XXXIX. On the [alpha] Particles of Radium, and their Loss of 
Range in passing through various Atoms and Molecules. By 
W. H. Bragg, M.A., Elder Professor of Mathematics and 
Physics in the University of Adelaide, and R. Kleeman, 
P.Sc, Demonstrator [Communicated by the Authors. Read before the Royal Society of 
South Australia, June 6, 1904.]. 

In previous papers which we have contributed to this 
Magazine [citation redacted] we have shown that the [alpha] particle moves 
always in a rectilinear course, spending its energy as it 
traverses atoms of matter, until its velocity becomes so small 
that it cannot ionize and there is in consequence no further 
evidence of its motion. Each [alpha] particle possesses therefore 
a definite range in a given medium, the length of which 
depends on the initial velocity of the particle and the nature 
of the medium. Moreover, the [alpha] particles of radium which is 
in radioactive equilibrium can be divided into four groups, 
each group being produced by one of the first four radioactive changes in which [alpha] particles are emitted. All the 
particles of any one group have the same range and the same 
initial velocity. 

The present paper may be regarded as a continuation of 
the papers cited. Its contents are arranged under the 
following heads : — 

1. Improvements in the apparatus used for measuring the 
ranges and relative strength of the four groups of rays. 

2. Results of experiments with the new apparatus giving 
the following values of the ranges in air at a pressure of 
76 cm. and a temperature of 20° 0. 

Radium
Emanation or Radium A
Radium A or Emanation
Radium C

[table redacted]

These are correct, we believe, to '05 cm. The pressure 
and temperature are stated, since a change of 1 cm. in the 
pressure or 5 C C. in the temperature would produce an effect 
which could be observed. We have not yet determined 
which of the two middle groups belongs to the Emanation 
and which to Ra A ; but we have constructed a special piece 
of apparatus which will, we hope, settle the point. 



[header] 319 

The results also show that the four groups are alike in all 
respects save that of initial speed ; and farther, that the 
[alpha] particle spends its energy at a rate which is approximately 
inversely proportional to the square root of its speed. 

3. Determinations of the loss of range of [alpha] particles in 
consequence of their passage through various substances, 
from which it appears that for all the materials examined the 
loss in traversing any atom is nearly proportional to the 
square root of the weight of that atom. The loss in the case 
of a complex molecule is proportional to the sum of the 
square roots of the weights of the constituent atoms. 

4. Discussion of these results. 



§i. 

In the apparatus which we first used for these experiments 
we found that our measurements were liable to considerable 
irregularities. The most troublesome of these was an 
occasional sudden and violent increase of the ionization 
current which would cause the electrometer spot to fly off 
the scale. This would occur in the middle of a period of 
satisfactory working. It appeared to be due to the liberation 
of emanation from the radium under observation, and we 
have therefore enclosed the whole of our apparatus in a metal 
vessel through which a current of dry air is made to pass 
continually. 

In other respects the apparatus now used differs but little 
from that described on p. 728 of the Phil. Mag., Dec. 1904 : 
except that we have added an arrangement by which an 
aluminium screen can be drawn over the radium so as to cut 
off all [alpha] radiation, and we have made it possible to set the 
ionization-chamber at any desired depth. Both these arrangements can be worked from the outside of the enclosing vessel. 
It is necessary that the air which is drawn through should be 
fairly dry. In this country a difference of 30° F. between 
the wet and dry bulb thermometers is not unusual, and at 
these times artificial drying is hardly necessary ; but we find 
it more satisfactory to draw the air at all times through a set 
of large calcium-chloride tubes, the current passing day and 
night during the progress of any series of experiments. The 
need for dryness appears to arise from the fact that moist 
air acts on the thin film of radium which we employ and 
liberates emanation. 

At one time we endeavoured to secure the complete removal 
of any liberated emanation by passing the whole stream of 
air directly over the radium just before it left the vessel ; 

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320 [header]

but with this arrangement the remaining moisture of the 
air seemed to do more harm in liberating emanation than 
the current did good by carrying it away. We now pass the 
current of dry air through the vessel from one end to the 
other ; but the radium film probably feels little draught, 
being protected by the set of vertical metal tubes which 
stand over it (see the previous papers). When this is done 
the leak which the electrometer shows, the radium being out 
of range, is very small compared with the principal leak and 
is fairly constant. In the experiments described later it 
amounted usually to one or two millimetres in ten seconds, 
whilst the principal leak might be as much as sixteen centimetres in the same time. 

This residual leak is due to various causes. One of them 
is the leak which takes place from the metal of the ionization-chamber, and the wire which connects it with the electrometer, 
to the earthed metal case which screens the chamber and its 
connexions from external influence. This current is supplied 
by the ions which are continually formed by various agents 
in the air within the earthed casing, and is driven by the Volta 
potential-differences between the metals of the connexions 
and the casing. It can be materially altered by changing 
the material of the casing, or part of it, e. g. exchanging zinc 
for copper. If a speck of radium is placed within the casing 
so as to increase the supply of ions the effect is surprising. 
As an illustration we allowed the electrometer connexions 
to end in a brass wire 15 cm. long, which projected horizontally in the open air, the ionization apparatus being disconnected. When a large earthed copper tube containing 
the radium speck was placed so that the brass wire was along 
its axis, the electrometer showed a large deflexion, whereas, 
when the copper was displaced by zinc, the deflexion was 
also large, but in the opposite direction. 

The whole of the apparatus including the keys which connect 
the electrometer to earth or the ionization-chamber is enclosed 
in earthed metal casing. The keys are worked by electromagnets which are fixed externally to the casing, and operate 
on iron armatures within. We have found it necessary to be 
careful as to the contacts of these keys. Want of perfect 
contact causes incomplete charging or discharging of the 
electrometer quadrants, shown by kicks and irregular movements of the light-spot when the keys are used. We 
have obtained good results by making the contacts of 
platinum surfaces, so arranged as to rub each other at the 
make or break. This does not introduce any want of 
definition into the beginning or ending of a leak, since both 



[header] 321 

these times are determined by the breakings of contacts, 
and these are done by the electromagnets with great 
suddenness, 

An arrangement which we find to be of great importance, 
is the ion-trap which is placed under the gauze of the 
ionization-chamber. The space below the gauze B, forming 
the lower plate of the ionization-chamber A B, is of course 

[figure redacted]


filled with the ions formed by the rays which cross it. When 
the gauze C is not present, then although B is at a high 
potential, some of these ions manage to cross it and add 
themselves to those in the chamber AB, thus disturbing the 
results to be measured. We were first aware of this effect 
occurring in any marked degree when we began to use a 
platinum dish on which had been evaporated a few drops of 
water containing a speck of very pure radium bromide. We 
were so very fortunate as to be presented by Mr. Soddy with 
a milligramme or two of this material; by its use our experiments were very greatly improved, as will be described a 
little later. On the first occasion of its use, however, we were 
puzzled by a rather curious result. The radium and the 
tubes above it were rather close up to the gauze B. We were 
measuring the various leaks as, millimetre by millimetre, we 
pushed the radium still closer. Every now and then we drew 
the aluminium screen over the radium so as to discover how 
much of what was observed was really due to the [alpha] rays. We 
found that after the screen had been so used and withdrawn, 
the proper leak was materially lessened, but recovered its old 
value in a short time. When the screen was drawn over 
again, the leak (which was then not due to [alpha] rays) fell 
instantly to its usual very small value, and again, when the 
screen was withdrawn, the proper leak was for a time too 
small. We guessed therefore that some of the leak, with the 
screen off, was due to ions made outside the chamber, which 
afterwards drifted into it. The interposition of the aluminium 



322 [header] 

screen instantly cleared all the space between itself and the 
gauze B of ions, because the gauze was at a high potential 
and the screen was earthed. No more ions were made in this 
space until the screen was withdrawn. When this was done, 
the space just below the gauze and above where the screen 
had been was momentarily empty of ions, and though the 
continued passage of the [alpha] rays through it soon refilled it, 
yet there was a short time during which the ions in the space 
were below normal value, and therefore the drift upwards 
into the ionization-chamber was small. If this drift existed, 
it was certainly to be avoided, and we therefore placed below 
the gauze B a parallel gauze C about three millimetres 
away, which was put to earth. No ions could cross the 
powerful field which existed between the two gauzes. The 
second gauze cut off a number of [alpha] rays which would otherwise have entered the chamber, but there were still quite 
enough. With this new arrangement the irregularity 
described above has disappeared completely. Another 
irregularity has also disappeared at the same time ; it was 
probably due to the same cause, and removed in the same 
way. It occurred when one or other of the bundles of rays 
was just out of range of the ionization-chamber, and took the 
form of a small leak which seemed to prelude the arrival of 
the real rays ; it formed a slight projection on the ionization 
curve just above the true and large increase which represented 
the entrance of the rays of the bundle into the ionization-chamber, as the radium was pushed higher and ' nearer. 
It often blurred the corners of the ionization curves, and 
made it more difficult to determine the exact ranges of the 
rays. 

The electrometer used in these experiments is of the 
Dolezalek pattern. It has been been frequently calibrated, 
either by charging it and causing it to share its charge with 
an auxiliary condenser, or by measuring a given radium leak, 
first, when the electrometer was in parallel with the condenser, 
and again when it was not. The deflexion for a given charge 
is wonderfully constant over a wide range of voltages of the 
needle ; though the deflexion for a given potential varies 
considerably. It is not found satisfactory to maintain the 
conductivity of the quartz fibre by dipping it in a solution of 
calcium chloride ; in dry weather it does not conduct. It is 
better to recharge the needle to 250 volts every few hours, 
if it is used for so long ; the needle may then leak considerably without alteration of the deflexion for a given 
charge. 



[header] 323 



Having made those various improvements in our apparatus, 
and become more familiar with its use, we made a new layer, 
as already mentioned, from the pure radium bromide which 
Mr. Soddy had so kindly sent us. This at once gave good 
results. The curves shown in fig. 1 show the considerable 
precision which it was now possible to attain. 


[figure redacted]


It may be well to repeat here that these ionization curves 
show the amount of the ionization due to the [alpha] rays at various 
distances from the radium layer, the medium ionized being 



324 [header] 


air at ordinary pressures and temperatures. A bundle of 
copper tubes is placed in a vertical position over the horizontal layer, so that only such [alpha] particles as move in a 
direction nearly vertical are allowed to proceed upwards. 
The bundle used at present contains about 100 tubes made of 
thin copper, each 2 mm. in diameter and 1 cm. long. The 
ionization-chamber consists of an upper horizontal plate of 
aluminium, and a lower plate of brass gauze ; the distance 
between the plates in most of the experiments described in 
this paper was set at two millimetres. The ordinates represent the distances from the radium plate to the gauze ; and 
the abscissae the leaks on the quadrant electrometer. The 
absolute value of these leaks was not accurately measured, as 
there was no object in knowing more than their relative 
values; but it was calculated that the greatest leak measured 
was about 10~ n ampere. 

Curve A, in fig. 1, shows the ionization due to the [alpha] rays 
when the dish was first prepared. It had been kept at a 
bright red heat for some minutes after preparation. The 
shape of the curve shows that all radioactive products except 
the radium itself had been completely removed. On comparison with the similar curve on p. 730 of the paper already 
cited, it will be seen that the new radium layer is thinner 
than that from which our first results were obtained ; for the 
maximum value of the ionization occurs at 2*85 cms. instead 
of at 2'5. The greatest range is about 34 as before. This 
means that the [alpha] particles from the bottom of the new layer 
lose, in coming up through the material of the layer, a range 
of 5*5 mm. measured in air : the corresponding amount for 
the older layers was 9 mm. The new layer is nevertheless 
nearly twenty times stronger than the old. The term layer 
is, in fact, rather inappropriate. Actually the radium is not 
distributed over the dish in a thin uniform sheet but is studded 
over the surface in the form of small crystals which can be 
easily seen under the microscope. Consequently a weaker 
solution of radium bromide does not give, when evaporated, 
a thinner layer; but simply a smaller number of crystals. The 
various bundles, and in particular those from Ra, Emanation, 
and Ra A do not therefore stand out any better from each 
other when a weaker solution is evaporated, as we found on 
making the experiment. But the greater purity of the new 
layer gives the result which we formerly sought to obtain by 
evaporating very weak solutions. Presumably the crystals 
are now more regularly arranged, and are not overlaid by other 
matter which acts as a screen. 

Since the radiation of the new layer is so strong, the 



[header] 325 

residual errors of the experiment become relatively small. In 
particular, consecutive readings of the same leak become 
much more nearly in agreement than before ; when the 
readings are large, the difference between two such readings 
is generally less than one per cent, of the whole. For small 
readings it is proportionately greater ; and it is quite clear 
that much of this irregularity is due to some extraneous 
cause, and is not due to variability of the principal leak, or 
inaccuracy either of the observer or his apparatus. Other 
experimenters have made a similar observation. 

In the case of all the measurements recorded in this paper, 
the current was allowed to run into the electrometer for ten 
seconds ; the mean of the first and second points of rest of 
the needle was taken as the correct reading. This was 
justifiable, as relative, not absolute, measurements were 
wanted ; and as the difference between these two measurements was very nearly proportional to the whole 
deflexion. 

Carves B, C, and D in fig. 1 show the state of the radium 
at definite intervals after preparation of the layer. Similar 
curves were published in our previous paper, but the curves 
now shown are much more accurate, and supply much more 
information. In the first place, the division of the [alpha] rays 
into four groups is now seen very clearly, and the range of 
each group can be measured accurately. In the former 
curves, the separation of the two central groups was not well 
effected, but now it is plain ; the improvement being mainly 
due to the greater thinness and evenness of the radium 
layer. 

In the same figure, curve B shows the state of the radium 
when 28 days old. According to Rutherford's theory the 
number of [alpha] particles in each group is the same, provided the 
radium preparation is old enough to be in radioactive equilibrium. This can be proved from the curve E in the following 
manner. 

The curved side ab, belonging to Ra C, is produced to c, as 
shown. The line d e represents a certain ionization produced 
by [beta] and [gamma] rays which is intercepted by the aluminium screen. 
It is the small difference between the readings at (say) 
7*5 cm. when the aluminium is on and off. When the radium 
is within range, and the ionization of the [alpha] rays is measured 
as the difference between the on and off readings, this small 
quantity of [beta] and [gamma] ionization is included in the difference. 
Its value must be nearly constant over all ranges, as it is a 
certain fraction of the total [beta] and [gamma] ionization, which latter 
is found to be constant by experiment. We may therefore 



326 [header]


consider the figure bounded by the vertical line through de 
and by the curved line dabc to represent the ionization by 
the Ra C particles over the whole of their course except the 
first two centimetres. 

This curve is now added to itself, being first lowered 
through 2*23 cm., and the points represented by dots in 
circles represent some of the results of the addition. It will 
be seen how nearly these points lie on the actual ionization 
curve, on which the experimental readings are marked by 
crosses. Again the curve dabc is lowered, by 6*0 mm. this 
time, and added on to the sum already obtained, and the new 
points which show the result of the addition are also marked 
as dots in circles. These also lie very nearly on the ionization 
curve. For the last time the curve is added on, being this 
time lowered 7*3 mm. ; and again the calculated points lie on 
the experimental carve except just at the peak. Thus the 
full curve is formed by the superposition of four simple 
curves, each alike in all respects but that of height ; and the 
inference is that the four groups of [alpha] particles are alike in 
every respect but that of initial velocity. The differences of 
the ranges are in this way given with more accuracy than 
that with which the actual ranges can be found, for it is hard 
to avoid all uncertainty about the latter because the gauze of 
the ionization-chamber is not easily made quite flat. If the 
curve fg is produced to meet the curve Jig also produced, then 
the meeting-point is at a height 3 '4 cm. This point should 
represent the arrival of the R[alpha] rays at the middle of the 
ionization-chamber, which is 1 mm. higher than the gauze. 
Hence the range of the particles from Ra is 8*50 cm.; and the 
ranges of the other three groups are 4*23, 4*83, and 7"06. 
These must be correct to 0*5 mm. 

Since the ionization curve can now be drawn with some 
accuracy, it becomes reasonable to make an attempt to discover the relation between the velocity of the [alpha] particle and 
the rate at which it spends its energy. 

Let v be the velocity of the particle, and s the distance it 
has yet to run. Suppose that the energy spent per 
cm. = k.v~ n j where k and n are constants. We seek a value 
For n. 

Then 

[formula redacted]


[header] 327 

Hence the rate of expenditure of energy on ionization 

[formula redacted]

If the strip of air (supposed thin) in which the ionization 
is measured is at such a height above the radium layer that 
the [alpha] rays from the top of the layer pass it by a distance a, 
and those from the bottom by a distance x — d, then the 
ionization produced in this strip by the [alpha] particles from all 
parts of the layer 

[formula redacted]



where A is a constant. If the rays from the top of the layer 
pass the strip by %, and those from the bottom do not reach 
it, then the ionization 

[formula redacted] 

In the curves as found experimentally the effect is further 
complicated by the fact that the ionization-ch amber has an 
appreciable depth of 2 mm., and that the cones of rays have 
an appreciable vertical angle. We need not, however, take 
these factors into account in the formula. We can give n 
different values, plot the corresponding curves as found from 
the formula, and round off the corners in accordance with the 
effect which the two disturbing factors must have. 

When this is done, it is found that n = 1/2 gives a curve 
which is very near to the actual form. Choosing the value 
5 mm. for d, which seems proper from an inspection of the 
curve and from trial, the ionization is equal to Aa4/5 from 
[formula redacted], and thereafter to [formula redacted]. The 
curve obtained from this formula is plotted in fig. 1, P ; and 
the corners are rounded off by the dotted line. The value of 
A is chosen so as to make the curve more easily comparable 
with the experimental curve E (portion d a be). 

Curves Q and R are derived from the formula when n is 
put equal to 1 and to 1/3 respectively. It will be seen that 
they do not approach the experimental form so well, and err 
in opposite directions. 



328 [header] 


The conclusion is that the [alpha] particle spends its energy at a 
rate which is approximately inversely proportional to the 
square root of its velocity. 

§iii. 

From the results described above as well as from those described in the previous papers [citation redacted] it will be 
clear that the law of the absorption of the [alpha] rays is considerably different from that which has been generally assumed 
hitherto. It has been supposed that a stream of radiation 
gradually diminishes in power as it penetrates any material 
substance, the rate o£ loss being approximately expressible 
by an " absorption coefficient," and the law being therefore 
nearly exponential. It is true that it has been pointed out 
that this coefficient is not constant for any one stream in any 
one gas, but varies with the distance of the stream from the 
source. If this variation were small, there might be some 
ground for considering that the law was fundamentally 
dependent on an exponential form, but varied from it on 
account of some secondary cause. Asa matter of fact, however, the variations are far too great to permit of such a 
supposition. 

The true state of affairs is very different. There is no such 
absorption coefficient, nor any approach to an exponential 
law. 

Each [alpha] particle pursues a rectilinear course, no matter what 
it encounters : it passes through all the atoms it meets, 
whether they form part of a solid or a gas (or in all probability of a liquid), suffering no deflexion on account of any 
encounter until, at any rate, it is very near the end of its 
course. It loses energy as it goes, a portion of this at least 
being spent in producing ions. This drain on its energy, at 
least, robs it of its extraordinary powers of penetration and 
ionization. 

From this it will be clear that there are two quite 
independent characteristics of a stream of a radiation : one, 
the number of [alpha] particles in it, the other, the energy of their 
motion. The latter may more or less be evenly distributed 
amongst the various particles. It is possible for the latter of 
these characteristics to vary considerably whilst the first does 
not change at all. For example, in the curves described 
above, the [alpha] particles from Ra C remain unchanged in number 
up to nearly 6*5 cms. from the commencement of their 
motion ; but their energy has almost vanished at the longer 
distance. Again, as will be seen later, a thin metal plate 



[header] 329 

may be placed in the way of the stream, and so rob every 
particle of some of its energy, but not a single one is brought 
to rest by collision with the atoms of metal, and the number 
of particles in the stream remains unchanged. 

In our experiments two different quantities are measured, 
one the range of the [alpha] particles, the other, the ionization 
which they produce. The range of the [alpha] particle in a given 
substance is the distance it can penetrate before losing its 
power of making ions in that substance, which can be 
collected and measured by electrical means. We assume 
that when it ceases to have this power, the energy has fallen 
to an amount which is very small compared to its initial 
energy (say 1/500), so that even if it varies in different 
substances, such a variation cannot affect the range appreciably. 
As a matter, of fact, it is probable that no such variation 
exists. 

The range of an [alpha] particle in any substance is therefore 
dependent on the original energy of projection. It is not 
quite proportional to it, because, as Ave have pointed out 
already, the [alpha] particle does not spend energy at exactly the 
same rate at all periods of its flight ; towards the end of its 
range its rate of expenditure is somewhat increased. If the 
particle is made to pass through some material other than 
air, its range may be much altered. For example, if it passes 
through a thin silver film whose thickness is '001 cm. its 
range in air, supposing it to be allowed to complete its course 
in that medium, is diminished by more than 3 cms. Or 
again, the [alpha] particle which has a range of 7*0 cms. in air has 
only a range of 3'3 cms. in methyl bromide at the same 
pressure and temperature. Consequently, if we measure the 
range of the [alpha] particles in different gases, or after their 
passage through thin films of matter, we obtain a measure of 
the comparative rates at which energy is expended by a 
particle in passing through these gases and materials. 

The second quantity which is measured by us is the 
ionization produced by the particle at various distances from 
its source. From this measurement we are able to discover, 
amongst other things, whether the stream has suffered in any 
other respect than that of loss of range when it has passed 
through thin material films, supposing that the rest of the 
flight is in ordinary air ; and if we compare the quantities as 
measured in different gases, we are enabled to compare the 
conductivities which are imparted to these gases by [alpha] particles 
moving through them under conditions otherwise similar. 

These two quantities are independent of each other. It is 
true that if the conductivity of a gas were proportional to the 



330 [header]

number of ions produced by the particle, and that if the total 
number of ions produced by an [alpha] particle were the same, no 
matter the gas in which it completed its course, then the 
product of the ranges and the ionization per cm. of path 
would be a constant. Now Rutherford has made measurements of the total ionization produced by the particle in some 
substances, and found it the same in each case. But there 
are other substances for which this is not true ; e. g., ether, ethyl 
chloride, and methyl bromide ; and in consequence the second 
of these suppositions is not justified. It is even possible that 
the first may also prove incorrect. It is conceivable that the 
[alpha] particle may spend energy on ionization whilst passing 
through a molecule, especially a complex molecule, and that 
the products may never get away from the molecule so as to 
be separated by the electrical field, and measured by the 
electrometer. That this actually occurs certainly seems a 
natural inference from some of the following results. 

Let us now consider the experimental evidence. In fig. 2 
are drawn three curves, A, B, and C. The first of these represents the ionization curve of radium in air. Curve B shows 
the result of placing a number of thin sheets of silver-leaf 
over the radium, so that the rays had to traverse these before 
reaching the ionization-chamber. Curve C shows the effect 
of substituting thin silver-foil for the leaf. The product of 
the density and the thickness was in the case of the leaf 
•00213, and in the case of the foil '009(57. These figures 
were readily obtained by weighing a measured area of the 
material in each case ; the leaf was not easy to handle, and 
the loss of range in its case not very great, so that the foil 
experiment is the more reliable. 

The curves ABC are clearly similar in shape, and differ 
only in their height above the zero line. The silver sheet 
has not in either case caused any modification of the a stream, 
except that it has cut off an equal amount from the range of 
each particle. 

If some of the particles had been stopped by the metal, or 
if some had lost more energy than others, there would have 
been more or less distortion of the curve. But the former 
condition does not occur, as has been already explained, and 
the latter was also prevented in this case by the great 
uniformity of the foil, which was polished on both sides. 

The loss of range in the case of the silver- foil is 33*5 mm. 
If we take the density of the air to be *0012_, we may say 
that a silver stratum for which thickness X density = '00967 
is equivalent to an air stratum for which the same product 
= 3-35 X '0012 = -004:02. The ratio of these quantities is 2*41 . 



[header] 331 

In fig. 2 are shown the results of some o£ our experiments 
of this kind on other metal films. All do not show the same 
regularity as the silver : for we have found great difficulty 
in obtaining uniform films in the majority of cases. The 

[figure redacted]



rolls used by the jewellers are not fine enough to give perfect 
results, and we believe there is no goldbeater in Australia at 
present. Nevertheless the metal workers have managed to 
roll for us films of gold, platinum, and copper which have 
given us fair results ; aluminium leaf was procurable and 



332 [header]

thin tinfoil. When a film is not uniform, the fact is made 
evident by a distortion of the curve, e. g. in the case of 
copper. It will be seen that the top of it slopes too much, 
implying that the [alpha] rays do not come into the ionization-chamber as suddenly as they ought to do. Some have, in 
fact, been less checked than others because they have passed 
through thinner portions of the somewhat uneven film. We 
have measured, in such cases, the drop of the curve as shown 
by its amount at the middle point of the top of the Ra C 
portion. E. g., in the case of platinum we have measured 
the depth of the middle point of the top of the curve below 
that of the middle point of the top of the normal curve. 

The results of these experiments are shown in the following 
table. The first column of figures gives the product of the 
thickness of the metal film and its density, the second the 
corresponding drop of the curve, multiplied by the density 
of air, and the third the ratio of these two products. 




[table redacted]



[Tinfoil contains a certain proportion of lead ; but this could not affect 
the result very appreciably.] 

It is remarkable that the numbers in the third column are 
nearly proportional to the square root of the atomic weights 
of the metals. To bring this out more clearly, the square 
roots are shown in a fourth column, and in a fifth the ratios of 
the numbers in the two previous columns. 

Moreover, air itself falls approximately into line with the 
metals. Its ionization ratio should be entered in the third 
column as unity, and the average square root of its atomic 
weight as [formula redacted]. The corresponding entry 
in the last column should be also 3*79. 

Also it is easily seen that hydrogen is not far away from 
the others. For it has been shown by Strutt that its conductivity under ionization as compared with air is '226. Assuming for the present that this means that a 1 cm. layer of 
hydrogen has the same effect as a '226 cm. layer of air, then 
the ratio of the product of the thickness and the density in 
the case of the hydrogen to the similar product in the case 
of the air is [formula redacted]. The square root of its atomic 
weight is 1, and [formula redacted]. 



[header] 333 

Since the atomic weight is of such consideration in this 
law, it is more direct to state the results in another way. 
Instead of comparing the stopping powers of strata of metal 
and air of equal weights, we can compare the stopping powers 
of strata containing equal numbers of atoms, and therefore 
the stopping powers of individual atoms. For example, a 
stratum of silver produces the same effect as a stratum of 
air whose weight is 2*41 times greater. Thus for equal 
weights silver stops 1/2'4I times as much as air ; but for 
equal numbers of atoms it stops [formula redacted] times as much 
as air. This ratio, which is equal to 3" 11, may be called the 
" stopping power " of the silver atom, referred to the air 
atom as a standard. The latter is an imaginary atom having 
an atomic weight 14'4, a molecular weight 28*8, and an 
atomic square root 3' 79. 

The stopping powers of the various metals examined will 
be set out below, in conjunction with those of certain cases. 

When we found that a simple law seemed to cover the 
behaviour of substances differing so widely in all their properties as those enumerated, we thought it advisable to 
examine such other substances as were available. We were 
unable to obtain other metal films; and we therefore turned 
our attention to gases. Now no striking evidence for the 
square-root law could be obtained from an examination of 
gases whose atomic weights were nearly the same as that of 
air, such as oxygen or nitrogen. Indeed, it had already been 
shown by Strutt that their behaviour was very much the same 
as that of air. Nevertheless, it was not to be forgotten that 
their proved properties were not against the square-root law. 

We therefore made experiments with the following gases, 
which contained atoms whose weights were very different 
from those of air atoms: — 

Methyl bromide, methyl iodide, ethyl chloride, carbon 
tetrachloride, ether, and hydrogen. 

Methyl bromide was a most suitable gas for our purpose. 
The ratio of its molecular weight to that of air is 3*28. If 5 
then, the loss of range in passing through this gas were 
proportional to the density, the range of the particle from 
Ha C would be only about 7'28 or 2*3 cm., provided the 
gas were at atmospheric pressure. But if the square- root 
law were true, the range would be much greater, and could 
be calculated thus : — 

The carbon atom should contribute a stopping power proportional to [formula redacted] the three hydrogen atoms to [formula redacted], and 
the bromine atom to v'80. Total [formula redacted]. 
In air the stopping power should be the average of that of 

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334 [header] 



four molecules of nitrogen and one of oxygen. The stopping- 
power of nitrogen should be proportional to 2 v^14 or 7*48, 
that of oxygen to [formula redacted]. Now [formula redacted]. 
Therefore the stopping power of the CH 3 Br molecule as 
compared to that of air should be 15 , [formula redacted] ; and the 
range of the [alpha] particle of Ra C should be 7/2*03 = 3*4 cm. 

A sufficient quantity of methyl bromide was prepared and 
kept liquid in a freezing-mixture. The vessel containing our 
apparatus was joined to an air-pump and exhausted till the 
remaining pressure was equal to about 6 cm. of mercury. 
The liquid was then allowed to pass in under atmospheric 
pressure until the vessel was full of the gas. The pressure 
was again reduced to 6 cm., and vapour introduced until 
the pressure in the vessel was once more equal to that of the 
atmosphere. 

The ionization curve was then obtained. It is plotted in 
fig. 2, and shows that the range is nearly as calculated from 
the square-root law. 

It was not advisable to take it for granted that the vessel 
contained vapour only ; and after a little time we hit upon a 
method of determining this point satisfactorily. The method 
also proved particularly useful in the case of mixtures of air 
and vapours, as will be described presently. Immediately 
after measuring the range of the particle in the gas, we 
opened a communication between the vessel and an exhausted 
globe of about one litre capacity. The capacity of the vessel 
itself was 6 litres. The weight of the gas so drawn over was 
compared with the weight of the air that came over under 
similar conditions when the larger vessel contained air only; 
and from this ratio the proportion of air and vapour could be 
deduced. For example, the weight of the mixture of air and 
methyl bromide was 2*599 grains. The corresponding weight 
of air was *800 gram. (It was not, of course, at atmospheric 
pressure.) Hence if a?= the ratio of the number of air 
molecules to the number of molecules of CHBr, 


[formula redacted]



The extreme range of the [alpha] particle of Ra C in CH 3 Br is 
shown by the curve to be 3*32, This is the distance from 
the radium to the gauze of the ionization-chamber. The 



[header] 335 

latter was 2 mm. deep, and half this, viz. 1 mm., should be 
added in order to get the true range, which may therefore 
be taken as 3 "42. The corresponding range in air is 7*06. 

Hence, if x — stopping power of the methyl-bromide 
molecule, 

[formula redacted]

which is very nearly the value already calculated on the square-root law. The errors of experiment were not so small that this 
almost absolute agreement can be looked on as more than 
accidental. It will be seen, however, that all the gases examined gave good results. 

The curve of a gas is different in some important respects 
from that which is obtained in examining the loss of range 
in metal films. In the latter case, all the ordinates are reduced from those of the normal air-curve by nearly the same 
amount ; in the former, they are reduced in nearly the same 
proportion. Again, in the case of the metal film (provided 
it is uniform) the abscissas are unaltered ; in "the case of the 
gas, the abscissae are all altered in the same proportion and 
show the amount of ionization produced by the [alpha] particle in 
traversing the gas. For example, the extreme abscissa of 
the Ra C group has the value 666 in the gas and 547 in air ; 
thus the ionization per cm. is 666/547 or 1*27 times greater 
in the gas than in the air. Since, however, the range is 
2*07 times shorter, the ratio of the total ionization in the gas 
to the total ionization in air is only l , [formula redacted] nearly. 

In most of the complex gases examined the [alpha] particle 
produces less ionization than in air. We propose to make a 
further examination of this point. 

In the case of the other gases, the procedure was very 
similar. Carbon tetrachloride, methyl iodide, and ether are 
liquid at ordinary temperatures and pressures, and in their 
case we introduced the necessary quantity of liquid to give a 
vapour pressure of about two-thirds that of saturation, and 
then filled up with air. We found it better to do this than 
to attempt the experiment with low pressures in our vessel, 
for the latter had so many joints and stuffing-boxes that it 
would not keep a vacuum very well. It was, however, quite 
airtight enough to retain a mixture unchanged for hours 
provided it was at atmospheric pressure. The proportion of 
air to vapour was afterwards determined in the manner already 
described. 

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336 [header]



Ethyl chloride was tried before we used the method of 
weighing a definite quantity of the gas. But the vessel was 
emptied and filled three times, and there must have been very 
little air in it. It cannot give a decisive answer as to the 
validity of the square-root law, because, as it happens, the 
square-root law and the simple density law give nearly the 
same value. On that account we have not yet repeated 
the experiment. 

Hydrogen presented some special difficulties. The range 
(on the square-root law) of the [alpha] particle of Ea C must be 
about 30 cm., and our apparatus only measures up to 8 cm. 
We therefore placed a piece of silver-foil over the radium, 
which was equivalent to 3'3 cm. of air. This cut down the 
range of the Ra C particles to 3*63, and the range of the 
swiftest of the others to 1'43. The former when multiplied 
by four would still be out of range, but the latter would be 
within it. 

Fig. 2 (p. 331) shows that this was the case. With a mixture 
of hydrogen and air in the proportion (by pressure) of 9 to 1 
it was at 4" 6. With mixtures containing a greater proportion 
of hydrogen it rose somewhat, but a small proportion of air 
made little relative difference. The curve is of course very 
much drawn out vertically, and drawn in horizontally. 

The results obtained for all the above substances are collected 
in the following table : — 



Table, showing " stopping power " of various atoms and 
molecules as compared with that of air. The atomic weight 
of the supposititious atom of air is taken as 14*4, and the 
" atomic square root " as 3" 79. 





Stopping power of atom or molecule. 


Ratio of square roots. 

Ratio of atomic or molecular weights. 


[table redacted] 



[header] 337 



These results are shown graphically in fig. 3, in which 
the ordinates and abscissæ represent the numbers in the first 


[figure redacted]




and second columns respectively. It is curious that the 
metals and gases seem to lie on rather different lines. Possibly this is due to the difference between solid and gas; 
possibly again to the fact that the gases tested have such 
complex molecules. Further research may make the point 
clearer. Several other points arose in the course o£ the 
experiments, which deserve further inquiry. For instance, 
the metal films did not cause exactly the same drop throughout all the curve ; the slower [alpha] particles were a little less 
affected than the swifter. 

§iv, 

From these results it appears that the following law is 
true for certain elements, at least to a first approximation. 

The energy spent by an [alpha] particle in its passage through 
an atom is proportional to the square root of the atomic 
weight. It can never be said that this is a law which is 
general to all the elements until all the elements have been 
experimented upon. In the case of many of them, the experimental difficulties will be very great. Since, however, 
the law holds with some accuracy in several cases, it becomes 
desirable to consider whether any physical interpretation can 
be placed upon it. 



338 [header]



Now the energy which is spent by the [alpha] particle is certainly 
spent, in part, in producing ions. If the rate of the expenditure of the energy as a whole is related to the atomic weight 
by so simple a rule as that of the square root, it is probable 
that the part which is spent on ionization obeys the same 
rule. For if not, and if the expenditure on ionization follows 
some other law, then the remaining expenditure must follow 
such a law that the two together compound into the simple 
rule of the square root. It is proper to put aside this more 
complicated hypothesis until we have considered the simpler 
one. 

We may therefore advance the law one stage and state it 
thus : — The energy spent on ionization by an [alpha] particle in its 
passage through an atom is proportional to the square root 
of the atomic weight. The question now arises : Is the 
variation from atom to atom due to a difference in the number 
of ions produced, or in the energy required to produce an 
ion, or in both these quantities? Because an oxygen atom 
absorbs four times as much energy as a hydrogen atom, are 
there four times as many ions produced from an oxygen 
atom, but the energy per ion the same ; or is the act of 
ionization four times as difficult, but the number of ions the 
same ; or are neither of these suppositions true, and is 
the difference between oxygen and hydrogen in this respect 
due to a variation in each of the two quantities ? 

Now the total conductivity imparted to a gas by the passage 
of [alpha] particle through it is very nearly the same for the simpler 
gases. This is true even though some of them differ widely 
from each other in their atomic weights, e. g. oxygen and 
hydrogen. From this it appears probable that the energy 
required to produce an ion is always the same. It is true 
that in some of the complex gases the total conductivity is 
less than in the simpler gases, but this can be explained on 
the hypothesis that the same number of ions is made in these 
heavy molecules, but that they find a difficulty in escaping 
from the molecule and are recombined, so that they add 
nothing to the conductivity of the gas. If this hypothesis is 
not entertained, we are driven to suppose that the energy 
required to make an ion is not the same in some of the 
complex molecules, and that the number made varies by just 
so much as to make the total loss of energy of the particle in 
each molecule follow the same simple law as holds for the 
simpler molecules. For the present at least this complicated 
supposition must also be set aside, and again we may make 
an advance in the statement of our law. It now stands : — 
The number of ions made by an [alpha] particle in passing 



[header] 339 

through an atom is proportional to the square root of the 
atomic weight. 

It should, perhaps, be pointed out that this does not mean 
that the [alpha] particle makes the same number of ions out of 
each atom of the gas through which it is passing ; but merely 
compares the average per atom. It asserts, for example, 
that in going through oxygen the [alpha] particle makes a number 
of ions which is four times as many as the number made by 
the particle moving with the same speed in passing through 
hydrogen at the same pressure and temperature. 

It is possible that this rule implies that [alpha] particle must 
make more than one pair of ions in passing through any one 
atom, unless ionization is only rarely the consequence of the 
encounter. For if only one pair could be made in each 
atom, and if the [alpha] particle made one pair in crossing each 
atom of hydrogen, then in oxygen at the same pressure and 
temperature as the hydrogen, only the same number of ions 
would be made per centimetre, which is not the case. Nor 
does it appear possible to suppose that ionization does not 
occur at a large proportion of encounters ; the number of 
ions made is of the same order as the number of atoms 
traversed, according to Rutherford. 

The most reasonable interpretation of these results seems 
therefore to be (1) that the [alpha] particle makes the same number 
of ions during its course no matter what the gas which it 
traverses ; ^2) that the energy required to make a pair of 
ions is always the same ; and (3) that the observed variations 
in the conductivities in some cases are due to the failure of 
ions to get free from the molecule in which they are made. 

Under these circumstances we must look for the origin of 
the square-root law in some disposition which limits the 
number of ions that can be made in an atom. It is not to 
depend on any variation of the energy required to make a 
pair of ions ; but must be due to some condition which only 
gives the [alpha] particle such an opportunity of making ions as is 
to be measured by the square-root of the atomic weight; 
and, where it forbids the act of ionization, forbids also the 
corresponding expenditure of energy. 

We can only make guesses as to what this condition may 
be. It has been maintained, on good evidence [citation redacted], that the atom has a 
disk-like form, and that the various atoms and molecules 
differ in two dimensions only. It is possible that an explanation of the square-root law may be found in the 
hypothesis that ions can only be formed on the circumference 
of the atom's disk, for the amount of that portion of the atom 



340 [header]

which lies on the circumference is proportional to the square 
root of the whole. Under such circumstances an [alpha] particle, 
if it struck the atom anywhere except at the edge, would pass 
through without result. 

Since the energy required to make a pair of ions is 
probably the same no matter what the atom or molecule may 
be in which they are made, and no matter whether it be 
solitary or a constituent of a complex molecule, we seem 
driven to the belief that ionization consists in breaking bonds 
which are always the same, both in character and in strength. 
The electron is torn from its union with something else which 
is always the same, and must form some constituent of all 
atoms. This hypothesis also makes reasonable the supposition 
that an act of ionization may be performed within a complex 
molecule, and yet no conductivity be imparted to the gas. 
For the act would then consist in the breaking of an electron 
from its attachment to this common constituent, and would 
not of necessity imply separation from the system of the 
molecule. The idea of a common constituent is, of course, 
an old one. It is certainly strengthened by the discovery 
that radium and its successive products emit [alpha] particles which 
are exactly alike. 

We wish to express our gratitude to Mr. J. P. V. Madsen, 
B.Sc., for the generous assistance which he gave us during 
several weeks of full work, and to Professor Rennie, D.Sc., 
and Mr. A. J. Higgin for their kindness in making the 
chemical preparations.