TRANSFORMATION PRODUCTS OF URANIUM, THORIUM, AND ACTINIUM.
=205.= In the last chapter the mathematical theory of successive changes
has been considered. The results there obtained will now be applied to
explain the radio-active phenomena observed with uranium, thorium,
actinium, radium, and their products.
Transformation products of Uranium.
It has been shown in sections 127 and 129 that a radio-active
constituent Ur X can be separated from uranium by several different
processes. The activity of the separated Ur X decays with the time,
falling to half value in about 22 days. At the same time the uranium,
from which the Ur X has been separated, gradually regains its lost
activity. The laws of decay of Ur X and of the recovery of the lost
activity of the uranium are expressed by the equations
$$ \frac {I} {I₀} = e^{–λt} $$,
and
$$ \frac {I_t} {I₀} = 1 − e^{–λt} $$,
where λ is the radio-active constant of Ur X. The substance Ur X is
produced from uranium at a constant rate, and the constant
radio-activity observed in uranium represents a state of equilibrium,
where the rate of production of new active matter is balanced by the
rate of change of the Ur X already produced.
The radio-active processes occurring in uranium present several points
of difference from the processes occurring in thorium and radium. In the
first place, uranium does not give off an emanation, and in consequence
does not produce any excited activity on bodies. So far only one active
product Ur X has been observed in uranium. This active product Ur X
differs from Th X and the emanations, inasmuch as the radiation from it
consists almost entirely of β rays. This peculiarity of the radiations
from Ur X initially led to some confusion in the interpretation of
observations on Ur X and the uranium from which it had been separated.
When examined by the photographic method, the uranium freed from Ur X
showed no activity, while the Ur X possessed it to an intense degree.
With the electric method, on the other hand, the results obtained were
exactly the reverse. The uranium freed from Ur X showed very little loss
of activity, while the activity of the Ur X was very small. The
explanation of these results was given by Soddy[296] and by Rutherford
and Grier[297]. The α rays of uranium are photographically almost
inactive, but produce most of the ionization in the gas. The β rays, on
the other hand, produce a strong photographic action, but very little
ionization compared with the α rays. When the Ur X is separated from the
uranium, the uranium does not at first give out any β rays. In the
course of time fresh Ur X is produced from the uranium, and β rays begin
to appear, gradually increasing in intensity until they reach the
original value shown before the separation of the Ur X.
In order to determine the recovery curves of uranium after the
separation of Ur X, it was thus necessary to measure the rate of
increase of the β rays. This was done by covering the uranium with a
layer of aluminium of sufficient thickness to absorb all the α rays, and
then measuring the ionization due to the rays in an apparatus similar to
Fig. 17.
Uranium has not yet been obtained inactive when tested by the electric
method. Becquerel[298] has stated that he was able to obtain inactive
uranium, but in his experiments the uranium was covered with a layer of
black paper, which would entirely absorb the α rays. There is no
evidence that the α radiation of uranium has been altered either in
character or amount by any chemical treatment. The α rays appear to be
inseparable from the uranium, and it will be shown later that thorium
and radium as well as uranium also possess a non-separable activity
consisting entirely of α rays. The changes occurring in uranium must
then be considered to be of two kinds, (1) the change which gives rise
to the α rays and the product Ur X, (2) the change which gives rise to
the β rays from Ur X.
The possibility of separating the Ur X, which gives rise to the β rays
of uranium, shows that the α and β rays are produced quite independently
of one another, and by matter of different chemical properties.
Following the general considerations discussed in section 136 we may
suppose that every second some of the atoms of uranium—a very minute
fraction of the total number present will suffice—become unstable and
break up, expelling an α particle with great velocity. The uranium atom,
minus one α particle, becomes the atom of the new substance, Ur X. This
in turn is unstable and breaks up with the expulsion of the β particle
and the appearance of a γ ray.
The changes occurring in uranium are graphically shown in Fig. 77.
[Illustration: Fig. 77.]
On this view the α ray activity of uranium should be an inherent
property of the uranium, and should be non-separable from it by physical
or chemical means. The β and γ ray activity of uranium is a property of
Ur X, which differs in chemical properties from the parent substance and
can at any time be completely removed from it. The final product, after
the decay of Ur X, is so slightly active that its activity has not yet
been observed. We shall see later (chapter XIII.) that there is some
reason to believe that the changes in uranium do not end at this point
but continue through one or more stages, finally giving rise to radium,
or in other words that radium is a product of the disintegration of the
uranium atom. Meyer and Schweidler[299], in a recent paper, state that
the activity due to uranium preparations increases somewhat in a closed
vessel. On removing the uranium no residual activity, however, was
observed. They consider that this effect may be due to a very
short-lived emanation emitted by uranium.
=206. Effect of crystallization on the activity of uranium.= Meyer and
Schweidler[300] recently observed that uranium nitrate, after certain
methods of treatment, showed remarkable variations of its activity,
measured by the β rays. The α ray activity, on the other hand, was
unaltered. Some uranium nitrate was dissolved in water and then shaken
up with ether, and the ether fraction drawn off. The early experiments
of Crookes showed that, by this method, the uranium in the ether portion
was photographically inactive. This is simply explained by supposing
that the uranium X is insoluble in ether, and consequently remained
behind in the water fraction. The ether fraction gradually regained its
β ray activity at the normal rate to be expected if Ur X was produced by
the uranium at a constant rate, for it recovered half its final activity
in about 22 days. Some of the uranium in the water fraction was
crystallized and placed under an electroscope. The β ray activity fell
rapidly at first to half its value in the course of four days. The
activity then remained constant, and no further change was observed over
an interval of one month. Other experiments were made with crystals of
uranium nitrate, which had not been treated with ether. The nitrate was
dissolved in water and a layer of crystals separated. The β ray activity
of these crystals fell rapidly at first, the rate varying somewhat in
different experiments, but reached a minimum value after about five
days. The β ray activity then rose again at a slow rate for several
months.
The rapid drop of activity of the crystals seemed, at first sight, to
indicate that crystallization was able in some way to alter the activity
of uranium.
Dr Godlewski, working in the laboratory of the writer, repeated the work
of Meyer and Schweidler, and obtained results of a similar character,
but the initial drop of activity was found to vary both in rate and
amount in different experiments. These results were at first very
puzzling and difficult to explain, for the mother liquor, left behind
after removal of the crystals, did not show the corresponding initial
rise, which would be expected if the variation of activity were due to
the partial separation of some new product of uranium.
The cause of this effect was, however, rendered very evident by a few
well-considered experiments made by Godlewski. The uranium nitrate was
dissolved in hot water in a flat dish, and allowed to crystallize under
the electroscope. Up to the moment of crystallization the β ray activity
remained constant, but as soon as the crystals commenced to form at the
bottom of the solution the β ray activity rapidly rose in the course of
a few minutes to five times the initial value. After reaching a maximum,
the activity very gradually decreased again to the normal value. If,
however, the plate of crystals was reversed, the β ray activity was
found at first to be much smaller than the normal, but increased as fast
as that of the other side diminished.
The explanation of this effect is simple. Ur X is very soluble in water
and, at first, does not crystallize with the uranium, but remains in the
solution, and, consequently, when the crystallization commences at the
bottom of the vessel the upper layer of liquid becomes richer in uranium
X. Since the β rays arise only from the product Ur X and not from the
uranium itself, and the Ur X is mostly confined to the upper layer, a
much greater proportion of the β rays escape than if the Ur X were
uniformly distributed throughout the thick layer of uranium. When the
amount of water added is just sufficient to supply the water of
crystallization, the Ur X in the upper layer of crystals gradually
diffuses back through the mass and, in consequence, the activity of the
upper surface diminishes and of the lower surface rises. A similar
explanation applies to the effects observed by Meyer and Schweidler. The
water fraction, left behind after treatment with ether, contained all
the Ur X. The first layer of crystals formed in it contained some Ur X,
and this was for the most part confined to the top layer of crystals.
The amount of β rays at first diminished owing to the gradual diffusion
of the Ur X from the surface. In the first experiment, the amount of Ur
X present was in radio-active equilibrium with the uranium, and, after
the initial drop, the β ray activity remained constant. In the second
experiment, the gradual rise is due to the fact that the crystals of
uranium first formed contained less than the equilibrium amount of Ur X.
After falling to a minimum, the β ray activity, in consequence, slowly
rose again to the equilibrium value.
These effects exhibited by uranium are of great interest, and illustrate
in a striking manner the difference in properties of Ur X and the
uranium. The gradual diffusion of the Ur X throughout the mass of
crystals is noteworthy. By measurements of the variation with time of
the β ray activity, it should be possible to deduce its rate of
diffusion into the crystallized mass.
Transformation products of Thorium.
=207. Analysis of the active deposit.= The radio-active processes
occurring in thorium are far more complicated than those in uranium. It
has already been shown in chapter vi that a radio-active product Th X is
continuously produced from the thorium. This Th X breaks up, giving rise
to the radio-active emanation. The emanation produces from itself a type
of active matter which is deposited on the surface of bodies, where it
gives rise to the phenomena of excited or induced activity. This active
deposit possesses some distinctive chemical and physical properties
which distinguish it from the emanation and the Th X. We have seen
(section 180) that the rate at which the active deposit loses its
activity depends upon the time of exposure of the body made active to
the emanation. The explanation of the activity curves for different time
of exposure will now be considered.
The curve of variation of activity for a short exposure of 10 minutes
has already been given in Fig. 65. The activity is small at first but
increases rapidly with the time; it passes through a maximum about 4
hours later, and finally decays exponentially with the time, falling to
half value in 11 hours. This remarkable effect can be explained
completely[301] if it be supposed that the active deposit consists of
two distinct substances. The matter initially deposited from the
emanation, which will be called thorium _A_, is supposed to be changed
into thorium _B_. Thorium _A_ is transformed according to the ordinary
exponential law, but the change is not accompanied by any ionizing rays.
In other words, the change from _A_ to _B_ is a “rayless” change. On the
other hand, _B_ breaks up into _C_ with the accompaniment of all three
kinds of rays. On this view the activity of the active deposit at any
time represents the amount of the substance _B_ present, since _C_ is
inactive or active to a very minute extent.
If the variation of the activity imparted to a body exposed for a short
interval in the presence of the thorium emanation, is due to the fact
that there are two successive changes in the deposited matter _A_, the
first of which is a “rayless” change, the activity _I_{t}_ at any time
_t_ after removal should be proportional to the number _Q_{t}_ of
particles of the matter _B_ present at that time. Now, from equation (4)
section 197, it has been shown that
$$ Q = \frac {nλ_1} {λ_1 − λ_2} (e^{–λ_2 t} -
e^{–λ_1 t}) $$ .... (4).
The value of _Q_{t}_ passes through a maximum _Q_{T}_ at the time _T_
when
$$ \frac {λ_2} {λ_1} − e^{-(λ_1–λ_2) T} $$ .
The maximum activity _I_{T}_ is proportional to _Q_{T}_ and
$$ \frac {I_t} {I_T} = \frac {Q_t} {Q_T} = \frac {e^{–λ_2 t} -
e^{–λ_1 t}} {e^{–λ_2 T} − e^{–λ_1 T}} $$ .
It will be shown later that the variation with time of the activity,
imparted to a body by a short exposure, is expressed by an equation of
the above form. It thus remains to fix the values of λ₁, λ₂. Since the
above equation is symmetrical with regard to λ₁, λ₂, it is not possible
to settle from the agreement of the theoretical and experimental curve
which value of λ refers to the first change. The curve of variation of
activity with time is unaltered if the values of λ₁ and λ₂ are
interchanged.
It is found experimentally that the activity 5 or 6 hours after removal
decays very approximately according to an exponential law with the time,
falling to half value in 11 hours. This is the normal rate of decay of
thorium for all times of exposure, provided measurements are not begun
until several hours after the removal of the active body from the
emanation.
This fixes the value of the constants of one of the changes. Let us
assume for the moment that this gives the value of λ₁.
Then λ₁ = 1·75 × 10⁻⁵ (sec)⁻¹.
Since the maximum activity is reached after an interval _T_ = 220
minutes (see Fig. 65), substituting the values of λ₁ and _T_ in the
equation, the value of λ₂ comes out to be
λ₂ = 2·08 × 10⁻⁴ (sec)⁻¹.
This value of λ₂ corresponds to a change in which half the matter is
transformed in 55 minutes.
Substituting now the values of λ₁, λ₂, _T_, the equation reduces to
$$ \frac {I_t} {I_T} = 1\cdot37 (e^{–λ_2 t} − e^{–λ_2 t}) $$ .
The agreement between the results of the theoretical equation and the
observed values is shown in the following table:
Time in Theoretical Observed value
minutes value of of
_I_{t}_/_I_{T}_ _I_{t}_/_I_{T}_
15 ·22 ·23
30 ·38 ·37
60 ·64 ·63
120 ·90 ·91
220 1·00 1·00
305 ·97 ·96
After 5 hours the activity decreased nearly exponentially with the time,
falling to half value in 11 hours.
It is thus seen that the curve of rise of activity for a short exposure
is explained very satisfactorily on the supposition that two changes
occur in the deposited matter, of which the first is a rayless change.
Further data are required in order to fix which of the time constants of
the changes refers to the first change. In order to settle this point,
it is necessary to isolate one of the products of the changes and to
examine the variation of its activity with time. If, for example, a
product can be separated whose activity decays to half value in 55
minutes, it would show that the second change is the more rapid of the
two. Now Pegram[302] has examined the radio-active products obtained by
electrolysis of thorium solutions. The rates of decay of the active
products depended upon conditions, but he found that, in several cases,
rapidly decaying products were obtained whose activity fell to half
value in about 1 hour. Allowing for the probability that the product
examined was not completely isolated by the electrolysis, but contained
also a trace of the other product, this result would indicate that the
last change which gives rise to rays is the more rapid of the two.
This point is very clearly brought out by some recent experiments of
Miss Slater[303], who has made a detailed examination of the effect of
temperature on the active deposit of thorium.
A platinum wire was made active by exposure for a long interval to the
thorium emanation, and then heated for a few minutes to any desired
temperature by means of the electric current. The wire, while being
heated, was surrounded by a lead cylinder in order that any matter
driven off from it should be collected on its surface. The decay of
activity both of the wire and of the lead cylinder was then tested
separately. After heating to a dull red heat, no sensible diminution of
the activity was observed at first, but the rate of decay of the
activity on the wire was found to be more rapid than the normal. The
activity of the lead cylinder was small at first but increased to a
maximum after about 4 hours and then decayed at the normal rate with the
time.
These results are to be expected if some thorium A is volatilized from
the wire; for the rise of activity on the lead cylinder is very similar
to that observed on a wire exposed for a short time in the presence of
the thorium emanation, _i.e._, under the condition that only thorium A
is initially present.
On heating the wire above 700° C. the activity was found to be reduced,
showing that some thorium B had also been removed. By heating for a few
minutes at about 1000° C. nearly all the thorium A was driven off. The
activity on the wire then decayed exponentially with the time, falling
to half value in about 1 hour. After heating for a minute at about 1200°
C. all the activity was removed. These results show that thorium A is
more volatile than B, and that the product which gives out rays, viz.
thorium B, has a period of about 55 minutes.
Another series of experiments was made, in which an active aluminium
disc was placed in an exhausted tube, and exposed to the cathode ray
discharge. Under these conditions, a part of the activity of the disc
was removed. When the disc was made the anode, the loss of activity was
usually 20 to 60 per cent. for half-an-hour’s exposure. If the disc was
made the cathode, the loss was much greater, amounting to about 90 per
cent. in 10 minutes. Part of the active matter removed from the disc was
collected on a second disc placed near it. This second disc on removal
lost its activity at a far more rapid rate than the normal. The rate of
decay on the first disc was also altered, the activity sometimes even
increasing after removal. These results indicate that, in this case, the
apparent volatility of the products is reversed. Thorium B is driven off
from the disc more readily than thorium A. The rates of decay obtained
under different conditions were satisfactorily explained by supposing
that the surfaces of the discs after exposure to the discharge were
coated with different proportions of thorium A and B.
The escape of thorium B from the disc under the influence of the
discharge seems rather to be the result of an action similar to the
well-known “sputtering” of electrodes than to a direct influence of
temperature.
The results obtained by von Lerch[304] on the electrolysis of a solution
of the active deposit also admit of a similar interpretation. Products
were obtained on the electrodes of different rates of decay, losing half
their activity in times varying from about 1 hour to 5 hours. This
variation is due to the admixture of the two products in different
proportions. The evidence, as a whole, thus strongly supports the
conclusion that the active deposit from thorium undergoes two successive
transformations as follows:
(1) A “rayless” change for which λ₁ = 1·75 × 10⁻⁵, _i.e._, in which half
the matter is transformed in 11 hours;
(2) A second change giving rise to α, β and γ rays, for which λ₂ = 2·08
× 10⁻⁴, _i.e._, in which half the matter is transformed in 55
minutes[305].
It is, at first sight, a somewhat unexpected result that the final rate
of decay of the active deposit from thorium gives the rate of change not
of the last product itself, but of the preceding product, which does not
give rise to rays at all.
A similar peculiarity is observed in the decay of the excited activity
of actinium, which is discussed in section 212.
For a long exposure in the presence of a constant supply of thorium
emanation, the equation expressing the variation of activity with time
is found from equation (8), section 198,
$$ \frac {I_t} {I₀} = \frac {Q} {Q₀} = \frac {λ_2} {λ_2 -
λ_1} e^{–λ_1 t} − \frac {λ_1} {λ_1 − λ_2}
e^{–λ_2 t} $$
$$ = \frac {λ_2 e^{–λ_1 t}} {λ_2 -
λ_1} (1 − \cdot083 e^{−1\cdot90 × 10^{−4} t} ) $$ .
About 5 hours after removal the second term in the brackets becomes very
small, and the activity after that time will decay nearly according to
an exponential law with the time, falling to half value in 11 hours. For
any time of exposure _T_, the activity at time _t_ after the removal
(see equation 11, section 199) is given by
$$ \frac {I_t} {I₀} = \frac {Q} {Q_T} = \frac {ae^{–λ_2 t} -
be^{–λ_1 t}} {a − b} $$,
where _I₀_ is the initial value of the activity, immediately after
removal, and
$$ a = \frac {1 − e^{–λ_2 T}} {λ_2} $$,
$$ b = \frac {1 − e^{–λ_1 T}} {λ_1} $$,
By variation of _T_ the curves of variation of activity for any time of
exposure can be accurately deduced from the equation, when the values of
the two constants λ₁, λ₂ are substituted. Miss Brooks[306] has examined
the decay curves of excited activity for thorium for different times of
exposure and has observed a substantial agreement between experiment and
theory.
[Illustration: Fig. 78.]
The results are shown graphically in Fig. 78. The maximum value of the
activity is, for each time of exposure, taken as 100. The theoretical
and observed values are shown in the Figure.
=208. Analysis of the decay and recovery curves of Th X.= The
peculiarities of the initial portions of the decay and recovery curves
of Th X and thorium respectively (Curves _A_ and _B_, Fig. 47, p. 221),
will now be considered. It was shown that when the Th X was removed from
the thorium by precipitation with ammonia, the radiation increased about
15 per cent. during the first day, passed through a maximum, and then
fell off according to an exponential law, decreasing to half value in
four days. At the same time the activity of the separated hydroxide
decreased for the first day, passed through a minimum, and then slowly
increased again, rising to its original value after the lapse of about
one month.
When a thorium compound is in a state of radio-active equilibrium, the
series of changes in which Th X, the emanation, and thorium A and B are
produced, go on simultaneously. Since a state of equilibrium has been
reached for each of these products, the amount of each product changing
in unit time is equal to the amount of that product supplied from the
preceding change in unit time. Now the matter Th X is soluble in
ammonia, while thorium A and B are not. The Th X is thus removed from
the thorium by precipitation with ammonia, but A and B are left behind
with the thorium. Since the active deposit is produced from the
emanation, which in turn arises from Th X, on the removal of the parent
matter Th X, the radiation due to this active deposit will decay, since
the rate of production of fresh matter no longer balances its own rate
of change. Disregarding the initial irregularity in the decay curve of
the active deposit, its activity will have decayed to half value in
about 11 hours, and to one quarter value at the end of 22 hours. As
soon, however, as the Th X has been separated, new Th X is produced in
the thorium compound. The activity of this new Th X is not, however,
sufficient to compensate at first for the loss of activity due to the
change in the active deposit, so that, as a whole, the activity will at
first _decrease_, then pass through a minimum, then increase again.
The correctness of this point of view has been tested by Rutherford and
Soddy[307] as follows: If the precipitated thorium hydroxide after the
removal of Th X is put through a series of precipitations with ammonia
at short intervals, the Th X is removed almost as fast as it is formed,
and, at the same time, the activity of thorium B in the thorium decays.
The following table indicates the results obtained. A portion of the
precipitated hydroxide was removed after each series of precipitations
and its activity tested in the usual way.
Activity
of
hydroxide
per cent.
After 1 precipitation 46
After 3 precipitations at 39
intervals of 24 hours
After 3 more precipitations at 22
intervals of 24 hours and 3 at
intervals of 8 hours
After 3 more each of 8 hours 24
After 6 more each of 4 hours 25
[Illustration: Fig. 79.]
The differences in the last three numbers are not significant, for it is
difficult to make accurate comparisons of the activity of thorium
compounds which have been precipitated under slightly different
conditions. It is thus seen that as a result of successive
precipitations, the activity is reduced to a minimum of about 25 per
cent. The recovery curve of the activity of this 23 times precipitated
hydroxide is shown in Fig. 79. The initial drop in the curve is quite
absent, and the curve, starting from the minimum, is practically
identical with the curve shown in Fig. 48, which gives the recovery
curve of thorium hydroxide after the first two days. This residual
activity—about 25 per cent. of the maximum—is non-separable from the
thorium by any chemical process that has been tried.
The initial rise of activity of Th X, after it has been separated, will
now be considered. In all cases it was found that the activity of the
separated Th X had increased about 15 per cent. at the end of 24 hours,
and then steadily decayed, falling to half value in about four days.
This peculiarity of the Th X curve follows, of necessity, from the
considerations already advanced to explain the drop in the recovery
curve. As soon as the Th X is separated, it at once produces from itself
the emanation, and this in turn produces thorium A and B. The activity
due to B at first more than compensates for the decay of activity of the
Th X itself. The total activity thus increases to a maximum, and then
slowly decays to zero according to an exponential law with the time. The
curve expressing the variation of the activity of the separated Th X
with time can be deduced from the theory of successive changes already
considered in chapter IX. In the present case there are four successive
changes occurring at the same time, viz. the change of Th X into the
emanation, of the emanation into thorium A, of A into B, and of B into
an inactive product. Since, however, the change of the emanation into
thorium A (about half changed in one minute) is far more rapid than the
changes occurring in Th X or thorium A and B, for the purposes of
calculation it may be assumed without serious error that the Th X
changes at once into the active deposit. The 55 minute change will also
be disregarded for the same reason.
Let λ₁ and λ₂ be the constants of decay of activity of Th X and of
thorium A respectively. Since the activity of Th X and of thorium A
falls to half value in 4 days and 11 hours respectively, the value of λ₁
= ·0072 and of λ₂ = ·063, where 1 hour is taken as the unit of time.
The problem reduces to the following: _Given the matter A (thorium X)
all of one kind, which changes into B (thorium B), find the activity of
A and B together at any subsequent time._ This corresponds to Case I.
(section 197). The amount _Q_ of B at any time _T_ is given by
$$ Q = \frac {λ_1 n₀} {λ_1 − λ_2} (e^{–λ_2 t} -
e^{–λ_1 t}) $$,
and the activity _I_ at any time of the two together is proportional to
λ₁_P_ + _K_λ₂_Q_, where _K_ is the ratio of the ionization of B compared
with that of A.
Then
$$ \frac {I_t} {I₀} = \frac {λ_1 P + Kλ_2 Q} {λ_1
n₀} $$
$$ = e^{–λ_1 t} (1 + \frac {Kλ_2} {λ_2 − λ_1}
(1 − e^{-(λ_2 − λ_1) t})) $$,
where _I₀_ is the initial activity due to _n₀_ particles of Th X.
By comparison of this equation with the curve of variation of the
activity of Th X with time, shown in Fig. 47, it is found that _K_ is
almost ·44. It must be remembered that the activity of the emanation and
Th X are included together, so that the activity of thorium B is about
half of the activity of the two preceding products.
The calculated values of _I_{t}_/_I₀_ for different values of _t_ are
shown in the second column of the following table, and the observed
values in the third column.
Time Theoretical Observed
value value
0 1·00 1·00
·25 days 1·09 —
·5 „ 1·16 —
1 „ 1·15 1·17
1·5 „ 1·11 —
2 „ 1·04 —
3 „ ·875 ·88
4 „ ·75 ·72
6 „ ·53 ·53
9 „ ·315 ·295
13 „ ·157 ·152
[Illustration: Fig. 80.]
The theoretical and observed values thus agree within the limit of error
in the measurements. The theoretical curve is shown in Curve _A_, Fig.
80 (with the observed points marked, for comparison). The curve _B_
shows the theoretical curve of the decay of the activity of Th X and the
emanation, supposing there is no further change into the active deposit.
Curve _C_ shows the difference curve between the curves _A_ and _B_,
_i.e._ the proportion of the activity at different times due to the
active deposit. The activity due to the latter thus rises to a maximum
about two days after removal of the Th X, and then decays with the time
at the same rate as the Th X itself, _i.e._ the activity falls to half
value every four days. When _t_ exceeds four days, the term
$$ e^{-(λ_2 − λ_1) t} $$
in the theoretical equation is very small.
The equation of decay after this time is therefore expressed by
$$ \frac {I_t} {I₀} = (1 + \frac {Kλ_2} {λ_2 − λ_1})
e^{–λ_1 t} $$,
_i.e._ the activity decays according to an exponential law with the
time.
=209. Radiations from Thorium products.= It has been shown in the last
section that the activity of thorium, by successive precipitations with
ammonia, is reduced to a limiting value of almost 25 per cent. of the
initial activity. This “non-separable activity” consists of α rays, the
β and γ rays being altogether absent. According to the disintegration
theory, this is an expression of the fact that the initial break-up of
the thorium atom is accompanied only by the expulsion of α particles. We
have seen in section 156 that the thorium emanation also gives out only
α rays. In the active deposit, thorium A gives out no rays, while
thorium B emits all three types of rays.
Some hours after separation, Th X gives out α, β, and γ rays, but the
appearance of β and γ rays is probably due to the thorium B associated
with it. The β and γ ray activity of Th X is much reduced if a current
of air is continuously aspirated through a solution of Th X to remove
the emanation. It seems likely that if the emanation could be removed as
fast as it was formed, so as to prevent the formation of thorium B in
its mass, Th X itself would give out only α rays: but, on account of the
rapid rate of change of the thorium emanation, it is difficult to
realize this experimentally.
=210. Transformation products of Thorium.= The transformation products
of thorium and the rays emitted by them are graphically shown below
(Fig. 81).
[Illustration: Fig. 81.]
A table of the transformation products of thorium is shown below, with
some of their physical and chemical properties.
Product Time to be λ (sec)⁻¹ Radiations Physical and
half chemical
transformed properties
Thorium α rays Insoluble in
ammonia
Th. X 4 days 2·00 × α rays Soluble in
10⁻⁶ ammonia
Emanation 54 secs. 1·28 × α rays Inert gas,
10⁻² condenses
−120° C.
Thorium A 11 hours 1·75 × no rays Soluble in
10⁻⁵ strong acids.
Volatile at
a white heat.
B can be
separated
from A by
electrolysis
and by
difference
of volatility.
Thorium B 55 mins. 2·1 × α, β, γ rays Same
10⁻⁴
? — — — -
=211. Transformation products of Actinium.= It has previously been
pointed out (sections 17 and 18) that the actinium of Debierne and the
emanium of Giesel contain the same radio-active constituent. Both give
out a short-lived emanation which imparts activity to the surface of
bodies. Recently, thanks to Dr Giesel of Braunschweig, preparations of
“emanium” have been placed on the market, and most of the investigations
that are described later have been made with this substance.
_Actinium X._ Actinium and thorium are very closely allied in
radio-active properties. Both emit an emanation which is rapidly
transformed, but the rate of change of the actinium emanation is still
more rapid than that of thorium, the activity decreasing to half value
in 3·7 seconds. Miss Brooks[308] has analysed the active deposit from
the emanation of actinium, and has shown that two successive changes
occur in it, very similar in character to those observed in the active
deposit of thorium. It thus seemed probable, from analogy, that an
intermediate product, corresponding to Th X in thorium, would be found
in actinium[309]. Recent work has verified this supposition. Giesel[310]
and Godlewski[311] independently observed that a very active substance
could be separated from “emanium,” very similar in chemical and physical
properties to Th X in thorium. This product will, from analogy, be
called “actinium X.” The same method, which was used by Rutherford and
Soddy to separate Th X from thorium, is also effective in separating
actinium X from actinium. After precipitation of the active solution
with ammonia, actinium X is left behind in the filtrate. After
evaporation and ignition, a very active residue remains. At the same
time, the precipitated actinium loses a large proportion of its
activity.
Giesel observed the separation of an active product, using a fluorescent
screen to detect the radiations. A very complete examination of the
product actinium X has been made by Godlewski in the laboratory of the
writer.
After separation of actinium X, the activity, whether measured by the α
or β rays, increases about 15 per cent. during the first day, and
afterwards decays exponentially with the time, falling to half value in
10·2 days. The activity of the separated actinium was small at first but
steadily increased with the time, reaching a practical maximum after an
interval of sixty days. After the first day, the decay and recovery
curves of activity are complementary to one another. The curves of rise
and decay are shown graphically in Fig. 82, curves I and II
respectively.
Godlewski observed that a solution of actinium, freed from actinium X,
gave out very little emanation, while a solution of actinium X gave off
the emanation in large quantity. The amount of emanation from the
solution was measured by observing the activity produced in a testing
vessel, similar to that shown in Fig. 51, when a constant current of air
was passed through the solution. The emanating power of actinium X
decreased exponentially with the time at the same rate as that at which
the actinium X lost its activity. At the same time the actinium solution
increased in emanating power, reaching its original value after about 60
days. The behaviour of actinium and thorium is thus quite analogous, and
the explanation advanced to explain the decay and recovery curves of
thorium applies equally well to the corresponding curves of actinium.
[Illustration: Fig. 82.]
The actinium X is produced at a constant rate from the parent matter
actinium, and is transformed according to an exponential law with the
time. The constant of change λ = ·068 (day)⁻¹, and this value is
characteristic of the product actinium X. As in the case of thorium, the
above experiments show that the emanation does not arise from actinium
itself but from actinium X. The emanation in turn breaks up and gives
rise to an active deposit on the surface of bodies.
=212. Analysis of the active deposit from the emanation.= Debierne[312]
observed that the excited activity produced by actinium decayed to half
value in about 41 minutes. Miss Brooks[313] showed that the curves of
decay of the excited activity after removal depended upon the duration
of exposure to the emanation. The curves for different times of exposure
have already been shown in Fig. 69.
Bronson, using the direct deflection method described in section 69,
accurately determined the activity curve corresponding to a short
exposure to the actinium emanation. The curve obtained is shown in Fig.
83.
[Illustration: Fig. 83.]
This curve is similar in shape to the corresponding curve obtained for
the active deposit from thorium, and is explained in a similar way. The
activity _I_{t}_ at any time _t_ is given by
$$ \frac {I_t} {I_T} = \frac {e^{–λ_2 t} − e^{–λ_1 t}}
{e^{–λ_2 T} − e^{–λ_1 T}} $$,
where λ₁ and λ₂ are two constants, and _I{_T_} the maximum activity
reached after an interval _T_. After 20 minutes the activity decreased
exponentially with the time, falling to half value in 35·7 minutes. This
gives the value λ₁ = ·0194 (min.)⁻¹. By comparison with the curve, the
value of λ₂ was found to be ·317 (min.)⁻¹. This corresponds to a change
in which half the matter is transformed in 2·15 minutes. Exactly as in
the analogous curve for thorium, it can be shown that the matter
initially deposited undergoes two changes, the first of which is a
rayless one. The same difficulty arises in fixing which of the values of
λ refers to the first change. An experiment made by Miss Brooks (_loc.
cit._) shows that the rayless product has the slower period of
transformation. The active deposit of actinium was dissolved off a
platinum wire and then electrolysed. The anode was found to be active,
and the activity fell off exponentially with the time, decreasing to
half value in about 1·5 minutes. Allowing for the difficulty of
accurately measuring such a rapid rate of decay, this result indicates
that the product which gives out rays has the rapid period of 2·15
minutes. The analysis of the active deposit of actinium thus leads to
the following conclusions:
(1) The matter initially deposited from the emanation, called actinium
A, does not give out rays, and is half transformed in 35·7 minutes.
(2) A changes into B, which is half transformed in 2·15 minutes, and
gives out both α and β (and probably γ) rays.
Godlewski found that the active deposit of actinium was very easily
volatilized. Heating for several minutes at a temperature of 100° C. was
sufficient to drive off most of the active matter. The active deposit is
readily soluble in ammonia and in strong acids.
=213. Radiations from actinium and its products.= Actinium in
radio-active equilibrium gives out α, β, and γ rays. Godlewski found
several points of distinction between the β and γ rays of actinium and
of radium. The β rays of actinium appear to be homogeneous, for the
activity measured by an electroscope was found to fall off accurately
according to an exponential law with the thickness of matter traversed.
The β rays were half absorbed in a thickness of 0·21 mm. of aluminium.
This indicates that the β particles are all projected from actinium with
the same velocity. In this respect actinium behaves very differently
from radium, for the latter gives out β particles whose velocities vary
over a wide range.
After the β rays were absorbed, another type of more penetrating rays
was observed, which probably corresponds to the γ rays from the other
radio-elements. The γ rays of actinium were, however, far less
penetrating than those from radium. The activity due to these rays was
reduced to one-half after passing through 1·9 mms. of lead, while the
thickness of lead required in order to absorb half the γ rays of radium
is about 9 mms.
The active deposit gave out α and β (and probably γ) rays. It was
difficult to decide definitely whether actinium X gave out β as well as
α rays. When the actinium X was heated to a red heat, the β activity was
temporarily reduced to about half its initial value. This decrease was
probably due to the removal of the active deposit, which, we have seen,
is readily volatilized by heat. If the β ray activity cannot be further
reduced, this would point to the conclusion that actinium X, as well as
actinium B, gives out β rays, but the evidence so far obtained is not
conclusive.
The ease with which the active deposit is volatilized by heat offers a
very simple explanation of the initial peculiarities of the decay and
recovery curves (Fig. 82) of actinium X. The activity of actinium X
rises at first, but there is no corresponding decrease in the activity
of the actinium left behind. It has been shown that the active deposit
is soluble in ammonia, and, in consequence, is removed with the actinium
X. The products actinium A and B and actinium X, immediately after
separation, are in radio-active equilibrium and we should not therefore
expect to find any increase of activity after removal, such as is
observed in the case of thorium, where thorium A and B are not removed
with thorium X. However, in heating the actinium X to drive off the
ammonium salts, some of the active deposit is volatilized. After
cooling, the amount of the active deposit increases to nearly its old
value and there is a corresponding increase of the activity.
[Illustration: Fig. 84.]
=214. Products of Actinium.= There is one very interesting point of
distinction between the radio-active behaviour of thorium and actinium.
The latter after removal of actinium X, shows only about 5 per cent. of
the original activity, while thorium, after removal of Th X, always
shows a residual activity of about 25 per cent. of the maximum value.
This very small residual activity indicates that actinium, if completely
freed from all its products, would not give out rays at all, in other
words, the first change in actinium is a rayless one.
The radio-active products of actinium are shown graphically in Fig. 84.
Some of their chemical and physical properties are tabulated below.
Products Time to be Rays Some Physical and
half Chemical properties
transformed
Actinium ? No rays Insoluble in ammonia
Actinium X 10·2 days α, (β and γ) Soluble in ammonia
Emanation 3·9 secs. α rays Behaves as a gas
Actinium A 35·7 mins. No rays Soluble in ammonia
and strong acids.
Actinium B 2·15 mins. α, β and γ Volatilized at
100°C. B can be
separated from A by
electrolysis
Footnote 296:
Soddy, _Trans. Chem. Soc._ 81, p. 460, 1902.
Footnote 297:
Rutherford and Grier, _Phil. Mag._ Sept. 1902.
Footnote 298:
Becquerel, _C. R._ 131, p. 137, 1900.
Footnote 299:
Meyer and Schweidler, _Wien Ber._ Dec. 1, 1904.
Footnote 300:
Meyer and Schweidler, _Wien Ber._ 113, July, 1904.
Footnote 301:
Rutherford, _Phil. Trans._ A. 204, pp. 169–219, 1904.
Footnote 302:
Pegram, _Phys. Rev._ p. 424, December, 1903.
Footnote 303:
Miss Slater, _Phil. Mag._ 1905.
Footnote 304:
von Lerch, _Ann. de d.] Phys._ November, 1903.
Footnote 305:
The ‘rayless change’ certainly does not give out α rays, and special
experiments showed that no appreciable amount of β rays were present.
On the other hand, the second change gives out all three types of
rays.
Footnote 306:
Miss Brooks, _Phil. Mag._ Sept. 1904.
Footnote 307:
Rutherford and Soddy, _Trans. Chem. Soc._ 81, p. 837, 1902. _Phil.
Mag._ Nov. 1902.
Footnote 308:
Miss Brooks, _Phil. Mag._ Sept. 1904.
Footnote 309:
Rutherford, _Phil. Trans._ A. p. 169, 1904.
Footnote 310:
Giesel, _Ber. d. D. Chem. Ges._ p. 775, 1905.
Footnote 311:
Godlewski, _Nature_, p. 294, Jan. 19, 1905.
Footnote 312:
Debierne, _C. R._ 138, p. 411, 1904.
Footnote 313:
Miss Brooks, _Phil. Mag._ Sept. 1904.