determined by the electric force and the mean free path of the
corpuscles. We have to consider how many of the nu/[lambda] collisions
which take place per second will produce ions. We should expect that
the ionization of a molecule would require a certain amount of energy,
so that if the energy of the corpuscle fell below this amount no
ionization would take place, while if the energy of the corpuscle were
exceedingly large, every collision would result in ionization. We
shall suppose that a certain fraction of the number of collisions
result in ionization and that this fraction is a function of the
energy possessed by the corpuscle when it collides against the
molecules. This energy is proportional to Xe[lambda] when X is the
electric force, e the charge on the corpuscle, and [lambda] the mean
free path. If the fraction of collisions which produce ionization is
[int](Xe[lambda]), then the number of ions produced per cubic
centimetre per second is [int](Xe[lambda])nu/[lambda]. If the
collisions follow each other with great rapidity so that a molecule
has not had time to recover from one collision before it is struck
again, the effect of collisions might be cumulative, so that a
succession of collisions might give rise to ionization, though none of
the collisions would produce an ion by itself. In this case [int]
would involve the frequency of the collisions as well as the energy of
the corpuscle; in other words, it might depend on the current through
the gas as well as upon the intensity of the electric field. We
shall, however, to begin with, assume that the current is so small
that this cumulative effect may be neglected.
Let us now consider the rate of increase, dn/dt, in the number of
corpuscles per unit volume. In consequence of the collisions,
[int](Xe[lambda])nu/[lambda] corpuscles are produced per second; in
consequence of the motion of the corpuscles, the number which leave
unit volume per second is greater than those which enter it by
(d/dx)(nu); while in a certain number of collisions a corpuscle will
stick to the molecule and will thus cease to be a free corpuscle. Let
the fraction of the number of collisions in which this occurs be
[beta]. Thus the gain in the number of corpuscles is
[int](Xe[lambda])nu/[lambda], while the loss is (d/dx)(nu) +
[beta](nu)/[lambda]; hence
dn nu d [beta]nu
-- = [int](Xe[lambda]) -------- - --(nu) - --------.
dt [lambda] dx [lambda]