TRANSFORMATION PRODUCTS OF RADIUM.
=215. Radio-activity of radium.= Notwithstanding the enormous difference
in their relative activities, the radio-activity of radium presents many
close analogies to that of thorium and actinium. Both substances give
rise to emanations which in turn produce “excited activity” on bodies in
their neighbourhood. Radium, however, does not give rise to any
intermediate product between the element itself and the emanation it
produces, or in other words there is no product in radium corresponding
to Th X in thorium.
Giesel first drew attention to the fact that a radium compound gradually
increased in activity after preparation, and only reached a constant
value after a month’s interval. If a radium compound is dissolved in
water and boiled for some time, or a current of air drawn through the
solution, on evaporation it is found that the activity has been
diminished. The same result is observed if a solid radium compound is
heated in the open air. This loss of activity is due to the removal of
the emanation by the process of solution or heating. Consider the case
of a radium compound which has been kept for some time in solution in a
shallow vessel, exposed to the open air, and then evaporated to dryness.
The emanation which, in the state of solution, was removed as fast as it
was formed, is now occluded, and, together with the active deposit which
it produces, adds its radiations to that of the original radium. The
activity will increase to a maximum value when the rate of production of
fresh emanation balances the rate of change of that already produced.
If now the compound is again dissolved or heated, the emanation escapes.
Since the active deposit is not volatile and is insoluble in water, it
is not removed by the process of solution or heating. Since, however,
the parent matter is removed, the activity due to the active deposit
will immediately begin to decay, and in the course of a few hours will
have almost disappeared. The activity of the radium measured by the α
rays is then found to be about 25 per cent. of its original value. This
residual activity of radium, consisting entirely of α rays, is
non-separable, and has not been further diminished by chemical or
physical means. Rutherford and Soddy[314] examined the effect of
aspiration for long intervals through a radium chloride solution. After
the first few hours the activity was found to be reduced to 25 per
cent., and further aspiration for three weeks did not produce any
further diminution. The radium was then evaporated to dryness, and the
rise of its activity with time determined. The results are shown in the
following table. The final activity in the second column is taken as one
hundred. In column 3 is given the percentage proportion of the activity
recovered.
Time in Activity Percentage
days Activity
recovered
0 25·0 0
0·70 33·7 11·7
1·77 42·7 23·7
4·75 68·5 58·0
7·83 83·5 78·0
16·0 96·0 95·0
21·0 100·0 100·0
The results are shown graphically in Fig. 85.
The decay curve of the radium emanation is shown in the same figure. The
curve of recovery of the lost activity of radium is thus analogous to
the curves of recovery of uranium and thorium which have been freed from
the active products Ur X and Th X respectively. The intensity _I_{t}_ of
the recovered activity at any time is given by
$$ \frac {I_t} {I₀} = 1 − e^{–λt} $$,
where _I₀_ is the final value, and λ is the radio-active constant of the
emanation. The decay and recovery curves are complementary to one
another.
[Illustration: Fig. 85.]
Knowing the rate of decay of activity of the radium emanation, the
recovery curve of the activity of radium can thus at once be deduced,
provided all of the emanation formed is occluded in the radium compound.
When the emanation is removed from a radium compound by solution or
heating, the activity _measured by the_ β _rays_ falls almost to zero,
but increases in the course of a month to its original value. The curve
showing the rise of β and γ rays with time is practically identical with
the curve, Fig. 85, showing the recovery of the lost activity of radium
measured by the α rays. The explanation of this result lies in the fact
that the β and γ rays from radium only arise from the active deposit,
and that the non-separable activity of radium gives out only α rays. On
removal of the emanation, the activity of the active deposit decays
nearly to zero, and in consequence the β and γ rays almost disappear.
When the radium is allowed to stand, the emanation begins to accumulate,
and produces in turn the active deposit, which gives rise to β and γ
rays. The amount of β and γ rays (allowing for a period of retardation
of a few hours) will then increase at the same rate as the activity of
the emanation, which is continuously produced from the radium.
=216. Effect of escape of emanation.= If the radium allows some of the
emanation produced to escape into the air, the curve of recovery will be
different from that shown in Fig. 85. For example, suppose that the
radium compound allows a constant fraction α of the amount of emanation,
present in the compound at any time, to escape per second. If _n_ is the
number of emanation particles present in the compound at the time _t_,
the number of emanation particles changing in the time _dt_ is λ_ndt_,
where λ is the constant of decay of activity of the emanation. If _q_ is
the rate of production of emanation particles per second, the increase
of the number _dn_ in the time _dt_ is given by
_dn_ = _qdt_ − λ_ndt_ − α_ndt_,
or _dn_
----- = _q_ − (λ + α)_n_.
_dt_
The same equation is obtained when no emanation escapes, with the
difference that the constant λ + α is replaced by λ. When a steady state
is reached, _dn_/_dt_ is zero, and the maximum value of _n_ is equal to
_q_/(λ + α).
If no escape takes place, the maximum value of _n_ is equal to _q_/λ.
The escape of emanation will thus lower the amount of activity recovered
in the proportion λ/(λ + α). If _n₀_ is the final number of emanation
particles stored up in the compound, the integration of the above
equation gives
$$ \frac {n} {n₀} = 1 − e^{-(λ + \alpha) t} $$ .
The curve of recovery of activity is thus of the same general form as
the curve when no emanation escapes, but the constant λ is replaced by λ
+ α.
For example, if α = λ = ¹⁄₄₆₃₀₀₀, the equation of rise of activity is
given by
$$ \frac {n} {n₀} = 1 − e^{−2λ t} $$,
and, in consequence, the increase of activity to the maximum will be far
more rapid than in the case of no escape of emanation.
A very slight escape of emanation will thus produce large alterations
both in the final maximum and in the curve of recovery of activity.
A number of experiments have been described by Mme Curie in her _Thèse
présentée à la Faculté des Sciences de Paris_ on the effect of solution
and of heat in diminishing the activity of radium. The results obtained
are in general agreement with the above view, that 75 per cent. of the
activity of radium is due to the emanation and the excited activity it
produces. If the emanation is wholly or partly removed by solution or
heating, the activity of the radium is correspondingly diminished, but
the activity of the radium compound is spontaneously recovered owing to
the production of fresh emanation. A state of radio-active equilibrium
is reached, when the rate of production of fresh emanation balances the
rate of change in the emanation stored up in the compound. The
differences observed in the rate of recovery of radium under different
conditions were probably due to variations in the rate of escape of the
emanation.
=217.= It has been shown in section 152 that the emanation is produced
at the same rate in the solid as in the solution, and all the results
obtained point to the conclusion that the emanation is produced from
radium at a constant rate, which is independent of physical conditions.
Radium, like thorium, shows a non-separable activity of 25 per cent. of
the maximum activity, and consisting entirely of α rays. The β and γ
rays arise only from the active deposit. The emanation itself (section
156) gives out only α rays. These results thus admit of the explanation
given in the case of thorium (section 136). The radium atoms break up at
a constant rate with the emission of α particles. The residue of the
radium atom becomes the atom of the emanation. This in turn is unstable
and breaks up with the expulsion of an α particle. The emanation is half
transformed in four days. We have seen that this emanation gives rise to
an active deposit. The results obtained up to this stage are shown
diagrammatically below.
α _particle_ α _particle_
/ /
/ /
RADIUM ATOM ——> ATOM OF EMANATION ——> ATOM OF ACTIVE DEPOSIT
=218. Analysis of the active deposit from radium.= We have seen in
chapter VIII that the excited activity produced on bodies, by the action
of the radium emanation, is due to a thin film of active matter
deposited on the surface of bodies. This active deposit is a product of
the decomposition of the radium emanation, and is not due to any action
of the radiations on the surface of the matter.
The curves showing the variation of the excited activity with time are
very complicated, depending not only upon the time of exposure in the
presence of the emanation, but also upon the type of radiation used for
measurement. The greater portion of the activity of this deposit dies
away in the course of 24 hours, but a very small fraction still remains,
which then changes very slowly.
It will be shown in this chapter that at least six successive
transformations occur in the active deposit. The matter initially
produced from the emanation is called radium A, and the succeeding
products B, C, D, E, F. The equations expressing the quantity of A, B,
C,...... present at any time are very complicated, but the comparison of
theory with experiment may be much simplified by temporarily
disregarding some unimportant terms: for example, the products A, B, C
are transformed at a very rapid rate compared with D. The activity due
to D + E + F is, in most cases, negligible compared with that of A or C,
being usually less than ¹⁄₁₀₀₀₀₀ of the initial activity observed for A
or C. The analysis of the active deposit of radium may thus be
conveniently divided into two stages:
(1) Analysis of the deposit of rapid change, which is mainly
composed of radium A, B, and C;
(2) Analysis of the deposit of slow change, which is composed of
radium D, E, and F.
=219. Analysis of the deposit of rapid change.= In the experiments
described below, a radium solution was placed in a closed glass vessel.
The emanation then collected in the air space above the solution. The
rod, to be made active, was introduced through an opening in the stopper
and exposed in the presence of the emanation for a definite interval. If
the decay was to be measured by the α rays, the rod was made the central
electrode in a cylindrical vessel such as is shown in Fig. 18. A
saturating voltage was applied, and the current between the cylinders
measured by an electrometer. If a very active rod is to be tested, a
sensitive galvanometer can be employed, but, in such a case, a large
voltage is required to produce saturation. A slow current of dust-free
air was continuously circulated through the cylinder, in order to remove
any emanation that may have adhered to the rod. For experiments on the β
and γ rays, it was found advisable to use an electroscope, such as is
shown in Fig. 12, instead of an electrometer. For measurements with the
γ rays, the active rod was placed under the electroscope, and before
entering the vessel the rays passed through a sheet of metal of
sufficient thickness to absorb all the α rays. For measurements with the
γ rays, the electroscope was placed on a lead plate 0·6 cms. thick, and
the active rod placed under the lead plate. The α and β rays were
completely stopped by the lead, and the discharge in the electroscope
was then due to the γ rays alone. The electroscope is very advantageous
for measurements of this character, and accurate observations can be
made simply and readily.
The curve of decay of activity, measured by the α rays, for an exposure
of 1 minute in the presence of the radium emanation is shown in Fig. 86,
curve _BB_.
The curve exhibits three stages:—
(1) A rapid decay in the course of 15 minutes to less than 10 per
cent. of the value immediately after removal;
(2) A period of 30 minutes in which the activity varies very little;
(3) A gradual decrease almost to zero.
The initial drop decays very approximately according to an exponential
law with the time, falling to half value in about 3 minutes. Three or
four hours after removal the activity again decays according to an
exponential law with the time, falling to half value in about 28
minutes. The family of curves obtained for different times of exposure
have already been shown in Fig. 67. These results thus indicate:—
(1) An initial change in which half the matter is transformed in 3
minutes;
(2) A final change in which half the matter is transformed in 28
minutes.
[Illustration: Fig. 86.]
Before considering the explanation of the intermediate portion of the
curve further experimental results will be considered.
The curve of decay of the excited activity for a long exposure (24
hours) is shown graphically in Fig. 86, curve _AA_. There is at first a
rapid decrease for the first 15 minutes to about 50 per cent. of the
initial value, then a slower decay, and, after an interval of about 4
hours, a gradual decay nearly to zero, according to an exponential law
with the time, falling to half value in 28 minutes.
The curves of variation with time of the excited activity when measured
by the β _rays_ are shown graphically in Figs. 87 and 88.
Fig. 87 is for a short exposure of 1 minute. Fig. 88 shows the decay for
a long exposure of about 24 hours.
[Illustration: Fig. 87.]
The curves obtained for the β rays are quite different from those
obtained for the α rays. For a short exposure, the activity measured by
the β rays is at first small, then passes through a maximum about 36
minutes after removal. There is then a gradual decrease, and after
several hours the activity decays according to an exponential law,
falling, as in the other cases, to half value in 28 minutes.
The curve shown in Fig. 88 for the β rays is very similar in shape to
the corresponding curve, Fig. 86, curve _AA_, for the α rays, with the
exception that the rapid initial drop observed for the α-ray curve is
quite absent. The later portions of the curve are similar in shape, and,
disregarding the first 15 minutes after removal, the activity decays at
exactly the same rate in both cases.
The curves obtained by means of the γ rays are identical with those
obtained for the β rays. This shows that the β and γ rays always occur
together and in the same proportion.
For increase of the time of exposure from 1 minute to 24 hours the
curves obtained are intermediate in shape between the two representative
limiting curves, Figs. 87 and 88. Some of these curves have already been
shown in Fig. 68.
[Illustration: Fig. 88.]
=220. Explanation of the curves.= It has been pointed out that the rapid
initial drop for curves _A_ and _B_, Fig. 86, is due to a change giving
rise to α rays, in which half of the matter is transformed in about 3
minutes. The absence of the drop in the corresponding curves, when
measured by the β rays, shows that the first 3-minute change does not
give rise to β rays; for if it gave rise to β rays, the activity should
fall off at the same rate as the corresponding α-ray curve.
It has been shown that the activity several hours after removal decays
in all cases according to an exponential law with the time, falling to
half value in about 28 minutes. This is the case whether for a short or
long exposure, or whether the activity is measured by the α, β, or γ
rays. This indicates that the final 28-minute change gives rise to all
three types of rays.
It will be shown that these results can be completely explained on the
supposition that three successive changes occur in the deposited matter
of the following character[315]:—
(1) A change of the matter A initially deposited in which half is
transformed in about 3 minutes. This gives rise only to α rays.
(2) A second “rayless” change in which half the matter B is
transformed in 21 minutes.
(3) A third change in which half the matter C is transformed in 28
minutes. This gives rise to α, β, and γ rays.
=221. Analysis of the β-ray curves=. The analysis of the changes is much
simplified by temporarily disregarding the first 3-minute change. In the
course of 6 minutes after removal, three quarters of the matter A has
been transformed into B and 20 minutes after removal all but 1 per cent.
has been transformed. The variation of the amount of matter B or C
present at any time agrees more closely with the theory, if the first
change is disregarded altogether. A discussion of this important point
is given later (section 228).
The explanation of the β-ray curves (see Figs. 87 and 88), obtained for
different times of exposure, will be first considered. For a very short
exposure, the activity measured by the β rays is small at first, passes
through a maximum about 36 minutes later, and then decays steadily with
the time.
The curve shown in Fig. 87 is very similar in general shape to the
corresponding thorium and actinium curves. It is thus necessary to
suppose that the change of the matter B into C does not give rise to β
rays, while the change of C into D does. In such a case the activity
(measured by the β rays) is proportional to the amount of C present.
Disregarding the first rapid change, the activity _I_{t}_ at any time
_t_ should be given by an equation of the same form (section 207) as for
thorium and actinium, viz.,
$$ \frac {I_t} {I_T} = \frac {e^{–λ_3 t} − e^{–λ_2 t}}
{e^{–λ_3 T} − e^{–λ_2 T}} $$,
where _I_{T}_ is the maximum activity observed, which is reached after
an interval _T_. Since the activity finally decays according to an
exponential law (half value in 28 minutes), one of the values of λ is
equal to 4·13 × 10⁻⁴. As in the case of thorium and actinium, the
experimental curves do not allow us to settle whether this value of λ is
to be given to λ₂ or λ₃. From other data (see section 226) it will be
shown later that it must refer to λ₃. Thus λ₃ = 4·13 × 10⁻⁴ (sec)⁻¹.
The experimental curve agrees very closely with theory if λ₂ = 5·38 ×
10⁻⁴ (sec)⁻¹.
The agreement between theory and experiment is shown by the table given
below. The maximum value _I_{T}_ (which is taken as 100) is reached at a
time _T_ = 36 minutes.
In order to obtain the β-ray curve, the following procedure was adopted.
A layer of thin aluminium was placed inside a glass tube, which was then
exhausted. A large quantity of radium emanation was then suddenly
introduced by opening a stop-cock communicating with the emanation
vessel, which was at atmospheric pressure. The emanation was left in the
tube for 1·5 minutes and then was rapidly swept out by a current of air.
The aluminium was then removed and was placed under an electroscope,
such as is shown in Fig. 12. The α rays from the aluminium were cut off
by an interposed screen of aluminium ·1 mm. thick. The time was reckoned
from a period of 45 seconds after the introduction of the emanation.
Time in Theoretical Observed
minutes value of value of
activity activity
0 0 0
10 58·1 55
20 88·6 86
30 97·3 97
36 100 100
40 99·8 99·5
50 93·4 92
60 83·4 82
80 63·7 61·5
100 44·8 42·5
120 30·8 29
There is thus a good agreement between the calculated and observed
values of the activity measured by the β rays.
The results are satisfactorily explained if it is supposed:—
(1) That the change B into C (half transformed in 21 minutes) does
not give rise to β rays;
(2) That the change C into D (half transformed in 28 minutes) gives
rise to β rays.
=222.= These conclusions are very strongly supported by observations of
the decay measured by the β rays for a long exposure. The curve of decay
is shown in Fig. 88 and Fig. 89, curve I.
[Illustration: Fig. 89.]
P. Curie and Danne made the important observation that the curve of
decay _C_, corresponding to that shown in Fig. 88, for a long exposure,
could be accurately expressed by an empirical equation of the form
$$ \frac {I_t} {I₀} = ae^{–λ_3 t} − (a − 1) e^{–λ_2 t} $$,
where λ₂ = 5·38 × 10⁻⁴ (sec)⁻¹ and λ₃ = 4·13 × 10⁻⁴ (sec)⁻¹, and α =
4·20 is a numerical constant.
I have found that within the limit of experimental error this equation
represents the decay of excited activity of radium for a long exposure,
measured by the β rays. The equation expressing the decay of activity,
measured by the α rays, differs considerably from this, especially in
the early part of the curve. Several hours after removal the activity
decays according to an exponential law with the time, decreasing to half
value in 28 minutes. This fixes the value of λ₃. The constant α and the
value of λ₂ are deduced from the experimental curve by trial. Now we
have already shown (section 207) that in the case of the active deposit
from thorium, where there are two changes of constants λ₂ and λ₃, in
which only the second change gives rise to a radiation, the intensity of
the radiation is given by
$$ \frac {I_t} {I₀} = \frac {λ_2} {λ_2 − λ_3}
e^{–λ_3 t} − \frac {λ_3} {λ_2 − λ_3}
e^{–λ_2 t} $$
for a long time of exposure (see equation 8, section 198). This is an
equation of the same form as that found experimentally by Curie and
Danne. On substituting the values λ₂, λ₃ found by them,
$$ \frac {λ_2} {λ_2 − λ_3} = 4\cdot3 $$, and
$$ \frac {λ_1} {λ_1 − λ_3} = 3\cdot3 $$ .
Thus the theoretical equation agrees in form with that deduced from
observation, and the values of the numerical constants are also closely
concordant. If the first as well as the second change gave rise to a
radiation, the equation would be of the same general form, but the value
of the numerical constants would be different, the values depending upon
the ratio of the ionization in the first and second changes. If, for
example, it is supposed that both changes give out β rays in equal
amounts, it can readily be calculated that the equation of decay would
be
$$ \frac {I_t} {I₀} = \frac {\cdot5λ_2} {λ_2 − λ_3}
e^{–λ_3 t} − \cdot5 (\frac {λ_3} {λ_2 − λ_3} -
1) e^{–λ_2 t} $$ .
Taking the values of λ₂ and λ₃ found by Curie, the numerical factor
$$ e^{–λ_2 t} $$
becomes 2·15 instead of 4·3 and 1·15 instead of 3·3. The theoretical
curve of decay in this case would be readily distinguishable from the
observed curve of decay. The fact that the equation of decay found by
Curie and Danne involves the necessity of an initial rayless change can
be shown as follows:—
Curve I (Fig. 89) shows the experimental curve. At the moment of removal
of the body from the emanation (disregarding the initial rapid change),
the matter must consist of both B and C. Consider the matter which
existed in the form C at the moment of removal. It will be transformed
according to an exponential law, the activity falling by one-half in 28
minutes. This is shown in curve II. Curve III represents the difference
between the ordinates of curves I and II. It will be seen that it is
identical in shape with the curve (Fig. 87) showing the variation of the
activity for a short exposure, measured by the β rays. It passes through
a maximum at the same time (about 36 minutes). The explanation of such a
curve is only possible on the assumption that the first change is a
rayless one. The ordinates of curve III express the activity added in
consequence of the change of the matter B, present after removal, into
the matter C. The matter B present gradually changes into C, and this,
in its change to D, gives rise to the radiation observed. Since the
matter B alone is considered, the variation of activity with time due to
its further changes, shown by curve III, should agree with the curve
obtained for a short exposure (see Fig. 87), and this, as we have seen,
is the case.
The agreement between theory and experiment is shown in the following
table. The first column gives the theoretical curve of decay for a long
exposure deduced from the equation
$$ \frac {I_t} {I₀} = \frac {λ_2} {λ_2 − λ_3}
e^{–λ_3 t} − \frac {λ_3} {λ_2 − λ_3}
e^{–λ_2 t} $$
taking the value of λ₂ = 5·38 × 10⁻⁴ and λ₃ = 4·13 × 10⁻⁴.
Time in Calculated Observed
minutes values values
0 100 100
10 96·8 97·0
20 89·4 88·5
30 78·6 77·5
40 69·2 67·5
50 59·9 57·0
60 49·2 48·2
80 34·2 33·5
100 22·7 22·5
120 14·9 14·5
The second column gives the observed activity (measured by means of an
electroscope) for a long exposure of 24 hours in the presence of the
emanation.
In cases where a steady current of air is drawn over the active body,
the observed values are slightly lower than the theoretical. This is
probably due to a slight volatility of the product radium B at ordinary
temperatures.
[Illustration: Fig. 90.]
=223. Analysis of the α-ray curves=. The analysis of the decay curves of
the excited activity of radium, measured by the α rays, will now be
discussed. The following table shows the variation of the intensity of
the radiation after a long exposure in the presence of the radium
emanation. A platinum plate was made active by exposure for several days
in a glass tube containing a large quantity of emanation. The active
platinum after removal was placed on the lower of two parallel insulated
lead plates, and a saturating electromotive force of 600 volts was
applied. The ionization current was sufficiently large to be measured by
means of a sensitive high-resistance galvanometer, and readings were
taken as quickly as possible after removal of the platinum from the
emanation vessel. The initial value of the current (taken as 100) was
deduced by continuing the curves backwards to meet the vertical axis
(see Fig. 90), and was found to be 3 × 10⁻⁸ ampere.
Time in Current
minutes
0 100
2 80
4 69·5
6 62·4
8 57·6
10 52·0
15 48·4
20 45·4
30 40·4
40 35·6
50 30·4
60 25·4
80 17·4
100 11·6
120 7·6
These results are shown graphically in the upper curve of Fig. 90. The
initial rapid decrease is due to the decay of the activity of the matter
A. If the slope of the curve is produced backwards from a time 20
minutes after removal, it cuts the vertical axis at about 50. The
difference between the ordinates of the curves _A_ + _B_ + _C_ and _LL_
at any time is shown in the curve _AA_. The curve _AA_ represents the
activity at any time supplied by the change in radium _A_. The curve
_LL_ starting from the vertical axis is identical with the curve already
considered, representing the decay of activity measured by the β rays
for a long exposure (see Fig. 88).
Time in Calculated Observed
minutes value of value of
activity activity
0 100 100
10 96·8 97·0
20 89·4 89·2
30 78·6 80·8
40 69·2 71·2
50 59·9 60·8
60 49·2 50·1
80 34·2 34·8
100 22·7 23·2
120 14·9 15·2
This is shown by the agreement of the numbers in the above table. The
first column in the table above gives the theoretical values of the
activity deduced from the equation
$$ \frac {I_t} {I₀} = \frac {λ_2} {λ_2 − λ_3}
e^{–λ_3 t} − \frac {λ_3} {λ_2 − λ_3}
e^{–λ_2 t} $$
for the values of λ₂, λ₃ previously employed. The second column gives
the observed values of the activity deduced from the decay curve _LL_.
The close agreement of the curve _LL_ with the theoretical curve deduced
on the assumption that there are two changes, the first of which does
not emit rays, shows that the change of radium B into C does not emit α
rays. In a similar way, as in the curve I, Fig. 89, the curve _LL_ may
be analysed into its two components represented by the two curves _CC_
and _BB_. The curve _CC_ represents the activity supplied by the matter
C present at the moment of removal. The curve _BB_ represents the
activity resulting from the change of B into C and is identical with the
corresponding curve in Fig. 89. Using the same line of reasoning as
before, we may thus conclude that the change of B into C is not
accompanied by α rays. It has already been shown that it does not give
rise to β rays, and the identity of the β and γ-ray curves shows that it
does not give rise to γ rays. The change of B into C is thus a “rayless”
change, while the change of C into D gives rise to all three kinds of
rays.
An analysis of the decay of the excited activity of radium thus shows
that three distinct rapid changes occur in the matter deposited, viz.:—
(1) The matter A, derived from the change in the emanation, is half
transformed in 3 minutes and is accompanied by α rays alone;
(2) The matter B is half transformed in 21 minutes and gives rise to
no ionizing rays;
(3) The matter C is half transformed in 28 minutes and is
accompanied by α, β, and γ rays;
(4) A fourth very slow change will be discussed later.
=224. Equations representing the activity curves.= The equations
representing the variation of activity with time are for convenience
collected below, where λ₁ = 3·8 × 10⁻³, λ₂ = 5·38 × 10⁻⁴, λ₃ = 4·13 ×
10⁻⁴:—
(1) Short exposure: activity measured by β rays,
$$ \frac {I_t} {I_T} = 10\cdot3 (e^{–λ_3 t} − e^{–λ_2 t}) $$
where _I_{T}_ is the maximum value of the activity;
(2) Long exposure: activity measured by β rays,
$$ \frac {I_t} {I₀} = 4\cdot3 (e^{–λ_3 t} − 3\cdot3 e^{–λ_2
t}) $$,
where _I₀_ is the initial value;
(3) Any time of exposure _T_: activity measured by the β rays,
$$ \frac {I_t} {I₀} = \frac {ae^{–λ_3 t} − be^{–λ_2 t}} {a −
b} $$,
where
$$ a = \frac {1 − e^{–λ_3 T}} {λ_3} $$,
$$ b = \frac {1 − e^{–λ_2 T}} {λ_2} $$;
(4) Activity measured by α rays: long time of exposure,
$$ \frac {I_t} {I₀} = \frac {1}{2} e^{–λ_1 t} + \frac {1}{2}
(4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ .
The equations for the α rays for any time of exposure can be readily
deduced, but the expressions are somewhat complicated.
[Illustration: Fig. 91.]
=225. Equations of rise of excited activity.= The curves expressing the
gradual increase to a maximum of the excited activity produced on a body
exposed in the presence of a constant amount of emanation are
complementary to the curves of decay for a long exposure. The sum of the
ordinates of the rise and decay curves is at any time a constant. This
follows necessarily from the theory and can also be deduced simply from
_à priori_ considerations. (See section 200.)
The curves of rise and decay of the excited activity for both the α and
β rays are shown graphically in Fig. 91. The thick line curves are for
the α rays. The difference between the shapes of the decay curves when
measured by the α or β rays is clearly brought out in the figure. The
equations representing the rise of activity to a maximum are given
below.
For the β and γ rays,
$$ \frac {I_t} {I_{max}} = 1 − (4\cdot3 e^{–λ_3 t} − 3\cdot3
e^{–λ_2 t}) $$ .
For the α rays,
$$ \frac {I_t} {I_{max}} = 1 − \frac {1}{2} e^{–λ_1 t} − \frac
{1}{2} (4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ .
=226. Effect of temperature.= We have so far not considered the evidence
on which the 28-minute rather than the 21-minute change is supposed to
take place in the matter C. This evidence has been supplied by some
recent important experiments of P. Curie and Danne[316] on the
volatilization of the active matter deposited by the emanation. Miss
Gates[317] showed that this active matter was volatilized from a
platinum wire above a red heat and deposited on the surface of a cold
cylinder surrounding the wire. Curie and Danne extended these results by
subjecting an active platinum wire _for a short time_ to the action of
temperatures varying between 15° C. and 1350° C., and then examining at
room temperatures the decay curves not only for the active matter
remaining on the wire, but also for the volatilized part. They found
that the activity of the distilled part always increased after removal,
passed through a maximum, and finally decayed according to an
exponential law to half value in 28 minutes. At a temperature of about
630° C. the active matter left behind on the wire decayed at once
according to an exponential law, falling to half value in 28 minutes. P.
Curie and Danne showed that the matter B is much more volatile than C.
The former is completely volatilized at about 600° C., while the latter
is not completely volatilized even at a temperature of 1300° C. The fact
that the matter C, left behind when B is completely volatilized, decays
at once to half value in 28 minutes shows that the matter C itself and
not B is half transformed in 28 minutes.
Curie and Danne also found that the rate of decay of the active matter
varied with the temperature to which the platinum wire had been
subjected. At 630° C. the rate of decay was normal, at 1100° C. the
activity fell to half value in about 20 minutes, while at 1300° C. it
fell to about half value in about 25 minutes.
I have repeated the experiments of Curie and Danne and obtained very
similar results. It was thought possible that the measured rate of decay
observed after heating might be due to a permanent increase in the rate
of volatilization of C at ordinary temperatures. This explanation,
however, is not tenable, for it was found that the activity decreased at
the same rate whether the activity of the wire was tested in a closed
tube or in the open with a current of air passed over it.
These results are of great importance, for they indicate that the rate
of change of the product C is not a constant, but is affected by
differences of temperature. This is the first case where temperature has
been shown to exert an appreciable influence on the rate of change of
any radio-active product.
=227. Volatility of radium B at ordinary temperature.= Miss Brooks[318]
has observed that a body, made active by exposure to the radium
emanation, possesses the power of exciting secondary activity on the
walls of a vessel in which it is placed. This activity was usually about
¹⁄₁₀₀₀ of the whole, but the amount was increased to about ¹⁄₂₀₀ if the
active wire was washed in water and dried over a gas flame—the method
often adopted to free the wire of any trace of the radium emanation.
This effect of producing activity was most marked immediately after
removal of the wire from the emanation, and was almost inappreciable ten
minutes afterwards.
The effect was particularly noticeable in some experiments with a copper
plate, which was made active by leaving it a short time in a solution of
the active deposit from radium. This active solution was obtained by
placing an active platinum wire in dilute hydrochloric acid. On placing
the copper plate in a testing vessel for a few minutes, and then
removing it, activity was observed on the walls of the vessel amounting
to about one per cent. of the activity of the copper plate.
It was found that this effect was not due to the emission of an
emanation from the active body, but must be ascribed to a slight
volatility of radium B at ordinary temperatures. This was proved by
observations on the variation of the activity of the matter deposited on
the walls of the vessel. The activity was small at first, but rose to a
maximum after about 30 minutes, and then decayed with the time. The
curve of rise was very similar to that shown in Fig. 87, and shows that
the inactive matter radium B was carried to the walls and there changed
into C, which gave rise to the radiation observed.
The product B only escapes from the body for a short time after removal.
This is a strong indication that its apparent volatility is connected
with the presence of the rapidly changing product radium A. Since A
breaks up with an expulsion of an α particle, some of the residual atoms
constituting radium B may acquire sufficient velocity to escape into the
gas, and are then transferred by diffusion to the walls of the vessel.
Miss Brooks observed that the activity was not concentrated on the
negative electrode in an electric field but was diffused uniformly over
the walls of the vessel. This observation is of importance in
considering the explanation of the anomalous effects exhibited by the
active deposit of radium, which will be discussed in the following
section.
=228. Effect of the first rapid change.= We have seen that the law of
decay of activity, measured by the β or γ rays, can be explained very
satisfactorily if the first 3-minute change is disregarded. The full
theoretical examination of the question given in sections 197 and 198
and the curves of Figs. 72 and 73 show, however, that the presence of
the first change should exercise an effect of sufficient magnitude to be
detected in measurements of the activity due to the succeeding changes.
The question is of great interest, for it involves the important
theoretical point whether the substances A and B are produced
independently of one another, or whether A is the parent of B. In the
latter case, the matter A which is present changes into B, and, in
consequence, the amount of B present after A is transformed should be
somewhat greater than if B were produced independently. Since the change
of A is fairly rapid, the effect should be most marked in the early part
of the curve.
In order to examine this point experimentally, the curve of rise of
activity, measured by the β rays, was determined immediately after the
introduction of a large quantity of the radium emanation into a closed
vessel. The curve of decay of activity on a body for a long exposure
after removal of the emanation, and the rise of activity after the
introduction of the emanation, are in all cases complementary to one
another. While, however, it is difficult to measure with certainty
whether the activity has fallen in a given time, for example, from 100
to 99 or 98·5, it is easy to be sure whether the corresponding rise of
activity in the converse experiment is 1 or 1·5 per cent. of the final
amount. Fig. 92, curve I, shows the rise of activity (measured by the β
rays) obtained for an interval of 20 minutes after the introduction of
the emanation. The ordinates represent the percentage amount of the
final activity regained at any time.
Curve III shows the theoretical curve obtained on the assumption that A
is a parent of B. This curve is calculated from equation (9) discussed
in section 198, and λ₁, λ₂, λ₃ are the values previously found.
Curve II gives the theoretical activity at any time on the assumption
that the substances A and B arise independently. This is calculated from
an equation of the same form as (8), section 198.
[Illustration: Fig. 92.]
It is seen that the experimental results agree best with the view that A
and B arise independently. Such a conclusion, however, is of too great
importance to be accepted before examining closely whether the
theoretical conditions are fulfilled in the experiments. In the first
place, it is assumed that the carriers which give rise to excited
activity are deposited on the surface of the body, to be made active
immediately after their formation. There is some evidence, however, that
some of these carriers exist for a considerable interval in the gas
before their deposit on the body. For example, it is found that if a
body is introduced for a short interval, about 1 minute, into a vessel
containing the radium emanation, which has remained undisturbed for
several hours, the activity after the first rapid decay (see Fig. 86,
curve _B_) is in much greater proportion than if an electric field had
been acting for some time previously. This result indicates that the
carriers of B and C both collect in the gas and are swept to the
electrode when an electric field is applied. I have also observed that
if radium emanation, which has stood undisturbed for some time, is swept
into a testing vessel, the rise curve is not complementary to the decay
curve, but indicates that a large amount of radium B and C was present
with the emanation. The experiments of Miss Brooks, previously referred
to, indicate that radium B does not obtain a charge and so will remain
in the gas. Dr Bronson, working in the laboratory of the writer, has
obtained evidence that a large amount of radium D remains in the gas
even in a strong electric field. If the matter B exists to some extent
in the gas, the difference between the theoretical curves for three
successive changes would be explained; for, in transferring the
emanation to another vessel, the matter B mixed with it would commence
at once to change into C and give rise to a part of the radiation
observed.
The equal division of the activity between the products A and C (see
Fig. 90) supports the view that C is a product of A, for when
radio-active equilibrium is reached, the number of particles of A
changing per second is equal to the number of B or C changing per
second. If each atom of A and C expels an α particle of the same mass
and with the same average velocity, the activity due to the matter A
should be equal to that due to the matter C; and this, as we have seen,
is the case.
While it is a matter of great difficulty to give a definite experimental
proof that radium A and B are consecutive products, I think there is
little doubt of its correctness. Accurate determinations of the curves
of rise and decay may throw further light on the complicated processes
which undoubtedly occur between the breaking up of the atoms of the
emanation and the appearance of the active deposit on the electrodes.
=229. Relative activity supplied by the α-ray products of radium.= There
are four products in radium which give out α rays, viz. radium itself,
the emanation, radium A and C. If these products are in radio-active
equilibrium, the same number of particles of each product are
transformed per second and, if each atom breaks up with the emission of
one α particle, the number of α particles expelled per second should be
the same for each product.
Since, however, the α particles from the different products are not
projected with the same velocity, the activity, measured by the
ionization current in the usual manner, will not be the same for all
products. The activity, when measured by the saturation current between
parallel plates at sufficient distance apart to absorb all the α rays in
the gas, is proportional to the energy of the α particles escaping into
the gas.
It has been shown that the minimum activity of radium after removal of
the emanation, measured by the α rays, is 25 per cent. of the maximum
value. The remaining 75 per cent. is due to the α particles from the
other products. Now the activity supplied by radium A and C is nearly
the same (section 228). If the emanation is introduced into a
cylindrical vessel about 5 cms. in diameter, the activity increases to
about twice its initial value owing to the deposit of radium A and C on
the surface of the vessel. This shows that the activity of the emanation
is of about the same magnitude as that supplied by radium A or C, but an
accurate comparison is beset with difficulty, for the emanation is
distributed throughout the gas, while radium A and C are deposited on
the walls of the vessel. In addition, the relative absorption of the
emanation compared with that of radium A and C is not known.
The writer has made some experiments on the decrease of activity of
radium immediately after heating to a sufficient temperature to drive
off the emanation. The results obtained by this method are complicated
by the alteration of the radiating surface in consequence of the
heating, but indicate that the emanation supplies about 70 per cent. of
the activity of radium A or C.
This points to the conclusion that the α particles from the emanation
are projected with less velocity than those from radium C.
The following table shows approximately the activity supplied by the
different products of radium in radio-active equilibrium.
Product Percentage
proportion
of total
activity
Radium 25 per
cent.
Emanation 17 „
Radium A 29 „
Radium B 0 „
Radium C 29 „
The products of radium and their radiation are graphically shown later
in Fig. 95.
=230. Active deposit of radium of slow transformation.= It has been
pointed out (section 183) that a body, exposed in the presence of the
radium emanation, does not lose all its activity for a long time after
removal; a small residual activity is always observed. The magnitude of
this residual activity is dependent not only upon the amount of
emanation employed, but also upon the time of exposure of the body in
the presence of the emanation. For an exposure of several hours in the
presence of the emanation, the residual activity is less than
one-millionth of the activity immediately after removal.
An account will now be given of some investigations made by the
writer[319] on the nature of this residual activity and the chemical
properties of the active matter itself. It is first of all necessary to
show that the residual activity arises in consequence of a deposit of
radio-active matter, and is not due to some action of the intense
radiations to which the body made active has been subjected.
The inside of a long glass tube was covered with equal areas of thin
metal, including aluminium, iron, copper, silver, lead, and platinum. A
large amount of radium emanation was introduced into the tube, and the
tube closed. After seven days the metal plates were removed, and, after
allowing two days to elapse for the ordinary excited activity to
disappear, the residual activity of the plates was tested by an
electrometer. The activity of the plates was found to be unequal, being
greatest for copper and silver, and least for aluminium. The activity of
copper was twice as great as that of aluminium. After standing for
another week the activity of the plates was again tested. The activity
of each had diminished in the interval to some extent, but the initial
differences observed had to a large extent disappeared. After reaching a
minimum value the activity of each plate slowly but steadily increased
at the same rate. After a month’s interval the activity of each of the
plates was nearly the same, and more than three times the minimum value.
The initial irregularities in the decay curves of the different metals
are, in all probability, due to slight but different degrees of
absorption of the radium emanation by the metal plates, the absorption
being greatest for copper and silver and least for aluminium. As the
occluded emanation was slowly released or lost its activity, the
activity of the metal fell to a limiting value. The absorption of the
radium emanation by lead, paraffin, and caoutchouc has been noticed by
Curie and Danne (section 182).
The residual activity on the plates comprised both α and β rays, the
latter being present, in all cases, in a very unusual proportion. The
equality of the activity and the identity of the radiation emitted from
each plate show that the residual activity is due to changes of some
form of matter deposited on the plates, and that it cannot be ascribed
to an action of the intense radiations; for if such were the case, it
would be expected that the activity produced on the different plates
would vary not only in quantity, but also in quality. This result is
confirmed by the observation that the active matter can be removed from
a platinum plate by solution in sulphuric acid, and has other
distinctive chemical and physical properties.
The variation with time of the residual activity measured by the α rays
will first be considered. A platinum plate was exposed in the presence
of the radium emanation for seven days. The amount of emanation
initially present was equal to that obtained from about 3 milligrams of
pure radium bromide. The plate immediately after removal gave a
saturation-current, measured between parallel plates by a galvanometer,
of 1·5 × 10⁻⁷ ampere. Some hours after removal, the activity decayed
according to an exponential law with the time, falling to half value in
28 minutes. Three days after removal the active plate gave a
saturation-current, measured by an electrometer, of 5 × 10⁻¹³ ampere;
_i.e._ ¹⁄₃₀0,000 of the initial activity. The activity was observed to
increase steadily with the time. The results are shown in Fig. 93, where
the time is reckoned from the middle of the time of exposure to the
emanation.
The curve is initially nearly a straight line passing through the
origin. The activity increases with the time for the interval of eight
months over which the observations have extended. The latter portions of
the curve, however, fall below the tangent to the curve drawn through
the origin, showing that the activity is not increasing proportionately
with the time.
The active deposit, obtained in a different manner, has been examined
for a still longer period. The emanation from 30 milligrams of radium
bromide was condensed in a glass tube and then sealed. After a month’s
interval, the tube was opened and dilute sulphuric acid introduced. The
acid dissolved off the active deposit in the tube and on driving off the
acid by heat, a radio-active residue was obtained. The activity of this
residue, measured by the α rays, steadily increased for a period of 18
months, but the curve of variation of activity with time plotted as in
Fig. 93 tends to become more flattened, and is obviously approaching a
maximum value.
[Illustration: Fig. 93.]
The explanation of this curve will be considered later in section 236.
=231. Variation of the β ray activity.= The residual activity consists
of both α and β rays, the latter being present initially in an unusually
large proportion. The proportion of α to β rays from the platinum plate,
one month after removal, was at the most one-fiftieth of that from a
thin film of radium bromide in radio-active equilibrium. Unlike the α
ray activity, the activity measured by the β rays remains constant after
the active deposit is about one month old, and, in consequence, the
proportion of α to β rays steadily increases with the time. The
experiments showed that the intensity of the β rays did not vary much,
if at all, over a further period of eighteen months. The want of
proportionality between the α and β rays shows that the two types of
rays arise from different products. This conclusion is confirmed by
experiments, to be described later, which show that the products giving
rise to α and β rays can be temporarily separated from one another by
physical and chemical means.
[Illustration: Fig. 94.]
If observations of the active deposit are begun shortly after its
formation, it is found that the activity, measured by the β rays, is
small at first, but increases with the time, reaching a practical
maximum about 40 days later. Experiments were made on a platinum plate,
which was exposed for 3·75 days in a vessel containing the radium
emanation. The observations of the β ray activity began 24 hours after
removal. The results are shown in Fig. 94, where the time was measured
from the middle of the time of exposure to the emanation. Similar
results were obtained for a negatively charged wire exposed to the
emanation. The curve, if produced back to the origin, is seen to be very
similar to the recovery curves of Ur X, and other active products, and
can be expressed by the equation
$$ \frac {I_t} {I₀} = 1 − e^{–λt} $$,
where _I₀_ is the maximum activity. The activity reaches half its final
value in about six days, and the value of λ is equal to ·115 (day)⁻¹. We
have shown in section 203 that a rising curve of this character
indicates that the β ray activity arises from a product which is
supplied at a constant rate from a primary source. Before discussing in
detail the explanation of these curves, showing the rise with time of
the α and β ray activity, further experimental results will be
considered.
=232. Effect of temperature on the activity.= A platinum plate, made
active in the manner described, was exposed to varying temperatures in
an electric furnace, and the activity tested at atmospheric temperature
after exposure. Four minutes’ exposure in the furnace, at first at 430°
C., and afterwards at 800° C., had little, if any, effect on the
activity. After four minutes at about 1000° C. the activity decreased
about 20 per cent., and a further exposure of eight minutes at a
temperature of about 1050° C. almost completely removed the α ray
activity. On the other hand, the β ray activity, when measured
immediately after removal, was not altered by the heating, but exposure
to a still higher temperature caused it to decrease. These results show
that the active matter consists of two kinds. The part which emits β
rays is not volatile at 1000° C., but the other part, which emits α
rays, is almost completely volatilized at that temperature.
It was found, however, that the β ray activity after heating to about
1000° was not permanent, but decayed according to an exponential law
with the time, the activity decreasing to half value in about 4·5 days.
From the recovery curve of the β ray activity already considered, it was
to be expected that the activity would decay to half value in six days.
This difference in the periods is possibly due to an effect of the high
temperature in altering the rate of decay of radium E. The period of six
days is more probably correct. The results obtained on the rise and
decay of the β rays, taken together, show:—
(1) That the product giving β rays is supplied at a constant rate
from some parent matter of very slow rate of change.
(2) That this parent matter is volatilized at or below 1000° C., and
the β ray product is left behind. Since the parent matter is
removed, the product immediately begins to lose its activity at its
characteristic rate, viz. the activity falls to half value in about
six days.
=233. Separation of the constituents by means of a bismuth plate.= The
active matter of slow decay was obtained in solution by introducing
dilute sulphuric acid into a glass tube in which the emanation from 30
milligrams of radium bromide had been stored for a month. The solution
showed strong activity and gave out both α and β rays, the latter, as in
other cases, being present in an unusually large proportion.
When a polished bismuth disk was kept for some hours in the solution, it
became strongly active. The active matter deposited on the bismuth gave
out α rays, but no trace of β rays. After several bismuth disks had been
successively left in the solution, the active matter, which emits α
rays, was almost completely removed. This was shown by evaporating down
the solution after treatment. The β ray activity remained unchanged, but
that of the α rays had been reduced to about 10 per cent. of its
original value. Three bismuth disks, made active in this way, were set
aside and their activity measured at regular intervals. The activity
fell off according to an exponential law with the time during the 200
days since their removal, while that of each fell to half value on an
average in about 143 days.
At the same time it was observed that the solution, from which the α ray
activity was removed, gradually regained its activity, showing that the
active substance which gave out α rays was continuously produced from
the matter left behind in the solution.
=234. Explanation of the results.= We have seen that a close examination
of the active deposit of slow change has disclosed,
(1) the presence of a β ray product which loses half of its activity
in about six days;
(2) the presence of an α ray product, which is deposited on bismuth
and is volatilized at 1000° C. This product loses half of its
activity in 143 days;
(3) the presence of a parent substance, which produces the β ray
product at a constant rate.
This parent product must be transformed very slowly since the β ray
product, which arises from it, soon reaches an equilibrium value, which
does not change appreciably over a period of more than one year. The
experimental evidence points to the conclusion that the parent product
does not give rise to β rays, but that the β rays arise entirely from
the next product. This parent product cannot give rise to α rays, for we
have seen that the initial α ray activity is at first extremely small,
but increases steadily with the time for a period of at least eighteen
months. Thus the parent product does not give rise to either α or β
rays, and must be a “rayless” product.
The first three transition products of the radium emanation, viz. radium
A, B and C, have already been analysed, and shown to be consecutive. It
thus seems probable that the active deposit of slow change must arise
from the successive transformations of the last product radium C. The
results already obtained can be completely explained if it is supposed
that three transition products, viz. radium D, E and F, are present in
the active deposit of slow rate of change. The properties of these
products are summarized below.
_Radium D_ is a rayless product of very slow rate of change. It will
be shown later that it is half transformed in about 40 years. It is
volatile below 1000° C. and is soluble in strong acids.
_Radium E_ is produced from radium D. In breaking up, it emits β
(and probably γ) rays but no α rays. It is half transformed in about
6 days and is not so volatile as radium D and F.
_Radium F_ is produced from radium E. It emits only α rays and is
half transformed in 143 days. This substance in solution attaches
itself to bismuth. It is volatile at about 1000° C.
Apart from their value and interest in showing the stages of
transformation of the radium atom, the results of this analysis have an
important bearing upon the origin of some of the well-known radio-active
substances separated from pitchblende; for it will be shown later that
the product radium F is the radio-active substance present in
radio-tellurium and probably also in polonium. In addition, there is
very strong evidence that the radio-active lead obtained by Hofmann
contains the three products radium D, E and F together.
The changes of radium as far as they are at present known, are shown
diagrammatically in Fig. 95. It is possible that further investigation
will show that the transformation does not end with radium F.
[Illustration: Fig. 95.]
While we have shown that radium D is the parent of E, we have not given
any conclusive evidence that E is the parent of F. This evidence is,
however, supplied by the following experiment. A platinum plate, made
active in the manner already described, was placed in an electric
furnace and heated for four minutes at about 1000° C. Most of the
products D and F were volatilized, but E was left behind. Since the
parent matter D was removed, E at once commenced to lose its β ray
activity. At the same time it was observed that the small α ray
activity, left behind on the platinum plate, increased rapidly at first
and then more slowly, as the activity of E became smaller and smaller.
This experiment shows conclusively that E was the parent of F, the α ray
product.
=235. Rate of transformation of radium D.= It has been observed
experimentally that each of the products of radium, which emit α rays,
supplies about an equal proportion of the activity of radium when in
radio-active equilibrium. Since, when equilibrium is reached, the same
number of particles of each of the successive products must break up per
second, this is an expression of the fact that every atom of each
product breaks up with the expulsion of an equal number (probably one)
of α particles. Now radium D is directly derived from radium C, and,
since the rate of change of D is very slow compared with that of C, the
number of particles of D initially present must be very nearly equal to
the number of particles of radium C which break up during the time that
radium D is being formed. Now D does not itself give out rays, but the
succeeding product E does. The products D and E are practically in
radio-active equilibrium one month after D is set aside, and the
variation of the β ray activity of E then serves as a measure of the
variation of the parent product D. Suppose that a vessel is filled with
a large quantity of radium emanation. After several hours, the product
radium C, which emits β rays, reaches a maximum value, and then
decreases at the same rate as the emanation loses its activity, _i.e._
it falls to half value in 3·8 days. If _N₁_ is the number of β particles
expelled from radium C at its maximum value, the total number _Q₁_ of β
particles expelled during the life of the emanation is given
approximately by
$$ Q_1 = \int₀^{\infty} N_1 e^{–λ_1 t} dt = \frac {N_1}
{λ_1} $$,
where λ₁ is the constant of change of the emanation.
After the emanation has disappeared, and the final products D + E are in
radio-active equilibrium, suppose that the number of β particles _N₂_
expelled per second by radium E is determined. If _Q₂_ is the total
number of particles expelled during the life of D + E, then _Q₂_ as
before is approximately given by _Q₂_ = _N₂_/λ₂ where λ₂ is the constant
of change of radium D. Now we have seen that if each particle of C and
of E gives rise to one β particle, it is to be expected that
_Q₁_ = _Q₂_,
or
λ₂ _N₂_
---- = ---- .
λ₁ _N₁_
The ratio _N₂_/_N₁_ was determined by measuring the activity due to the
β rays from C and E in the same testing-vessel. Then, since _N₂_/_N₁_ is
known, and also the value of λ₁, the value of the constant of change,
λ₂, of radium D is obtained. In this way it was calculated that D is
half transformed in about 40 years.
In the above calculations it is assumed, as a first approximation, that
the β rays from C and E have the same average velocity. This is probably
not accurately the case, but the above number certainly serves to fix
the order of magnitude of the period of the product D. This calculation
is confirmed by observations to be given later on the amount of D and E
in old radium.
It may be of interest to mention that the writer calculated the period
of radium F by a similar method, before its value was experimentally
determined, and found that F should be half transformed in about one
year. This is not very different from the experimental value of 143 days
found later. In addition, it was assumed in the calculation that the α
particles from C and F were projected with the same velocity, and in
consequence produced the same amount of ionization. In practice,
however, it is found that the α particle of F is absorbed in about half
the distance of the α particles of C, and in consequence produces only
about half of the ionization of the latter. If this correction were
made, the calculated period for half transformation would be six months
instead of one year.
A table of the transformation products of radium, together with some of
their physical and chemical properties, is given below.
Transformation Time to be Rays Chemical and
Products half Physical
transformed Properties
Radium 1200 years α rays —
Emanation 3·8 days α rays Chemically
inert gas;
condenses at
−150° C.
Radium A 3 mins. α rays Behaves as
(active deposit solid;
of rapid deposited on
change) the surface of
bodies;
concentrated on
cathode in
electric field.
Soluble in
strong acids;
volatile at a
white heat. B
is more
volatile than A
or C.
:: B (same) 21 mins. no rays Same
:: C (same) 28 mins. α, β, γ rays Same
:: D (active about 40 no rays Soluble in
deposit of slow years strong acids
change) and volatized
below 1000° C.
:: E (same) 6 days β (and γ) Non-volatile at
1000°C.
:: F (same) 143 days α rays Volatile at
1000° C;
deposited from
solution on to
bismuth plate.
? — — —
=236. Variation of the activity over long periods of time.= We are now
in a position to calculate the variation of the α and β ray activity of
the active deposit over long periods of time. If it is supposed that the
matter initially deposited consists only of D, the amounts _P_, _Q_ and
_R_ of radium D, E and F existing at any later time are given by the
equations 3, 4, 5, section 197.
Since, however, the intermediate product E has a much more rapid rate of
change than D or F, the equations can be simplified, without much loss
of accuracy, by disregarding the change E, and by supposing that D gives
out β rays and changes directly into the α ray product F.
Let λ₁, λ₂ be the constants of change D and F respectively. Let _n₀_ be
the number of particles of D present initially. Then using the notation
of section 197, the amount _P_ of radium D at any time _t_ is given by
$$ P = n₀ e^{–λ_1 t} $$ .
The amount _Q_ of radium F is given by
$$ Q = \frac {n₀ λ_1} {λ_1 − λ_2} (e^{–λ_2 t} -
e^{–λ_1 t}) $$ .
[Illustration: Fig. 96.]
The number of β particles emitted by D + E per second, some months
afterwards, is
$$ λ_1 n₀ e^{–λ_1 t} $$,
and the number of α particles emitted by radium F is
$$ \frac {λ_1 λ_2 n₀} {λ_1 − λ_2}
(e^{–λ_2 t} − e^{–λ_1 t} ) $$ .
The results are shown graphically in Fig. 96, by the curves _EE_ and
_FF_, in which the ordinates represent the number of β and α particles
expelled per second by the products D and F respectively. The complete
calculation for three changes shows that the number of β particles soon
reaches a practical maximum, and then decays nearly exponentially with
the time, falling to half value in 40 years. The number of α particles
expelled per second increases for several years, but reaches a maximum
after 2·6 years and then diminishes, finally falling off exponentially
with the time to half value in 40 years.
The experimental curve of the rise of α ray activity, shown in Fig. 93,
as far as it has been determined, lies accurately on this curve, if the
maximum is calculated from the above theory. The observed activity after
a period of 250 days is marked by the point _X_ on the curve.
=237. Experiments with old radium.= Since the substance radium D is
produced from radium at a constant rate, the amount present mixed with
the radium will increase with its age. The writer had in his possession
a small quantity of impure radium chloride, kindly presented by
Professors Elster and Geitel four years before. The amount of radium D
present in it was tested in the following way:—The substance was
dissolved in water and kept continuously boiling for a period of about
six hours. Under these conditions the emanation is removed as rapidly as
it is formed, and the β rays from the radium, due to the product radium
C, practically disappear. A newly prepared specimen of radium bromide
under these conditions retains only a fraction of 1 per cent. of its
original β radiation. The old radium, however, showed (immediately after
this treatment) an activity measured by the β rays of about 8 per cent.
of its original amount. The activity could not be reduced any lower by
further boiling or aspiration of air through the solution. This residual
β ray activity was due to the product radium E stored up in the radium.
The β ray activity due to radium E was thus about 9 per cent. of that
due to radium C. Disregarding the differences in the absorption of the β
rays, when the activity of the product E in radium reaches a maximum
value, the β ray activity due to it should be the same as that due to C.
Since the parent product D is half transformed in forty years, the
amount present in the radium after four years should be about 7 per
cent. of the maximum amount; _i.e._ it should show a β ray activity of
about 7 per cent. of that due to radium C. The observed and calculated
values (7 and 9 per cent. respectively) are thus of the same order of
magnitude. The amount of β rays from radium E present in pure radium
bromide about one year old was about 2 per cent. of the total.
The amount of radium F present in old radium was measured by
observations of the activity imparted to a bismuth disk left for several
days in the solution, and was found to be of the same order as the
theoretical value. Radium F is not deposited to an appreciable extent on
the bismuth from a water solution of radium bromide. If, however, a
trace of sulphuric acid is added to the solution, the radium F is
readily deposited on the bismuth. The addition of sulphuric acid to the
radium solution practically effected a separation of radium D, E and F
from the radium proper; for the latter was precipitated as sulphate and
the products D, E and F remained in solution. After filtering, the
solution contained the greater proportion of the products D, E, and F
and very little radium.
=238. Variation of the activity of radium with time.= It has been shown
that the activity of freshly prepared radium increases at first with the
time and practically reaches a maximum value after an interval of about
one month. The results already considered show that there is a still
further slow increase of activity with the time. This is the case
whether the activity is measured by the α or β rays. It will be shown
later that radium is probably half transformed in about 1000 years. From
this it can readily be calculated that after a lapse of about 200 years
the amount of the products radium D, E and F will have reached a maximum
value. The same number of atoms of each of the products C and E will
then break up per second. If each atom of these products in
disintegrating throws off an equal number (probably one) of β particles,
the number of β particles thrown off per second will be twice as great
as from radium a few months old. The number will increase at first at
the rate of about 2 per cent. a year.
Similar considerations apply to the α ray activity. Since, however,
there are four other products of radium besides radium itself which
expel α particles, the number of α particles emitted per second from old
radium will not be more than 25 per cent. greater than the number from
radium a few months old. The activity measured by the α rays will thus
not increase more than 25 per cent., and probably still less, as the α
particles from radium F produce less ionization than the α particles
expelled from the other radium products. The activity of radium will
consequently rise to a maximum after 200 years and then slowly die away
with the time.
=239. Presence of these products in pitchblende.= The products radium D,
E and F must be present in pitchblende in amounts proportional to the
quantity of radium present, and should be capable of separation from the
mineral by suitable chemical methods. The radio-active properties of
these substances, if obtained in the pure state, are summarized below.
_Radium D_ when first separated, should give out very little α or β
radiation. The β ray activity will rapidly increase, reaching half its
maximum value in 6 days. The α ray activity will at first increase
nearly proportionately with the time, and will reach a maximum value
after an interval of about 3 years. The α and β ray activity, after
reaching a maximum, will finally decay, the activity falling to half
value in about 40 years. Since radium D is half transformed in 40 years,
and radium in 1200 years, the maximum β ray activity of radium D, weight
for weight, will be about 300 times that of radium.
The α ray activity, at any time, will be removed by placing a bismuth
disk in the solution.
_Radium F_, after separation, will give out only α rays. Its activity,
after separation, will decrease according to an exponential law, falling
to half value in 143 days. Since radium in radio-active equilibrium
contains four products which emit α rays, the number of α particles
expelled per second from radium F will, weight for weight, be about 800
times as numerous as from new radium in radio-active equilibrium. Since
the α particles from radium F produce only about half as much ionization
as the α particles from the other radium products, the activity of
radium F, measured by the electric method, will be about 400 times that
of radium.
=240. Origin of radio-tellurium and polonium.= It is now necessary to
consider whether these products of radium have been previously separated
from pitchblende, and known by other names.
We shall first consider the α ray product, radium F. The radio-tellurium
of Marckwald and the polonium of Mme Curie both resemble radium F in
giving out only α rays, and in being deposited on a bismuth disk from a
solution. If the active constituent present in radio-tellurium is the
same as radium F, its activity should decay at the same rate as the
latter. The writer[320] has carefully compared the rates of decay of the
activity of radium F and of the radio-tellurium of Marckwald and found
them to be the same within the limits of experimental error. Both lose
half of their activity in about 143 days[321]. A similar value of the
rate of decay of radio-tellurium has been obtained by Meyer and
Schweidler[322].
The experiments on radio-tellurium were made upon the active bismuth
plates supplied by Dr Sthamer of Hamburg, which were prepared under
Marckwald’s directions.
An additional proof[323] of the identity of these two products was
obtained by comparing the absorption of the α rays by aluminium foil.
The α rays from different products are projected with different
velocities, and, in consequence, are unequally absorbed by matter. The
absorption of the rays from the two products by aluminium foil agreed
very closely, indicating the probable identity of the substances from
which they were emitted.
There can thus be no doubt that the active constituent present in the
radio-tellurium of Marckwald is identical with the product radium F.
This is a very interesting result, and shows how the close examination
of the successive transformations of the radio-active bodies may throw
light on the origin of the various substances found in pitchblende.
We have already seen (section 21) that Marckwald, by special chemical
methods, was able to obtain a few milligrams of very active substance by
working over 2 tons of pitchblende. We have already seen (section 239)
that this substance, if obtained in the pure state, should be about 400
times as active as radium. Comparative measurements of the activity of
this substance with radium will thus indicate the amount of impurity
that is present with the former. This method should be of value in
purifying radium F for the purpose of determining its spectrum, which
has not yet been observed.
=241. Polonium.= Since the separation of the active substance by
Marckwald, called by him radio-tellurium, there has been some discussion
as to whether the active constituent is the same as that present in the
polonium of Mme Curie. Both of these substances have similar
radio-active and chemical properties, but the main objection to the view
that the active constituents were identical has rested on an early
statement of Marckwald that the activity of one of his very active
preparations did not decay appreciably in the course of six months. This
objection is now removed, for we have seen that the activity of
radio-tellurium does decay fairly rapidly. It was early recognised that
the activity of the polonium, separated from pitchblende by the methods
of Mme Curie, was not permanent, but decayed with the time. Observations
on the rate of decay have not been very precise, but Mme Curie states
that some of her preparations lost half of their activity in about six
months but in others the rate of decay was somewhat smaller. It is
possible that the initial differences observed in the rates of decay of
different specimens of polonium may be due to the presence of some
radium D with the polonium. The polonium in my possession lost its
activity fairly rapidly, and was reduced to a small portion of its value
in the course of about four years. Rough observations of its activity,
made from time to time, showed that its activity diminished to half
value in about six months. If it is identical with radio-tellurium, the
activity should decay to half value in 143 days, and I think there is
little doubt that more accurate measurement will prove this to be the
case.
While the proof of the identity of the active constituent in polonium is
not so definite as for radio-tellurium, I think there can be no
reasonable doubt that these substances both contain the same active
substance, which is the seventh transformation product of radium.
Marckwald has noticed some chemical differences in the behaviour of
polonium and radio-tellurium, but little weight can be attached to such
observations, for it must be remembered that the active constituent in
both cases is present in minute quantity in the material under
examination, and that the apparent chemical properties of the active
substance are much influenced by the presence of impurities. The most
important and trustworthy test rests upon the identity of the radiations
and the period of decay.
=241 A. Origin of radio-active lead.= Some experiments will now be
discussed which show that the radio-lead first separated from
pitchblende by Hofmann (section 22) contains the products radium D, E
and F. Hofmann has observed that the activity of this substance did not
appreciably decay in the course of several years. In some recent
experiments, Hofmann, Gonder and Wölfl[324] have made a close chemical
examination of the radio-active lead, and have shown the presence of two
radio-active constituents, which are probably identical with the
products radium E and F. The radio-active measurements were
unfortunately not very precise, and the periods of change of the
separated products have not been examined very closely.
Experiments were made on the effect of adding substances to a solution
of radio-lead, and then removing them by precipitation. Small quantities
of iridium, rhodium, palladium, and platinum, in the form of chlorides,
were left in the solution for three weeks, and then precipitated by
formalin or hydroxylamine. All of these substances were found to give
out both α and β rays, the activity being greatest for rhodium and least
for platinum. A large proportion of the β ray activity disappeared in
the course of six weeks, and of the α ray activity in one year. It is
probable that the two products radium E and F were in part removed with
the metals from the radio-lead. We have seen that radium E gives out β
rays and loses half of its activity in about six days, while radium F
gives out only α rays and its activity falls to half value in 143 days.
This conclusion is further confirmed by experiments on the effect of
heat on the activity of these substances. By heating to a full red heat,
the α ray activity was lost in a few seconds. This is in agreement with
the results (section 232) where we have seen that radium F is
volatilized at about 1000° C. and radium E is left behind.
Salts of gold, silver and mercury added to the radio-lead were found to
show only α ray activity on removal. This is in accordance with the view
that radium F alone is removed with these substances. Bismuth salts on
the other hand showed initially α and β ray activity, but the latter
rapidly died away. The presence of β rays in freshly prepared polonium
was early observed by Mme Curie. The α and β ray activity of the
radio-lead is much reduced by the precipitation of bismuth added to the
solution. The α and β ray activity of the radio-lead, however, recovers
itself again. This result is exactly what is to be expected if
radio-lead contains radium D, E and F. Radium E and F are removed with
the bismuth, but the parent substance, radium D, is left behind, and, in
consequence, a fresh supply of radium E and F is produced.
While further experiments are required to settle definitely whether the
products separated from radio-lead are identical with radium E and F,
there can be little doubt that such is the case. This conclusion is
strengthened by some experiments which I have made on a specimen of
radio-lead, which was kindly forwarded to me by Mr Boltwood of New
Haven. This active lead gave out α and β rays, the latter being in
unusually large proportion. The active lead was four months old when
first tested. The β ray activity in the following six months has
remained sensibly constant, but the α ray activity has steadily
increased. These results are to be expected if the radio-lead contains
radium D. Radium E will reach a practical maximum about 40 days after
separation of the product radium D with the lead. The α ray activity due
to radium F should increase to a maximum in about 2·6 years (see section
236).
Further experiments are required to settle whether the lead immediately
after separation from pitchblende contains only radium D, or whether
radium E also appears with it. It seems likely, however, that the
bismuth, which is initially present in solution at the time of
separation of the lead, will retain both radium E and F, and that the
presence of these products in radio-lead is due to their production,
after separation, by the parent substance, radium D.
It would be of scientific value to separate radium D from pitchblende
and obtain it in the pure state, for, a month after removal, the β ray
activity from it would be about 300 times as great as from an equal
weight of radium. By placing a bismuth plate in a solution of this
substance, radium F (polonium) should be separated, and, provided a
sufficient interval is allowed to elapse, a fresh supply of radium F can
at any time be obtained.
The rate of transformation of radium D (half transformed in 40 years) is
sufficiently slow not to interfere seriously with its utility in most
experiments.
The results of the comparison of the products of radium with those
contained in polonium, radio-tellurium and radio-lead are summarized
below.
Radium D = product in _new radio-lead_, no rays. Half transformed in
40 years.
Radium E gives out β rays, separated with bismuth, iridium and
platinum. Half transformed in 6 days.
Radium F = product in _polonium_ and _radio-tellurium_. Gives out
only α rays. Half transformed in 143 days.
=242. Temporary activity of inactive matter separated from radio-active
substances.= We have seen in the last section that the platinum metals
and bismuth acquire temporary activity by their admixture with a
solution of radio-lead, and that these effects are very satisfactorily
explained on the view that some of the products of change of radio-lead
are removed with the inactive substances. Very similar effects have been
observed by Pegram and von Lerch (section 186), when inactive substances
were added to solutions of thorium and of the active deposit of thorium.
These results, too, are almost certainly due to the removal of one or
more of the products of thorium with the inactive matter. Examples of
this character may readily be multiplied, and some of the more
interesting and important of these will be briefly discussed later.
There have been two general points of view regarding the character of
this activity which is temporarily acquired by inactive matter. Some
people have supposed that the inactive molecules of the substance, mixed
with the solution, acquire by “radio-active induction” temporary
activity, the underlying idea being that the close admixture of an
inactive and an active substance has communicated the property of
radiating to some of the molecules of the former. According to the
disintegration theory of radio-activity, on the other hand, the
temporary activity of originally inactive matter is not due to any
alteration of the inactive substance itself, but to an admixture with it
of one or more of the numerous radio-active products. The idea of
“radio-active induction” has no definite experimental evidence in
support of it, while there is much indirect evidence against it.
We shall now consider how these facts are interpreted according to the
disintegration theory. In a specimen of old radium, for example, there
are present, besides radium itself, the seven successive products which
arise from it. Each of these differs in chemical and physical properties
from the others. If now, for example, a bismuth rod is introduced into
the solution, one or more of these products are deposited on the
bismuth. This action is most probably electrolytic in nature, and will
depend upon the electro-chemical behaviour of the bismuth compared with
that of the products in solution. An electro-negative substance will
tend to remove the product or products which are strongly
electro-positive. This point of view serves to explain why different
metals are made active to different degrees, depending upon their
position in the electro-chemical series.
It seems probable that the activity communicated to inactive matter by
precipitation from an active solution occurs only during the
precipitation. The correctness of this view could readily be tested by
observing whether the time that the inactive substance is present in
solution has any effect on the magnitude of the activity imparted to it.
When it is remembered that in pitchblende there are present the
radio-elements uranium, thorium, radium and actinium and their numerous
family of products, it is not surprising that many of the inactive
substances separated from it may show very considerable activity due to
the mixture of products which may be removed with them. In carrying out
experiments on the separation of radium from pitchblende, M. and Mme
Curie observed that the separation of the active substance is fairly
complete if the stage of purification is not far advanced. Copper,
antimony and arsenic can be separated only slightly active, but other
substances like lead and iron always show activity. When the stage of
precipitation is more advanced, every substance separated from the
active solution shows activity.
One of the earliest observations in this direction was made by Debierne,
who found that barium could be made active by solution with actinium.
The active barium removed from the actinium still preserved its activity
after chemical treatment, and, in this way, barium chloride was obtained
whose activity was 6000 times that of uranium. Although the activity of
the barium chloride could be concentrated in the same way as the
activity of radiferous barium chloride, it did not show any of the
spectroscopic lines of radium, and could not have been due to the
admixture of that element with the barium. The activity of the barium
was not permanent, and Debierne states that the activity fell to about
one-third of its value in three months. It seems probable that the
precipitated barium carried down with it the product actinium X, and
also some of the actinium itself, and that the decay observed was due to
the transformation of actinium X. It is interesting to note that barium
is capable of removing a large number of products of the different
radio-elements. This effect is probably connected with its position in
the electro-chemical series, for barium is highly electro-positive.
Giesel showed in 1900 that bismuth could be made active by placing it in
a radium solution, and considered that polonium was in reality bismuth
made active by the process of induction. In later experiments, he found
that the bismuth plate gave out only α rays, and that the activity of
the bismuth could not be ascribed to radium, since no β rays were
present. We have seen that this activity of the bismuth is due to the
product radium F deposited on its surface.
Mme Curie also found that bismuth was made active by solution with a
radium compound, and succeeded in fractionating the above bismuth in the
same way as polonium. In this way bismuth was obtained 2000 times as
active as uranium, but the activity, like that of polonium separated
from pitchblende, decreased with the time. In the light of the
experiments on the transformation products of radium, it is seen that
these early experiments of Mme Curie add additional confirmation to the
view that the product (radium F) separated from radium itself is
identical with the polonium obtained directly from pitchblende.
Footnote 314:
Rutherford and Soddy, _Phil. Mag._ April, 1903.
Footnote 315:
Rutherford, _Phil. Trans._ A. p. 169, 1904. Curie and Danne, _C. R._
p. 748, 1904.
Footnote 316:
P. Curie and Danne, _Comptes Rendus_, 138, p. 748, 1904.
Footnote 317:
Miss Gates, _Phys. Rev._ p. 300, 1903.
Footnote 318:
Miss Brooks, _Nature_, July 21, 1904.
Footnote 319:
Rutherford, _Phil. Mag._ Nov. 1904. _Nature_, p. 341, Feb. 9, 1905.
Footnote 320:
Rutherford, _Nature_, p. 341, Feb. 9, 1905.
Footnote 321:
Marckwald (_Ber. d. D. Chem. Ges._ p. 591, 1905) has recently found
that the activity of his radio-tellurium falls to half value in 139
days.
Footnote 322:
Meyer and Schweidler, _Wien Ber._ Dec. 1, 1904.
Footnote 323:
Rutherford, _Phil. Trans._ A. p. 169, 1904.
Footnote 324:
Hofmann, Gonder and Wölfl, _Annal. d. Phys._ 15, p. 615, 1904.