RATE OF EMISSION OF ENERGY.
=243.= It was early recognised that a considerable amount of energy is
emitted by the radio-active bodies in the form of their characteristic
radiations. Most of the early estimates of the amount of this energy
were based on the number and energy of the expelled particles, and were
much too small. It has been pointed out (section 114) that the greater
part of the energy emitted from the radio-active bodies in the form of
ionizing radiations is due to the α rays, and that the β rays in
comparison supply only a very small fraction.
Rutherford and McClung[325] made an estimate of the energy of the rays,
emitted by a thin layer of active matter, by determining the total
number of ions produced by the complete absorption of the α rays. The
energy required to produce an ion was determined experimentally by
observations of the heating effect of X rays, and of the total number of
ions produced when the rays were completely absorbed in air. The energy
required to produce an ion in air was found to be 1·90 × 10⁻¹⁰ ergs.
This, as will be shown in Appendix A, is probably an over-estimate, but
was of the right order of magnitude. From this it was calculated that
one gram of uranium oxide spread over a plate in the form of a thin
powdered layer emitted energy into the air at the rate of 0·032 gram
calories per year. This is a very small emission of energy, but in the
case of an intensely radio-active substance like radium, whose activity
is about two million times that of uranium, the corresponding emission
of energy is 69000 gram calories per year. This is obviously an
under-estimate, for it includes only the energy radiated into the air.
The actual amount of energy released in the form of α rays is evidently
much greater than this on account of the absorption of the α rays by the
active matter itself.
It will be shown later that the heating effect of radium and of its
products is a measure of the energy of the expelled α particles.
=244. Heat emission of radium.= P. Curie and Laborde[326] first drew
attention to the striking result that a radium compound kept itself
continuously at a temperature several degrees higher than that of the
surrounding atmosphere. Thus the energy emitted from radium can be
demonstrated by its direct heating effect, as well as by photographic
and electric means. Curie and Laborde determined the rate of the
emission of heat in two different ways. In one method the difference of
temperature was observed by means of an iron-constantine thermo-couple
between a tube containing one gram of radiferous chloride of barium, of
activity about ⅙ of pure radium, and an exactly similar tube
containing one gram of pure barium chloride. The difference of
temperature observed was 1·5° C. In order to measure the rate of
emission of heat, a coil of wire of known resistance was placed in the
pure barium chloride, and the strength of the electric current required
to raise the barium to the same temperature as the radiferous barium was
observed. In the other method, the active barium, enclosed in a glass
tube, was placed inside a Bunsen calorimeter. Before the radium was
introduced, it was observed that the level of the mercury in the stem
remained steady. As soon as the radium, which had previously been cooled
in melting ice, was placed in the calorimeter, the mercury column began
to move at a regular rate. If the radium tube was removed, the movement
of the mercury ceased. It was found from these experiments that the heat
emission from the 1 gram of radiferous barium, containing about ⅙ of
its weight of pure radium chloride, was 14 gram-calories per hour.
Measurements were also made with 0·08 gram of pure radium chloride.
Curie and Laborde deduced from these results that 1 gram of pure radium
emits a quantity of heat equal to about 100 gram-calories per hour. This
result was confirmed by the experiments of Runge and Precht[327] and
others. As far as observation has gone at present, this rate of emission
of heat is continuous and unchanged with lapse of time. Therefore, 1
gram of radium emits in the course of a day 2400, and in the course of a
year 876,000 gram-calories. The amount of heat evolved in the union of
hydrogen and oxygen to form 1 gram of water is 3900 gram-calories. It is
thus seen that 1 gram of radium emits _per day_ nearly as much energy as
is required to dissociate 1 gram of water.
In some later experiments using 0·7 gram of pure radium bromide, P.
Curie[328] found that the temperature of the radium indicated by a
mercury thermometer was 3° C. above that of the surrounding air. This
result was confirmed by Giesel, who obtained a difference of temperature
of 5° C. with 1 gram of radium bromide. The actual rise of temperature
observed will obviously depend upon the size and nature of the vessel
containing the radium.
During their visit to England in 1903 to lecture at the Royal
Institution, M. and Mme Curie performed some experiments with Professor
Dewar, to test by another method the rate of emission of heat from
radium at very low temperatures. This method depended on the measurement
of the amount of gas volatilized when a radium preparation was placed
inside a tube immersed in a liquefied gas at its boiling point. The
arrangement of the calorimeter is shown in Fig. 97.
[Illustration: Fig. 97.]
The small closed Dewar flask _A_ contains the radium in a glass tube
_R_, immersed in the liquid to be employed. The flask _A_ is surrounded
by another Dewar bulb _B_, containing the same liquid, so that no heat
is communicated to _A_ from the outside. The gas liberated in the tube
_A_ is collected in the usual way over water or mercury, and its volume
determined. By this method, the rate of heat emission of the radium was
found to be about the same in boiling carbon dioxide and oxygen, and
also in liquid hydrogen. Especial interest attaches to the result
obtained with liquid hydrogen, for at such a low temperature ordinary
chemical activity is suspended. The fact that the heat emission of
radium is unaltered over such a wide range of temperature indirectly
shows that the rate of expulsion of α particles from radium is
independent of temperature, for it will be shown later that the heating
effect observed is due to the bombardment of the radium by the α
particles.
The use of liquid hydrogen is very convenient for demonstrating the rate
of heat emission from a small amount of radium. From 0·7 gram of radium
bromide (which had been prepared only 10 days previously) 73 c.c. of gas
were given off per minute.
In later experiments P. Curie (_loc. cit._) found that the rate of
emission of heat from a given quantity of radium depended upon the time
which had elapsed since its preparation. The emission of heat was at
first small, but after a month’s interval practically attained a
maximum. If a radium compound is dissolved and placed in a sealed tube,
the rate of heat emission rises to the same maximum as that of an equal
quantity of radium in the solid state.
=245. Connection of the heat emission with the radiations.= The
observation of Curie that the rate of heat emission depended upon the
age of the radium preparation pointed to the conclusion that the
phenomenon of heat emission of radium was connected with the
radio-activity of that element. It had long been known that radium
compounds increased in activity for about a month after their
preparation, when they reached a steady state. It has been shown
(section 215), that this increase of activity is due to the continuous
production by the radium of the radio-active emanation, which is
occluded in the radium compound and adds its radiation to that of the
radium proper. It thus seemed probable that the heating effect was in
some way connected with the presence of the emanation. Some experiments
upon this point were made by Rutherford and Barnes[329]. In order to
measure the small amounts of heat emitted, a form of differential air
calorimeter shown in Fig. 98 was employed. Two equal glass flasks of
about 500 c.c. were filled with dry air at atmospheric pressure. These
flasks were connected through a glass =U=-tube filled with xylene, which
served as a manometer to determine any variation of pressure of the air
in the flasks. A small glass tube, closed at the lower end, was
introduced into the middle of each of the flasks. When a continuous
source of heat was introduced into the glass tube, the air surrounding
it was heated and the pressure was increased. The difference of
pressure, when a steady state was reached, was observed on the manometer
by means of a microscope with a micrometer scale in the eye-piece. On
placing the source of heat in the similar tube in the other flask, the
difference in pressure was reversed. In order to keep the apparatus at a
constant temperature, the two flasks were immersed in a water-bath,
which was kept well stirred.
[Illustration: Fig. 98.]
Observations were first made on the heat emission from 30 milligrams of
radium bromide. The difference in pressure observed on the manometer was
standardized by placing a small coil of wire of known resistance in the
place of the radium. The strength of the current through the wire was
adjusted to give the same difference of pressure on the manometer. In
this way it was found that the heat emission per gram of radium bromide
corresponded to 65 gram-calories per hour. Taking the atomic weight of
radium as 225, this is equivalent to a rate of emission of heat from one
gram of metallic radium of 110 gram-calories per hour.
The emanation from the 30 milligrams of radium bromide was then removed
by heating the radium (section 215). By passing the emanation through a
small glass tube immersed in liquid air, the emanation was condensed.
The tube was sealed off while the emanation was still condensed in the
tube. In this way the emanation was concentrated in a small glass tube
about 4 cms. long. The heating effects of the “de-emanated” radium and
of the emanation tube were then determined at intervals. It was found
that, after removal of the emanation, the heating effect of the radium
decayed in the course of a few hours to a minimum, corresponding to
about 25 per cent. of the original heat emission, and then gradually
increased again, reaching its original value after about a month’s
interval. The heating effect of the emanation tube was found to increase
for the first few hours after separation to a maximum, and then to decay
regularly with the time according to an exponential law, falling to half
its maximum value in about four days. The actual heat emission of the
emanation tube was determined by sending a current through a coil of
wire occupying the same length and position as the emanation tube.
The variation with time of the heating effect from 30 milligrams of
radium and the emanation from it is shown in Fig. 99.
[Illustration: Fig. 99.]
Curve _A_ shows the variation with time of the heat emission of the
radium and curve _B_ of the emanation. The sum total of the rate of heat
emission of the radium and the emanation together, was at any time found
to be equal to that of the original radium. The maximum heating effect
of the tube containing the emanation from 30 milligrams of radium
bromide was 1·26 gram-calories per hour. The emanation together with the
secondary products which arise from it, obtained from one gram of
radium, would thus give out 42 gram-calories per hour. The emanation
stored up in the radium is thus responsible for more than two-thirds of
the total heat emission from radium. It will be seen later that the
decrease to a minimum of the heating effect of radium, after removal of
the emanation, is connected with the decay of the excited activity. In a
similar way, the increase of the heating effect of the emanation to a
maximum some hours after removal is also a result of the excited
activity produced by the emanation on the walls of the containing
vessel. Disregarding for the moment these rapid initial changes in heat
emission, it is seen that the heating effect of the emanation and its
further products, after reaching a maximum, decreases at the same rate
as that at which the emanation loses its activity, that is, it falls to
half value in four days. If _Q__{max.} is the maximum heating effect and
_Q_{t}_ the heating effect at any time _t_ later, then
$$ \frac {Q_t} {Q_{max}} = e^{–λt} $$
where λ is the constant of change of the emanation.
The curve of recovery of the heating effect of radium from its minimum
value is identical with the curve of recovery of its activity measured
by the α rays. Since the minimum heating effect is 25 per cent. of the
total, the heat emission _Q_{t}_ at any time _t_ after reaching a
minimum is given by
$$ \frac {Q_t} {Q_{max}} = \cdot25 + \cdot75 (1 − e^{–λt}) $$,
where _Q__{max.} is the maximum rate of heat emission and λ, as before,
is the constant of change of the emanation.
The identity of the curves of recovery and fall of the heating effect of
radium and its emanation respectively with the corresponding curves for
the rise and fall of radio-activity shows that the heat emission of
radium and its products is directly connected with their radio-activity.
The variation in the heat emission of both radium and its emanation is
approximately proportional to their activity measured by the α rays. It
is not proportional to the activity measured by the β or γ rays, for the
intensity of these rays falls nearly to zero some hours after removal of
the emanation, while the α ray activity, like the heating effect, is 25
per cent. of the maximum value. These results are thus in accordance
with the view that the heat emission of radium accompanies the expulsion
of α particles, and is approximately proportional to the number
expelled. Before such a conclusion can be considered established, it is
necessary to show that the heating effect of the active deposit from the
emanation varies in the same way as its α ray activity. Experiments made
to test this point will now be considered.
=246. Heat emission of the active deposit from the emanation.= New
radium in radio-active equilibrium contains four successive products
which break up with the emission of α particles, viz. radium itself, the
emanation, radium A and C. Radium B does not emit rays at all. The
effect of the later products radium D, E and F may be neglected, if the
radium has not been prepared for more than a year.
It is not easy to settle definitely the relative activity supplied by
each of these products when in radio-active equilibrium, but it has been
shown in section 229 that the activity is not very different for the
four α ray products. The α particles from radium A and C are more
penetrating than those from radium itself and the emanation. The
evidence at present obtained points to the conclusion that the activity
supplied by the emanation is less than that supplied by the other
products. This indicates that the α particles from the emanation are
projected with less velocity than in the other cases.
When the emanation is suddenly released from radium by heat or solution,
the products radium A, B and C are left behind. Since the parent matter
is removed, the amount of the products A, B, C at once commences to
diminish, and at the end of about three hours reaches a very small
value. If the heating effect depends upon the α ray activity, it is thus
to be expected that the heat emission of the radium should rapidly
diminish to a minimum after the removal of the emanation.
When the emanation is introduced into a vessel, the products radium A, B
and C at once appear and increase in quantity, reaching a practical
maximum about 3 hours later. The heating effect of the emanation tube
should thus increase for several hours after the introduction of the
emanation.
In order to follow the rapid changes in the heating effect of radium,
after removal of the emanation, Rutherford and Barnes (_loc. cit._) used
a pair of differential platinum thermometers. Each thermometer consisted
of 35 cms. of fine platinum wire, wound carefully on the inside of a
thin glass tube 5 mms. in diameter, forming a coil 3 cms. long. The
glass tube containing the radium and also the tube containing the
emanation were selected to slide easily into the interior of the coils,
the wire thus being in direct contact with the glass envelope containing
the source of heat. The change in resistance of the platinum
thermometers, when the radium or emanation tube was transferred from one
coil to the other, was readily measured.
[Illustration: Fig. 100.]
The heating effect of the radium in radio-active equilibrium was first
accurately determined. The radium tube was heated to drive off the
emanation, which was rapidly condensed in a small glass tube 3 cms. long
and 3 mms. internal diameter. After allowing a short time for
temperature conditions to become steady, the heating effect of the
radium tube was measured. The results are shown in Fig. 100. An
observation could not be taken until about 12 minutes after the removal
of the emanation, and the heating effect was then found to have fallen
to about 55 per cent. of the maximum value. It steadily diminished with
the time, finally reaching a minimum value of 25 per cent. several hours
later.
It is not possible in experiments of this character to separate the
heating effect of the emanation from that supplied by radium A. Since A
is half transformed in three minutes, its heating effect will have
largely disappeared after 10 minutes, and the decrease is then mainly
due to changes in radium B and C.
The variation with time of the heating effect of the active deposit is
still more clearly brought out by an examination of the rise of the
heating effect when the emanation is introduced into a small tube, and
of the decrease of the heating effect after the emanation is removed.
The curve of rise is shown in the upper curve of Fig. 101. 40 minutes
after the introduction of the emanation, the heating effect had risen to
75 per cent. of the maximum value which was reached after an interval of
about 3 hours.
[Illustration: Fig. 101.]
After the heating effect of the emanation tube had attained a maximum,
the emanation was removed, and the decay with time observed as soon as
possible afterwards. The results are shown in the lower curve of Fig.
101. It is seen that the two curves of rise and decay are complementary
to one another. The first observation was made 10 minutes after removal,
and the heating effect had then dropped to 47 per cent. of the original
value. This sudden drop is due partly to the removal of the emanation,
and partly to the rapid transformation of radium A. The lower curve is
almost identical in shape with the corresponding α ray curve for the
decay of the excited activity after a long exposure (see Fig. 86) and
clearly shows that the heating effect is directly proportional to the
activity measured by the α rays over the whole range examined. The
heating effect decreases according to the same law and at the same rate
as the activity measured by the α rays.
Twenty minutes after the removal of the emanation, radium A has been
almost completely transformed, and the activity is then proportional to
the amount of radium C present, since the intermediate product B does
not give out rays. The close agreement of the activity and heat emission
curves shows that the heating effect is proportional also to the amount
of radium C. We may thus conclude that the rayless product B supplies
little if any of the heat emission observed. If radium B supplied the
same amount as radium C, the curve of decrease of heating effect with
time would differ considerably from the activity curve.
The conclusion that the transformation of radium B is not accompanied by
the release of as much heat as the other changes is to be expected if
the heating effect is mainly due to the energy of motion of the expelled
α particles.
The relative heating effect due to the radium products is shown in the
following table. The initial heating effect of C is deduced by
comparison with the corresponding activity curve.
Products Radiation Initial rate of heat emission
Radium α rays 25 per cent. of total
Emanation α „
Radium A α „ 44 „ „
Radium B no rays 0 „ „
Radium C α, β, γ 31 „ „
rays
Since radium A and C supply almost an equal proportion of activity, it
is probable that they have equal initial heating effects. If this is the
case, the heating effect of the emanation alone is 13 per cent. of the
total.
=247. Heating effects of the β and= γ =rays=. It has been shown in
section 114 that the kinetic energy of the β particles emitted from
radium is probably not greater than one per cent. of that due to the α
particles. If the heat emission is a result of bombardment by the
particles expelled from its mass, it is to be expected that the heating
effect of the β rays will be very small compared with that due to the α
rays. This anticipation is borne out by experiment. Curie measured the
heating effect of radium (1) when enclosed in a thin envelope, and (2)
when surrounded by one millimetre of lead. In the former case a large
proportion of the β rays escaped, and, in the latter, nearly all were
absorbed. The increase of heating effect in case (2) was not more than
five per cent., and this is probably an over-estimate.
In a similar way, since the total ionization due to the β rays is about
equal to that produced by the γ rays, we should expect that the heating
effect of the γ rays will be very small compared with that arising from
the α rays.
Paschen made some experiments on the heating effect of radium in a
Bunsen ice calorimeter where the radium was surrounded by a thickness of
1·92 cms. of lead—a depth sufficient to absorb a large proportion of the
γ rays. In his first publication[330], results were given which
indicated that the heating effect of the γ rays was even greater than
that of the α rays. This was not confirmed by later observations by the
same method. He concluded that the ice calorimeter could not be relied
on to measure such very small quantities of heat.
After the publication of Paschen’s first paper Rutherford and
Barnes[331] examined the question by a different method. An air
calorimeter of the form shown in Fig. 98 was employed which was found to
give very satisfactory results. The heat emission of radium was measured
(1) when the radium was surrounded by a cylinder of aluminium and (2)
when surrounded by a cylinder of lead of the same dimensions. The
aluminium absorbed only a small fraction of the γ rays while the lead
stopped more than half. No certain difference between the heating effect
in the two cases was observed, although from the earlier experiments of
Paschen a difference of at least 50 per cent. was to be expected.
We must therefore conclude that the β and γ rays together do not supply
more than a small percentage of the total heat emission of radium—a
result which is in accordance with the calculations based on the total
ionization produced by the different types of rays.
=248. Source of the energy.= It has been shown that the heating effect
of radium is closely proportional to the activity measured by the α
rays. Since the activity is generally measured between parallel plates
such a distance apart that most of the α particles are absorbed in the
gas, this result shows that the heating effect is proportional to the
energy of the emitted α particles. The rapid heat emission of radium
follows naturally from the disintegration theory of radio-activity. The
heat is supposed to be derived not from external sources, but from the
internal energy of the radium atom. The atom is supposed to be a complex
system consisting of charged parts in very rapid motion, and in
consequence contains a large store of latent energy, which can only be
manifested when the atom breaks up. For some reason, the atomic system
becomes unstable, and an α particle, of mass about twice that of the
hydrogen atom, escapes, carrying with it its energy of motion. Since the
α particles would be practically absorbed in a thickness of radium of
less than ·001 cm., the greater proportion of the α particles, expelled
from a mass of radium, would be stopped in the radium itself and their
energy of motion would be manifested in the form of heat. The radium
would thus be heated by its own bombardment above the temperature of the
surrounding air. The energy of the expelled α particles probably does
not account for the whole emission of heat by radium. It is evident that
the violent expulsion of a part of the atom must result in intense
electrical disturbances in the atom. At the same time, the residual
parts of the disintegrated atom rearrange themselves to form a
permanently or temporarily stable system. During this process also some
energy is probably emitted, which is manifested in the form of heat in
the radium itself.
The view that the heat emission of radium is due very largely to the
kinetic energy possessed by the expelled α particles is strongly
confirmed by calculations of the magnitude of the heating effect to be
expected on such an hypothesis. It has been shown in section 93 that one
gram of radium bromide emits about 1·44 × 10¹¹ α particles per second.
The corresponding number for 1 gram of radium (Ra = 225) is 2·5 × 10¹¹.
Now it has been calculated from experimental data in section 94, that
the average kinetic energy of the α particles expelled from radium is
5·9 × 10⁻⁶ ergs. Since all of the α particles are absorbed either in the
radium itself or the envelope surrounding it, the total energy of the α
particles emitted per second is 1·5 × 10⁶ ergs. This corresponds to an
emission of energy of about 130 gram calories per hour. Now the observed
heating effect of radium is about 100 gram calories per hour.
Considering the nature of the calculation, the agreement between the
observed and experimental values is as close as would be expected, and
directly supports the view that the heat emission of radium is due very
largely to the bombardment of the radium and containing vessel by the α
particles expelled from its mass.
=249. Heating effect of the radium emanation.= The enormous amount of
heat liberated in radio-active transformations which are accompanied by
the expulsion of α particles is very well illustrated by the case of the
radium emanation.
The heat emission of the emanation released from 1 gram of radium is 75
gram calories per hour at its maximum value. This heat emission is not
due to the emanation alone, but also to its further products which are
included with it. Since the rate of heat emission decays exponentially
with the time to about half value in four days, the total amount of heat
liberated during the life of the emanation from 1 gram of radium is
equal to
$$ \int₀^{\infty} 75 e^{–λt} dt = \frac {75} {λ} $$
= 10,000 gram calories approximately,
since λ = ·0072(hour)⁻¹. Now the volume of the emanation from 1 gram of
radium is about 1 cubic millimetre at standard pressure and temperature
(section 172). Thus 1 cubic centimetre of the emanation would during its
transformation emit 10⁷ gram calories. The heat emitted during the
combination of 1 c.c. of hydrogen and oxygen to form water is about 2
gram calories. The emanation thus gives out during its changes 5 × 10⁶
times as much energy as the combination of an equal volume of hydrogen
and oxygen to form water, although this latter reaction is accompanied
by a larger release of energy than any other known to chemistry.
The production of heat from 1 c.c. of the radium emanation is about 21
gram calories per second. This generation of heat would be sufficient to
heat to redness, if not to melt down, the walls of the glass tube
containing the emanation.
The probable rate of heat emission from 1 gram weight of the emanation
can readily be deduced, assuming that the emanation has about 100 times
the molecular weight of hydrogen. Since 100 c.c. of the emanation would
weigh about 1 gram, the total heat emission from 1 gram of the emanation
is about 10⁹ gram calories.
It can readily be calculated that one pound weight of the emanation
would, at its maximum, radiate energy at the rate of about 10,000
horse-power. This radiation of energy would fall off with the time, but
the total emission of energy during the life of the emanation would
correspond to 60,000 horse-power days.
=250. Heating effects of uranium, thorium, and actinium.= Since the heat
emission of radium is a direct consequence of its bombardment by the α
particles expelled from its mass, it is to be expected that all the
radio-elements which emit α rays should also emit heat at a rate
proportional to their α ray activity.
Since the activity of pure radium is probably about two million times
that of uranium or thorium, the heat emission from 1 gram of thorium or
uranium should be about 5 × 10⁻⁵ gram calories per hour, or about 0·44
gram calories per year. This is a very small rate of generation of heat,
but it should be detectable if a large quantity of uranium or thorium is
employed. Experiments to determine the heating effect of thorium have
been made by Pegram[332]. Three kilograms of thorium oxide, enclosed in
a Dewar bulb, were kept in an ice-bath, and the difference of
temperature between the thorium and ice-bath determined by a set of
iron-constantan thermo-electric couples. The maximum difference of
temperature observed was 0·04° C., and, from the rate of change of
temperature, it was calculated that one gram of thorium oxide liberated
8 × 10⁻⁵ gram calories per hour. A more accurate determination of the
heat emission is in progress, but the results obtained are of the order
of magnitude to be expected.
=251. Energy emitted by a radio-active product.= An important
consequence follows from the fact that the heat emission is a measure of
the energy of the expelled α particles. If each atom of each product
emits α particles, the total emission of energy from 1 gram of the
product can at once be determined. The α particles from the different
products are projected with about the same velocity, and consequently
carry off about the same amount of energy. Now it has been shown that
the energy of each α particle expelled from radium is about 5·9 × 10⁻⁶
ergs. Most of the products probably have an atomic weight in the
neighbourhood of 200. Since there are 3·6 × 10¹⁹ molecules in one cubic
centimetre of hydrogen, it can easily be calculated that there are about
3·6 × 10²¹ atoms in one gram of the product.
If each atom of the product expels one α particle, the total energy
emitted from 1 gram of the matter is about 2 × 10¹⁶ ergs or 8 × 10⁸ gram
calories. The total emission of energy from a product which emits only β
rays is probably about one-hundredth of the above amount.
In this case we have only considered the energy emitted from a single
product independently of the successive products which may arise from
it. Radium, for example, may be considered a radio-active product which
slowly breaks up and gives rise to four subsequent α ray products. The
total heat emission from one gram of radium and products is thus about
five times the above amount, or 4 × 10⁹ gram calories.
The total emission of energy from radium is discussed later in section
266 from a slightly different point of view.
=252. Number of ions produced by an α particle.= In the first edition of
this book it was calculated by several independent methods that 1 gram
of radium emitted about 10¹¹ α particles per second. Since the actual
number has later been determined by measuring the charge carried by the
α rays (section 93) we can, conversely, use this number to determine
with more certainty some of the constants whose values were assumed in
the original calculation.
For example, the total number of ions produced by an α particle in the
gas can readily be determined. The method employed is as follows. 0·484
mgr. of radium bromide was dissolved in water and then spread uniformly
over an aluminium plate. After evaporation, the saturation ionization
current, due to the radium at its minimum activity, was found to be 8·4
× 10⁻⁸ ampere. The plates of the testing vessel were sufficiently far
apart to absorb all the α rays in the gas. The number of α particles
expelled per second into the gas was found experimentally to be 8·7 ×
10⁶. Taking the charge on an ion as 1·13 × 10⁻¹⁹ coulombs (section 36),
the total number of ions produced per second in the gas was 7·5 × 10¹¹.
Thus each α particle on an average produced 86,000 ions in the gas
before it was absorbed.
Now Bragg (section 104) has shown that the α particles from radium at
its minimum activity are stopped in about 3 cms. of air. The results
obtained by him indicate that the ionization of the particles per cm. of
path is less near the radium than some distance away. Assuming, however,
as a first approximation that the ionization is uniform along the path,
the number of ions produced per cm. of path by the α particle is 29,000.
Since the ionization varies directly as the pressure, at a pressure of 1
mm. of mercury the number of ions per unit path would be about 38. Now
Townsend (section 103) found that the maximum number of ions produced
per unit path of air at 1 mm. pressure by an electron in motion was 20,
and in this case a fresh pair of ions was produced at each encounter of
the electron with the molecules in its path. In the present case the α
particle, which has a very large mass compared with the electron,
appears to have a larger sphere of influence than the electron and to
ionize twice as many molecules.
In addition, the α particle produces many more ions per unit path than
an electron moving with the same velocity, for it has been shown
(section 103) that the electron becomes a less efficient ionizer after a
certain velocity is reached. As Bragg (_loc. cit._) has pointed out,
this is to be expected, since the α particle consists of a large number
of electrons and consequently would be a far more efficient ionizer than
an isolated electron. A calculation of the energy required to produce an
ion by an α particle is given in Appendix A.
=253. Number of β particles expelled from one gram of radium.= It is of
importance to compare the total number of β particles expelled from one
gram of radium in radio-active equilibrium, as, theoretically, this
number should bear a definite relation to the total number of α
particles emitted. We have seen that new radium in radio-active
equilibrium contains four products which emit α rays, viz. radium
itself, the emanation, radium A and radium C. On the other hand, β rays
are expelled from only one product, radium C. The same number of atoms
of each of these successive products in equilibrium break up per second.
If the disintegration of each atom is accompanied by the expulsion of
one α particle and, in the case of radium C, also of one β particle, the
number of α particles emitted from radium in radio-active equilibrium
will be four times the number of β particles.
The method employed by Wien to determine the number of β particles
emitted from a known quantity of radium has already been discussed in
section 80. On account of the absorption of some of the β particles in
the radium envelope and in the radium itself, the number found by him is
far too small. It has been shown in section 85 that a number of easily
absorbed β rays are projected from radium, many of which would be
stopped in the radium itself or in the envelope containing it.
In order to eliminate as far as possible the error due to this
absorption, in some experiments made by the writer, the active deposit
obtained from the radium emanation rather than radium itself was used as
a source of β rays. A lead rod, 4 cms. long and 4 mms. in diameter, was
exposed as the negative electrode in a large quantity of the radium
emanation for three hours. The rod was then removed and the γ ray effect
from it immediately measured by an electroscope and compared with the
corresponding γ ray effect from a known weight of radium bromide in
radio-active equilibrium. Since the active deposit contains the product
radium C which alone emits β rays, and, since the intensities of the β
and γ rays are always proportional to each other, the number of β
particles expelled from the lead rod per second is equal to the
corresponding number from the weight of radium bromide which gives the
same γ ray effect as the lead rod.
The rod was then enveloped in a thickness of aluminium foil of ·0053
cms.—a thickness just sufficient to absorb the α rays—and made the
insulated electrode in a cylindrical metal vessel which was rapidly
exhausted to a low pressure. The current in the two directions was
measured at intervals by an electrometer, and, as we have seen in
section 93, the algebraic sum of these currents is proportional to _ne_,
where _n_ is the number of β particles expelled per second from the lead
rod, and _e_ the charge on each particle. The activity of the radium C
decayed with the time, but, from the known curve of decay, the results
could be corrected in terms of the initial value immediately after the
rod was removed from the emanation.
Taking into account that half of the β particles emitted by the active
deposit were absorbed in the radium itself, and reckoning the charge on
the β particle as 1·13 × 10⁻¹⁹ coulombs, two separate experiments gave
7·6 × 10¹⁰ and 7·0 × 10¹⁰ as the total number of β particles expelled
per second from one gram of radium. Taking the mean value, we may
conclude that the total number of β particles expelled per second from
one gram of radium in radio-active equilibrium is about 7·3 × 10¹⁰.
The total number of α particles expelled from one gram of radium at its
minimum activity has been shown to be 6·2 × 10¹⁰ (section 93). The
approximate agreement between these numbers is a strong indication of
the correctness of the theoretical views previously discussed. It is to
be expected that the number of β particles, deduced in this way, will be
somewhat greater than the true value, since the β particles give rise to
a secondary radiation consisting also of negatively charged particles
moving at a high speed. These secondary β particles, arising from the
impact of the β particles on the lead, will pass through the aluminium
screen and add their effect to the primary β rays.
The results, however, indicate that four α particles are expelled from
radium in radio-active equilibrium for each β particle and thus confirm
the theory of successive changes.
Footnote 325:
_Phil. Trans._ A. p. 25, 1901.
Footnote 326:
P. Curie and Laborde, _C. R._ 136, p. 673, 1903.
Footnote 327:
Runge and Precht, _Sitz. Ak. Wiss. Berlin_, No. 38, 1903.
Footnote 328:
P. Curie, Société de Physique, 1903.
Footnote 329:
Rutherford and Barnes, _Nature_, Oct. 29, 1903. _Phil. Mag._ Feb.
1904.
Footnote 330:
Paschen, _Phys. Zeit._ Sept. 15, 1904.
Footnote 331:
Rutherford and Barnes, _Nature_, Dec. 18, 1904; _Phil. Mag._ May,
1905.
Footnote 332:
Pegram, _Science_, May 27, 1904.