Radioactivity

Radioactivity. The subject of radioactivity deals with phenomena exhibited by a special class of bodies of high atomic weight of which uranium, thorium, radium and actinium are the best known examples. These substances possess the property of spontaneously emitting radiations of a special character which are able to penetrate through matter opaque to ordinary light. The beginning of this subject dates from 1896, and was an indirect consequence of the discovery of the X rays made a few months before by Röntgen. It was known that the production of X rays in a vacuum tube was accompanied by a strong phosphorescence of the glass, and it occurred to several investigators that ordinary substances made phosphorescent by visible light might emit a penetrating radiation similar to X rays. Following out this idea, H. Becquerel (1),1 a distinguished French physicist, exposed amongst other substances a phosphorescent compound of uranium, uranium 1 These numbers refer to papers noted under References (below).

		RAD I	EMANATION
Aillih.

potassium sulphate, enveloped in paper beneath a photographic plate. A weak photographic effect was obtained. This was shown to be due to a penetrating radiation capable of passing through sheets of matter opaque to ordinary light. Further investigation showed that this photographic action was exhibited by all compounds of uranium and by the metal itself, and had nothing to do with phosphorescence. It was shown equally if the uranium were kept in darkness and did not vary appreciably with time. Becquerel showed that the rays from uranium like X rays were capable of discharging a body whether positively or negatively electrified. A uranium compound brought close to the charged plate of a gold leaf electroscope causes a rapid collapse of the gold leaves. This property of uranium, and also of the radioactive bodies in general, has supplied a delicate and quantitative method of accurate comparison of the intensity of the radiations from substances under varying conditions. A modified form of gold leaf electroscope has come into general use for comparison of the radioactivity of substances. Rutherford (2) made a systematic examination of the discharging effect produced by the rays from uranium and showed that it was due to the production of charged carriers or ions in the volume of the gas through which the radiations pass. In an electric field, the positive ions travel to the negative electrode and vice versa, 4 8 16 z0 2 4. Time I X Days thus causing a discharge of the electrified body. If a sufficiently strong field is used, the ions are all swept to the electrodes before appreciable loss of their number can occur by recombination. The rate of discharge then reaches a steady maximum value which is not altered by a large increase in voltage. This maximum current through the gas is called the saturation current. The ions produced in gases by the rays from uranium and other radioactive substances are in general identical with those produced by X rays, and the mechanism of conductivity of the gas is very similar in both cases (see Electric conduction: § Through Gases). Some time after Becquerel's discovery, Mme Curie (3) made a systematic examination of the electric method of a large number of chemical elements and their compounds to test whether they possessed the "radioactive" property of uranium. Only one other element, thorium, was found to show this effect to a degree comparable with that of uranium - a result independently observed by Schmidt. Mme Curie examined the activity of the various compounds of uranium and found that their radioactivity was an atomic property, i.e. the activity was proportional to the amount of the element uranium present, and was independent of its combination with other substances. In testing the activity of the minerals containing uranium, Mme Curie found that the activity was always four to five times as great as that to be expected from their content of uranium. If the radioactivity were an atomic phenomenon, this could only be explained by the presence in these minerals of another substance more active than uranium itself. Relying on this hypothesis, Mme Curie made a chemical examination of uranium minerals in order to try to separate this new radioactive substance. In these experiments, the Austrian Government generously provided Mme Curie with a ton of the residues from the State manufactory of uranium at Joachimstahl, Bohemia. At that place there are extensive deposits of pitchblende or uranite which are mined for the uranium. After separation of the latter, the residues are three to five times as radioactive weight for weight as the uranium. From this residue Mme Curie separated a substance far more radioactive than uranium, which she called polonium in honour of the country of her birth. This substance is usually separated with bismuth in the mineral, but by special methods can be partly separated from it. A further examination revealed the presence of a second radioactive substance which is normally separated with the barium, to which the name "radium" was given. This name was happily chosen, for in the pure state radium bromide has a very great activity - about two million times as great as an equal weight of uranium. By means of successive fractionations of the chloride, the radium was gradually concentrated, until finally the radium was obtained so that the barium lines showed very faintly. The atomic weight was found by Mme Curie to be 225. In a recent redetermination, using a larger quantity of o4 grams of pure radium chloride, Mme Curie (4) found the atomic weight to be 226.2. Thorpe (5) using a smaller quantity obtained a value 227. The spectrum of the purified sample of radium chloride obtained by Mme Curie was first examined by Demarcay. It was found to have a characteristic spark spectrum of bright lines analogous in many respects to the spectra of the alkaline earths. Giesel (6) found that pure radium bromide gives a brilliant carmine colour to the buiisen flame. The flame spectrum shows two broad bright bands in the orange-red. There is also a line in the blue-green and two weak lines in the violet. Giesel (7) has taken an active part in the preparation of pure radium compounds, and was the first to place preparations of pure radium bromide on the market. He found that the separation of radium from the barium mixed with it proceeded much more rapidly if the crystallizations were carried out using the bromide instead of the chloride. He states that six to eight crystallizations are sufficient for an almost complete separation. From the chemical point of view radium possesses all the characteristic properties of a new element. It has a definite atomic weight, a well-marked and characteristic spectrum, and distinct chemical properties. Its comparative ease of separation and great activity has attracted much attention to this substance, although we shall see that very similar radioactive properties are possessed by a large number of distinct substances.

Radium emits three distinct types of radiation, known as the a, s and 'y rays, of which an account will be given later. It produces in addition a radioactive emanation or gas which is about roo,000 times as active weight for weight as radium itself. The emanation released from to milligrams of pure radium bromide causes a glass tube into which it is introduced to phosphoresce brightly. A brilliant luminosity is produced in phosphorescent substances like zinc sulphide, willemite and barium platino-cyanide when introduced into a tube containing the emanation. The radium emanation, a more detailed account of which will be given later, has proved of the greatest utility in radioactive experiments. The property of radium of producing the emanation has been utilized as a very delicate and certain method, not only of detection but of estimation of small quantities of radium. This "emanation method" depends upon the introduction of the emanation, liberated from a substance by boiling or heating, into a suitable electroscope. The rate of discharge of the electroscope due to the emanation affords a quantitative measure of the amount of radium present. In this way, it is not difficult to determine with certainty the ioo 8 0 .4 k0 ' '2.0 ' '0 presence of radium in a body which contains only 10 11 gram of radium. With care, 1012 gram can just be detected. This emanation method has been employed with great success in measuring the quantity of radium in minerals and in rocks. A very simple method has been devised of determining the quantity of radium present when it is not less than 1/Ioo milligram. The tube containing the radium is placed some distance from an electroscope which is surrounded by a lead screen about 3 mms. thick. This cuts off the a and 0 rays and the effect in the electroscope is then due to the penetrating y rays. By comparison of the rate of discharge with that of a standard preparation of radium at the same distance, the quantity of radium can at once be deduced, provided the radium is in equilibrium with its emanation. This is usually the case if the radium preparation is one month old. This' method is simple and direct, and has the great advantage that the radium tube under test need not be opened, nor its contents weighed. We shall see later that the amount of radium in an old mineral is always proportional to the amount of uranium present. Rutherford and Boltwood (8) found that 3.4 parts of radium by weight are present in ten million parts of uranium. Consequently an old mineral containing 1000 kilos of uranium should contain 340 milligrams of pure radium.

In addition to radium and polonium, a number of other radioactive substances have been found in uranium minerals. With the exception of the radium emanation, none of these have yet been isolated in a pure state, although preparations of some of them have been obtained comparable in activity with radium itself. Debierne (9) found a radioactive substance which was separated from pitchblende with the rare earths and had chemical properties similar to those of thorium. This he called actinium. Giesel (10) independently noted the presence of a new radioactive substance which was usually separated with lanthanum and cerium from the minerals. It possessed the property of giving out a radioactive emanation or gas, the activity of which died away in a few seconds. For this reason he called it the emanating substance and afterwards emanium. Later work has shown that emanium is identical in chemical and radioactive properities with actinium, so that the former name will be retained.

We have already seen that Mme Curie gave the name polonium to a radioactive substance separated with bismuth. Later Marckwald found that a very radioactive substance was deposited from a solution of a radioactive mineral on a polished bismuth plate. The active matter was found to be deposited in the bismuth with tellurium, and he gave the, name radiotellurium to this substance. In later work, he showed that the new substance could be chemically separated from tellurium. By treating the residues from 15 tons of Joachimsthal pitchblende, Marckwald (I I) finally obtained 3 milligrams of intensely active material - far more active weight for weight than radium. It has been definitely settled that the active substance of Marckwald is identical with polonium. Both substances give out a type of easily absorbed a rays and both lose their activity at the same rate. The activity of polonium decays in a geometrical progression with the time and falls to half its initial value in 140 days. This law of decay, as we shall see, is characteristic of all radioactive products, although the period of decay is different in each case.

Mme Curie and Debierne (12) have described further experiments with polonium. The latter substance was extracted from several tons of pitchblende and purified until 2 milligrams of material were obtained containing about i/10 milligram of pure polonium. From a knowledge of the relative periods of transformation of radium and polonium, it can be calculated that the amount of polonium in a radium mineral is 1/5000 of the amount of radium, while the activity of pure polonium measured by the a rays should be 5000 times greater than that of radium.. As we have seen, polonium is rapidly transformed, and it is of great interest to determine the nature of the substance into which polonium changes. We shall see later that there is considerable evidence that polonium changes into lead.

Recently Boltwood (13) has separated another substance from uranium minerals which he has called "ionium." This substance is sometimes separated from the mineral with actinium and has chemical properties very similar to those of thorium. Preparations of ionium have been obtained several thousand times as active as uranium. Ionium emits a rays of short range and has a period of transformation probably much longer than that of radium. Ionium has a special interest inasmuch as it is the substance which changes directly into radium. A preparation of ionium initially free from radium grows radium at a rapid rate. Hofmann found that the lead separated from uranium minerals and named it radiolead. The active constituent in the lead is radium D, which changes into radium E and then into radium F (polonium). Both radium D and radium F are products of the transformation of radium. In addition to these radioactive substances mentioned above, a large number of other radioactive substances have been discovered. Most of these lose their activity in the course of a few hours or days. The properties of these substances and their position in the radioactive series will be discussed later.

Radiations from Radioactive Substances

All the radioactive substances possess in common the property of emitting radiations which darken a photographic plate and cause a discharge of electrified bodies. Very active preparations of radium, actinium and polonium also possess the property of causing strong phosphorescence in some substances. Bodies which phosphoresce under X rays usually do so under the rays from radioactive matter. Barium platinocyanide, the mineral willemite (zinc silicate) and zinc sulphide are the best known examples.

There are in general three types of radiation emitted by the radioactive bodies, called the a, 0 and y rays. Rutherford (2) in 1899 showed that the radiation from uranium was complex and consisted of (a) an easily absorbed radiation stopped by a sheet of paper or a few centimetres of air which he called the a rays and (b) a far more penetrating radiation capable of passing through several millimetres of aluminium, called the 0 rays. Later Villard found that radium emitted a very penetrating kind of radiation called the rays capable of passing before absorption through twenty centimetres of iron and several centimetres of lead.

Giesel and, later, Curie and Becquerel showed that the 0 rays of radium were deflected by a magnetic field. By the work of Becquerel and Kaufmann the /3 rays have been shown to consist of negatively charged particles projected with a velocity approaching that of light, and having the same small mass as the electrons set free in a vacuum tube. In fact the 0 rays are electrons spontaneously ejected from the radioactive matter at a speed on an average much greater than that observed in the electrons set free in a vacuum tube.

The very penetrating y rays are not deflected in a magnetic or electric field and are believed to be a type of radiation similar to X rays. The y rays are only observed in radioactive substances which emit /3 rays, and the penetrating power of the y rays appears to be connected with the initial velocity of expulsion of the /3 rays. Two general theories have been advanced to account for the properties of these rays. On one view, the y rays are to be regarded as electromagnetic pulses which have their origin in the expulsion of the /3 particle from the atom. On the other hand Bragg has collected evidence in support of the view that the y rays are corpuscular and consist of uncharged particles or "neutral doublets." There is as yet no general consensus of opinion as to the true nature of the y rays.

Rutherford (14) showed in 1903 that the a rays were deflected in a powerful magnetic or electric field. The amount of deflection is very small compared with the /3 rays under similar conditions. The direction of deflection in a magnetic field is opposite to that of the /3 rays, showing that the a rays consist of a stream of positively charged particles. A pencil of rays from a thick layer of radioactive matter is complex and consists of particles moving at varying velocities If, however, a thin film of radioactive matter of one kind is taken, the particles which escape without absorption are found to be homogeneous and consist of particles projected at an identical speed. Observations of the velocity and mass of the particle have been made by Rutherford. The general method employed for this purpose is similar to that used for the determination of the velocity and mass of the electron in a vacuum tube. The deflection of a pencil of rays in a vacuum is determined for both a magnetic and electric field. From these observations the velocity and value elm (the ratio of the charge carried by the particle to its mass) are determined. The value of elm has been found to be the same for the particles from all the types of radioactive matter that have been examined, indicating that the a particles from all radioactive substances are identical in mass. The value of elm found for the a particle is 5.0 7 X 10 3. Now the value of elm for the hydrogen atom set free in the electrolysis of water is 9660. On the assumption that the value of the charge e is the same for the a particle as for the hydrogen atom, the value would indicate that the a particle has about twice the mass of the hydrogen atom, i.e. has the same mass as the hydrogen molecule. If the charge on the a particle is twice that on the hydrogen atom, the value of elm indicates that the a particle is a helium atom, for the latter has an atomic weight of four times that of hydrogen. It was difficult at first to decide between these and other hypotheses, but we shall show later that there is now no doubt that the a particle is in reality a helium atom carrying two elementary charges. We may consequently regard the a rays as a stream of helium atoms which are projected from a radioactive substance with a high velocity. The maximum velocity of the a particle from radium is 2 X Io 9 cms. per second, or onefifteenth of the velocity of light. Although the a rays are the least penetrating of the radiations, it will be seen that they play an extremely important part in radioactive phenomena. They are responsible for the greater part of the ionization and heating effects of radioactive matter and are closely connected with the transformations occurring in them.

Under ordinary experimental conditions the greater part of the ionization observed in a gas is due to the a particles. This ionization due to the a rays does not extend in air at atmospheric pressure for more than 7 cms. from radium, and 8.6 cms. from thorium. If a screen of aluminium about oi cms. thick is placed over the active material, the a rays are completely absorbed, and the ionization above the screen is then due to the 0 and y rays alone. If a layer of lead about 2 mms. thick is placed over the active material, the 0 rays are stopped, and the ionization is then due almost entirely to the penetrating y rays. By the use of screens of suitable thickness we are thus able to sift out the various types of rays. These three types of radiations all set up secondary radiations in passing through matter. A pencil of 0 rays falling on matter is widely scattered in all directions. This scattered radiation is sometimes called the secondary 0 rays. The y rays give rise to secondary rays which consist in part of scattered y rays and in part electrons moving with a high velocity. These secondary rays in turn produce tertiary rays and so on. The impact of the a rays on matter sets free a number of slow moving electrons which are very easily deflected by a magnetic or electric field. This type of radiation was first observed by J. J. Thomson, and has been called by him the S rays.

Emanations or Radioactive Gases

In addition to their power of emitting penetrating radiations, the substances thorium, actinium and radium possess another very striking and important property. Rutherford (15) in 1900 showed that thorium compounds (especially the oxide) continuously emitted a radioactive emanation or gas. This emanation can he carried away by a current of air and its properties tested apart from the substance which produces it. A little later Dorn showed that radium possesses a similar property, while Giesel and Debierne observed a similar effect with actinium. These emanations all possess the property of ionizing a gas and, if sufficiently intense, of producing marked photographic and phosphorescent action. The activity of the radioactive gases is not permanent but disappears according to a definite law with the time, viz. the activity falls off in a geometric progression with the time. The emanations are distinguished by the different rates at which they lose their activity. The emanation of actinium is very shortlived, the time for the activity to fall to half value, i.e. the period of the emanation, being 3.7 seconds. The period of the thorium emanation is 54 seconds and of the radium emanation 3.9 days. This property of emitting an emanation is shown in a very striking manner by actinium. A compound of actinium is wrapped in a sheet of thin paper and laid on a screen of phosphorescent zinc sulphide. In a dark room the phosphorescence, marked by the characteristic scintillation, is seen to extend on all sides from the active body. A puff of air is seen to remove the emanation and with it the greater part of the phosphorescence. Fresh emanation immediately diffuses out and the experiment may be repeated indefinitely. The emanations have all the properties of radioactive gases. They can be transferred from point to point by currents of air. The emanations can be separated from the air or other gas with which they are mixed by the action of extreme cold. Rutherford and Soddy (16) showed that under ordinary conditions the temperature of condensation of the radium emanation mixed was - 150° C.

The emanations are produced from the parent matter and escape into the air under some conditions. Rutherford and Soddy (17) made a systematic examination of the emanating power of thorium compounds under different conditions. The hydroxide emanates most freely, while in thorium nitrate, practically none of the emanation escapes into the air. Most of the compounds of actinium emanate very freely. Radium compounds, except in very thin films, retain most of the emanation in the compound. The occluded emanation can in all cases be released by solution or by heating. On account of its very slow period of decay, `hc emanation of radium can be collected like a gas and stored, when it retains its characteristic properties for a month or more.

Induced Activity

Curie (18) showed that radium possessed another remarkable property. The surface of any body placed near radium, or still better, immersed in the emanation from it, acquires a new property. The surface after removal is found to be strongly active. Like the emanations, this induced activity in a body decays with the time, though at quite a different rate from the emanation itself. Rutherford (19) independently showed that thorium possessed a like property. He showed that the bodies made active behaved as if a thin film of intensely active matter were deposited on their surface. The active matter could be partly removed by rubbing, and could be dissolved off by strong acids. When the acid was evaporated the active matter remained behind. It was shown that induced activity was due to the emanations, and could not be produced if no emanation was present. We shall see that induced activity on bodies is due to a deposit of non-gaseous matter derived from the transformation of the emanations. Each emanation gives a distinctive active deposit which decays at different rates. The active deposits of radium, thorium and actinium are very complex, and consist of several types of matter. Several hours after removal from the emanation the active deposit from radium decays to half-value--26 minutes, for actinium half-value-34 minutes, for thorium half-valueo. 5 hours. The active deposits obtained on a platinum wire or plate are volatilized before a white heat, and are again deposited on the cooler bodies in the neighbourhood. Rutherford showed that the induced activity could be concentrated on the negative electrode in a strong electric field, indicating that the radioactive carriers had a positive charge. The distribution of the active deposit in a gas at low pressure has been investigated in detail by Makower and Russ.

Theor y of Radioactive Transformations

We have seen that the radioactive bodies spontaneously and continuously emit a great number of a and 0 particles. In addition, new types of radioactive matter like the emanations and active deposits appear, and these are quite distinct in chemical and physical properties from the parent matter. The radiating power is an atomic property, for it is unaffected by combination of the active element with inactive bodies, and is uninfluenced by the most powerful chemical and physical agencies at our command. In order to explain these results, Rutherford and Soddy (20) in 1903 put forward a simple but comprehensive theory. The atoms of radioactive matter are unstable, and each second a definite fraction of the number of atoms present break up with explosive violence, in most cases expelling an a or (3 particle with great velocity. Taking as a simple illustration that an a particle is expelled during the explosion, the resulting atom has decreased in mass and possesses chemical and physical properties entirely distinct from the parent atom. A new type of matter has thus appeared as a result of the transformation. The atoms of this new matter are again unstable and break up in turn, the process of successive disintegration of the atom continuing through a number of distinct stages. On this view, a substance like the radium emanation is derived from the transformation of radium. The atoms of the emanation are far more unstable than the atoms of radium, and break up at a much quicker rate. We shall now consider the law of radioactive transformation according to this theory. It is experimentally observed that in all simple radioactive substances, the tensity of the radiation decreases in a geometrical progression with the time, i.e. I/Io =e -At where I is the intensity of the radiation at any time 1, I. the initial intensity, and X a constant. Now according to this theory, the intensity of the radiation is proportional to the number of atoms breaking up per second. From this it follows that the atoms of active matter present decrease in a geometrical progression with the time, i.e. N/No= at where N is the number of atoms present at a time t, N. the initial number, and X the same constant as before. Differentiating, we have dN/dt= -AN, i.e. X represents the fraction of the total number of atoms present which break up per second. The radioactive constant X has a definite and characteristic value for each type of matter. Since X is usually a very small fraction, it is convenient to distinguish the products by stating the time required for half the matter to be transformed. This will be called the period of the product, and is numerically equal to log c2 JX. As far as our observation has gone, the law of radioactive change is applicable to all radioactive matter without exception. It appears to be an expression of the law of probability, for the average number breaking up per second is proportional to the number present. Viewed from this point of view, the number of atoms breaking up per second should have a certain average value, but the number from second to second should vary within certain limits according to the theory of probability. The theory of this effect was first put forward by Schweidler, and has since been verified by a number of experimenters, including Kohlrausch, Meyer, and Begener and H. Geiger. This variation in the number of atoms breaking up from moment to moment becomes marked with weak radioactive matter, where only a few atoms break up per second. The variations observed are in good agreement with those to be expected from the theory of probability. This effect does not in any way invalidate the law of radioactive change. On an average the number of atoms of any simple kind of matter breaking up per second is proportional to the number present. We shall now consider how the amount of radioactive matter which is supplied at a constant rate from a source varies with the time. For clearness, we shall take the case of the production of emanation, by radium. The rate of transformation of radium is so slow compared with that of the emanation that we may assume without sensible error that the number of atoms of radium breaking up per second, i.e. the supply of fresh emanation, is on the average constant over the interval required. Suppose that initially radium is completely freed from emanation. In consequence of the steady supply, the amount of emanation present increases, but not at a constant rate, for the emanation is in turn breaking up. Let q be the number of atoms of emanation produced by the radium per second and N the number present after an interval t, then dN/dt=q-AN where X is the radioactive constant of the emanation. It is obvious that a steady state will ultimately be reached when the number of atoms of emanation supplied per second are on the average to the atoms which break up per second. If No be the maximum number, q=XN 0 . Integrating the above equation, it follows that N/No = 1 - P e. If a curve be plotted with N as ordinates and time as abscissae, it is seen that the recovery curve is complementary to the decay curve. The two curves for the radium emanation period, 3.9 days, are shown in fig. 1, the maximum ordinate being in each case loo.

This process of production and disappearance of active matter holds for all the radioactive bodies. We shall now consider some special cases of the variation of the amount of active matter with time which have proved of great importance in the analysis of radioactive changes.

(a) Suppose that initially the matter A is present, and this changes into B and B into C, it is required to find the number of atoms P, Q and R of A, B and C present at any subsequent time t.. Let X 1, X2, X3 be the constants of transformation of A, B and C respectively. Suppose n be the number of atoms of A initially present. From the law of radioactive change it follows: P = dQ/dt= A 1 P (I) dR/dt= A2Q-X3R. .. .. .. .. (2) Substituting the value of P in terms of n in (t), dQ/dl = A,ne Alt-A2Q; the solution of which is of the form Q=n(ae Alt+be-A20, where a and b are constants. By substitution it is seen that a= Al/(A2-Ai). Since Q=o when t=o, b= -Al/(A2 - A1) Thus Q = (eA 2 t e - Al t). (3) Similarly it can be shown that R =n(ae A i t +be A 2 t +ce - 1 3 1 ) (4) where a = AlA2 b = X`X' X 2)(A 1 -A 3) (A2-A1)(A 2 A3) c= (A8-A1) (Aa-A2) It will be seen from (3), that the value of Q, initially zero, increases to a maximum and then decays; finally, according to an exponential law, with the period of the more slowly transformed product, whether A or B.

(b) A primary source supplies the matter A at a constant rate, and the process has continued so long that the amounts of the products A, B, C have reached a steady limiting value. The primary source is then suddenly removed. It is required to find the amounts of A, B and C remaining at any subsequent time t. In this case of equilibrium, the number n of particles of A supplied per second from the source is equal to the number of particles which change into B per second, and also of B into C. This requires the relation no =A1 =y2Q o = A3Ro where P °, Q„ R o are the initial number of particles of A, B, C present, and A lt A 21 A3 are their constants of transformation.

Using the same quotations as in case (t), but remembering the new initial conditions, it can easily be shown that the number of particles P, Q and R of the matter A, B and C existing at the time t after removal are given by P = ?° e A11, Q '_' o (At e ?2t -?lt Al - A2 R =n o (ae Alt where a=(A1- A3) , b c = A3(A1-A3)(A4-A3)The curves expressing the rate of variation of P, Q, R with time are in these cases very different from case (t).

(c) The matter A is supplied at a constant rate from a primary source. Required to find the number of particles of A, B and C present at any time t later, when initially A, B, and C were absent.

This is a converse case from case (2) and the solutions can be obtained from general considerations. Initially suppose A, B and C are in equilibrium with the primary source which supplied A at a constant rate. The source is then removed and the amounts of A, B and C vary according to the equation given in case (2). The source after removal continues to supply A at the same rate as before. Since initially the product A was in equilibrium with the source, and the radioactive processes are in no way changed by the removal of the source, it is clear that the amount of A present in the two parts in which the matter is distributed is unchanged. If P, be the amount of A produced by the source in the time t, and P the amount remaining in the part removed, then P i -FP = P o where P D is the equilibrium value. Thus P t /P o = I - P/Po.

The ratio P/P o can be written down from the solution given in case (2). Similarly the corresponding values of Q l /Q o, R1/R o may be at once derived. It is obvious in these cases that the curve plotted with P/P o as ordinates and time as abscissae is complementary to the corresponding curve with P 1 /P o as ordinates. This simple relation holds for all recovery and decay curves of radioactive products in general.

We have so far considered the variation in the number of atoms of successive products with time when the periods of the products are known. In practice, the variation of the number of atoms is deduced from measurements of activity, usually made by the electric method. Using the same notation as before, the activity of any product is proportional to its rate of breaking up, i.e. to X1P where P is the number of atoms present. If two products are present, the activity is the sum of two corresponding terms X I P and X2Q. In practice, however, no two products emit a or 0 particles with the same velocity. The difference in ionizing power of a single a particle from the two products has thus to be taken into account. If, under the experimental conditions, the ionization produced by an a particle from the second product is K times that from the first product, the activity observed is proportional to X 1 P-{-KX 2 Q. In this way, it is possible to compare the theoretical activity curves of a mixture of products with those deduced experimentally.

Analysis of Radioactive Changes

The analysis of the successive changes occurring in uranium, thorium, radium and actinium has proved a very difficult matter. In order to establish the existence of a new product and to fix its position in the scheme of changes, it is necessary to show (a) that the new product has a distinctive period of decay and shows some distinctive physical or chemical properties; (b) that the product under consideration arises directly from the product preceding it in the scheme of changes, and is transformed into the product succeeding it.

In general, it has been found that each product shows some distinctive chemical or physical behaviour which allows of its partial or complete separation from a mixture of other products. It must be remembered that in most cases the amount of radioactive matter under examination is too small to detect by weight, but its presence is inferred from its characteristic radiations and rate of change. In some cases, a separation may be effected by ordinary chemical methods; for example thorium X is separated from thorium by precipitation of thorium with ammonia. The Th X remains in the filtrate and is practically free from thorium. In other cases, a separation is effected by a separation of a metal in the solution of active matter. For example, polonium (radium F) always comes down with bismuth and may be separated by placing a bismuth plate in a solution. Radium C is separated from radium B by adding nickel filings to a solution of the two. Radium C is deposited on the nickel. In other cases, a partial separation may be effected by electrolysis or by differences in volatility when heated. For example, when radium A, B and C are deposited on a platinum plate, on heating the plate, radium B is volatilized and is deposited on any cold surface in the neighbourhood. A very striking method of separating certain products has been recently observed depending upon the recoil of an atom which breaks up with the expulsion of an a particle. The residual atom acquires sufficient velocity in consequence of the ejection of an a particle to escape and be deposited on bodies in the neighbourhood. This is especially marked in a low vacuum. This property was independently investigated by Russ and Makower (21) and by Hahn (22). The latter has shown that by means of the recoil, actinium C may be obtained pure from the active deposit containing actinium A, B and C, for B emits a rays, and actinium C is driven from the plate by the recoil. In a similar way a new product, thorium D, has been isolated. By the recoil method, radium B may be separated from radium A and C. The recoil method is one of the most definite and certain methods of settling whether an a ray product is simple or complex.

While in the majority of cases the products break up either with the emission of a or /3 particles, some products have been observed which do not emit any characteristic radiation and have been called "rayless products." For example, radium D and thorium A are changing substances which break up without emitting either penetrating a or /i rays. They appear to emit slow b rays which can only be detected by special methods. The presence and properties of a rayless product can be easily inferred if it is transformed into a product emitting a radiation, for the variation in activity of the latter affords a method of determining the amount of the parent product present. The distinction between a "ray" and a "rayless" product is not clear. It may be that the atom of a rayless product undergoes a re-arrangement of its constituent parts giving rise to an atom of the same mass but of different properties. In the case of an a ray or /3 ray product, the expulsion of an a or /3 particle affords an obvious explanation of the appearance of a new product with distinctive physical properties.

In the table a list of the known products of transformation is given. In each case, the half period of transformation is given and the type of radiation emitted. If the product emits a rays, the range of ionization of the a particle in air is given.

Product.	Half Period of Transforma- tion.	Rays	Range of Rays in Air in Cms.
URANIUM -	5 X Io 9 years	a	3.5
Uranium X .	22 days	0-}-7
Ionium .	?	a	2.8
RADIUM -	1760 years	a	3.5
Ra Emanation.	3.86 days	a	4'33
Radium A .	3 mins.	a	4'83
Radium B .	26 mins.	slow I	..
Radium C .	19 mins.	a+13+7	7.06
Radium D	17 years	slow 0
Radium E .	5 days	0	..
Radium F	140 days	a	3.86
Radium G=lead?	..		. .
THORIUM -	about 10 10 yrs.		3'5
(Th. I)	5.5 years	rayless	. .
Mesothorium (Th. 2)	6.2 hours
Radiothorium .	737 days	a	3'9
Thorium X	3.6 days	a	5.7
Th Emanation	54 secs	a.	5'5
Thorium A	Io6 hours	0
Thorium B .	55 mins.	a	5o
Thorium	very short?	a	8.6
Thorium D .	3 mins.
ACTINIUM -	?	rayless	..
Radioactinium .	19.5 days	a+0	4.8
Actinium	II-8 days	a	6.55
Act Emanation	3.7 secs.	a	5.8
Actinium A	36 mins.	0	..
Actinium B.	2.15 mins.	a	5.50
Actinium	5.1 mins.

Table Oi' Radioactive Products In each of the groups under the heading uranium, thorium and actinium, each product is derived from the direct transformation of the product above it.

Products of Radium. - Radium is transformed directly into the emanation which in turn goes through a rapid series of transformations called radium A, B and C. The complete analysis of these changes has involved a large amount of work. The emanation changes first into radium A, a substance of period 3 minutes emitting only a rays. Radium A changes into radium B, a product of period 26 minutes emitting 0 rays of penetrating power small compared with those emitted from the next product radium C. The product radium C has proved of considerable importance, for it not only emits very penetrating a rays and 0 rays, but is the origin of the 'y rays arising from radium in equilibrium. When a wire charged negatively has been exposed for some time in the presence of the radium emanation, it becomes coated with an invisible film of radium A, B and C. After removal from the emanation for 20 minutes, radium A has practically disappeared and the a rays arise entirely from radium C. Radium C has proved very valuable in radioactive measurements as providing an intense source of homogeneous a rays. Twenty-four hours after removal, the activity due to radium B and C has become exceedingly small. The wire, however, still shows a very small residual activity, first noted by Mme Curie. This residual activity measured by the a rays rapidly increases with the time and reaches a maximum in about three years. The active deposit of slow change has been examined in detail by Rutherford (23) and by Meyer and Schweidler (24). It has been shown to consist of three successive products called radium D, E and F. Radium D is a rayless substance of slow period of transformation. Its period has been calculated by Rutherford to be about 40 years, and by Meyer and Schweidler about 12 years. Antonoff (25) fixes the period of about 17 years. Radium D changes into E, a (3 ray product of period about 5 days, and E into F, an a ray product of period 140 days. It was at first thought that radium E was complex, but no evidence of this has been observed by Antonoff. The product radium F is of special interest, for it is identical with polonium - the first active body separated by Mme Curie. In a similar way it has been shown that radium D is the primary source of the activity observed in lead or "radiolead" separated by Hofmann. It is interesting to note what valuable results have been obtained from an examination of the minute residual activity observed on bodies exposed in the presence of the radium emanation.

Radium Emanation

The radium emanation is to be regarded as a typical radioactive product or transition element which exists in a gaseous form. It is produced from radium at a constant rate, and is transformed into radium A and helium. Its half-period of transformation is 3.86 days. The emanation from radium has been purified by condensing it in liquid air, and pumping out the residual gases. The volume (26) of the emanation at normal pressure and temperature to be derived from one gram of radium in equilibrium is about o6 cubic millimetres. This small quantity of gas contains initially more than three-quarters of the total activity of the radium before its separation. In a pure state, the emanation is ioo,000 times as active weight for weight as pure radium. Pure emanation in a spectrum tube gives a characteristic spectrum of bright lines (27). The discharge in the gas is bluish in colour. With continued sparking, the emanation is driven into the walls of the tube and the electrodes. Notwithstanding the minute volume of emanation available, the boiling-point of the emanation has been determined at various pressures. At atmospheric pressure Rutherford (28) found the boiling-point to be - 67° C., and Gray and Ramsay (29) 71° C. Liquid emanation appears colourless when first condensed; when the temperature is lowered, the liquid emanation freezes, and at the temperature of liquid air glows with a bright rose colour. The density of liquid emanation has been estimated at 5 or 6.

Approximate estimates of the molecular weight of the radium emanation were early made by diffusion methods. The molecular weight in most cases came out about zoo. In a comparison by Perkins of the rate of diffusion of the emanation with that of a monatomic vapour of high molecular weight, viz. mercury, the value deduced was 234. Since the radium atom in breaking up gives rise to one atom of the emanation and one atom of helium, its atomic weight should be 226 - 4 = 222. The emanation appears to have no definite chemical properties, and in this respect belongs to the group of inert monatomic gases of which helium and argon are the best known examples. It is partially soluble in water, and readily absorbed by charcoal.

Thorium

The first product observed in thorium was the emanation. This gives rise to the active deposit which has been analysed by Rutherford, Miss Brooks and by Hahn, and shown to consist of probably four products - thorium A, B, C and D. Thorium A is a rayless product of period 105 hours; thorium B an a ray product of period about one hour. The presence of thorium C has been inferred from the two types of a rays present in the active deposit, but no chemical separation of B and C has yet been found possible. Hahn has shown that thorium D - a (3 ray product of period 3 minutes - can easily be separated by the recoil method. A special interest attaches to the product thorium X (30), which was first separated by Rutherford and Soddy, since experiments with this substance laid the foundation of the general theory of radioactive transformations. A close analysis of thorium has led to the separation of a number of new products. Hahn (31) found that a very active substance emitting a rays, which gave rise to thorium X, could be separated from thorium minerals. This active substance, called radiothorium, has been closely examined by Hahn and Blanc. Its period of decay was found by Hahn to be about 2 years, and by Blanc to be 737 days. From an examination of the activity of commercial thorium nitrate of different ages, Hahn showed that another product must be present, which he called mesothorium. This is separated from thorium with Th X by precipitation with ammonia. Thorium is first transformed into the rayless product mesothorium, of period about 5 years. This gives rise to a (3 ray product of quick transformation, which in turn changes into radiothorium. This changes into thorium X, and so on through a long series of changes. When isolated in the pure state, radiothorium would have an activity about a thousand times greater than radium, but would lose its activity with time with a period of about 2 years. Mesothorium, when first separated, would be inactive, but in consequence of the production of radiothorium, its activity would rapidly increase for several years. After reaching a maximum, it would finally decay with a period of five years. Since a large amount of thorium is separated annually from thorium minerals, it would be of great importance at the same time to separate the radiothorium and mesothorium present. For many purposes active preparations of these substances would be as valuable as radium itself, and the amount of active matter from this source would be greater than that at present available from the separation of radium from uranium minerals.

Actinium

The transformations observed in actinium are very analogous to those in thorium. Actinium itself is a rayless product which changes into radioactinium, an a ray product of period 19.5 days, first separated by Hahn (32). This changes into actinium X, of period io2 days, first separated by Godlewski (33)Actinium X is transformed into the emanation which in turn gives rise to three further products, called actinium A, B and C. Although very active preparations of actinium have been prepared, it has so far not been found possible to separate the actinium from the rare earths with which it is mixed. We do not in consequence know its atomic weight or spectrum.

Origin of Radium. - According to the transformation theory, radium, like all other radioactive products, must be regarded as a changing element. Preliminary calculations showed that radium must have a period of transformation of several thousand years. Consequently in order that any radium could exist in old minerals, the supply must be kept up by the transformation of some other substance. Since radium is always found associated with uranium minerals, it seemed probable from the beginning that uranium must be the primary element from which radium is derived. If this were the case, in old minerals which have not been altered by the action of percolating waters, the ratio of the amount of radium to uranium in a mineral must be a constant. This must evidently be the case, for in a state of equilibrium the rate of breaking up of radium must equal the rate of supply of radium from uranium. If P, Q be the number of atoms of uranium and radium respectively in equilibrium, and X, X2 their constants of change, then X 2 Q = A 1 P or Q/P =X1 /X2 = T2/T1.

where T2 and T 1 are the half-periods of transformation of uranium and radium respectively. The work of Boltwood (34), Strutt (35) and McCoy (36) has conclusively shown that the ratio of radium to uranium in old minerals is a constant. Boltwood and Strutt determined the quantity of radium present in a mineral by the emanation method, and the amount of uranium by analysis.

In order, however, to obtain a direct proof of the genetic relation between uranium and radium, it is necessary to show that radium appears after some time in a uranium compound from which all trace of radium has been initially removed. It can readily be calculated that the growth of radium should be easily observed by the emanation method in the course of one week; using a kilogram of uranium nitrate. Experiments of this kind were first made by Soddy (37), but initially no definite evidence was obtained that radium grew in the solution at all. The rate of production of radium, if it took place at all, was certainly less than o oth part of the amount to be expected if uranium were transformed directly into radium. It thus appeared probable that one or more products of slow period of transformation existed between uranium and radium. Since uranium must be transformed through these intermediate stages before radium appears, it is evident that the initial rate of production of radium under these conditions might be extremely small. This conclusion has been confirmed by Soddy, who has shown that radium does appear in the solution which has been placed aside for several years.

Since the direct parent of radium must be present in radioactive minerals, one of the constituents separated from the mineral must grow radium. This was shown to be the case by Boltwood (38), who found that actinium preparations produced radium at a fairly rapid rate. By the work of Rutherford and Boltwood, it was found that the growth of radium was not due to actinium itself, but to a new substance separated in some cases with the actinium. This new substance, which emits a rays, was separated by Boltwood (38), and called by him "Ionium." It has chemical properties very similar to thorium. Soddy has shown that the period of ionium is probably not less than 20,000 years, indicating that ionium must exist in uranium minerals in not less than ten times the quantity of radium. It has not yet been directly shown that uranium produces ionium, but there can be no doubt that it does do so. Since ionium produces radium, Boltwood (38) has determined by direct experiment that radium is half transformed in 2000 years - a number in good agreement with other data on that subject. The constant relation between uranium and radium will only hold for old minerals where there has been no opportunity for chemical alteration or removal of its constituents by the action of percolating water or other agencies. It is quite possible that altered minerals of no great age will not show this constant relation. It seems probable that this is the explanation of some results of Mlle Gleditsch, where the relation between uranium and radium has been found not to be constant for some mineral specimens.

Uranium	1.00	Radium B. .	0.04(?)
Ionium	0.34	Radium C. .	0.91
Radium .	0.45	Radium F. .	o46
Emanation	0.62	Actinium and its
Radium A	0.54	products. .	0.28

Connexion of the Radioelements

We have already seen that a number of slowly transforming radioactive substances, viz. polonium (radium F), radiolead (radium D) and ionium are linked up to the uranium-radium series of transformations. Boltwood (39), has made a systematic examination of the relative activity in the form of very thin films due to each of the products present in the uranium-radium family. The results are shown in the following table, where the activity of pure uranium itself is taken as unity: Total activity mineral, 4.64 times uranium.

Taking into account the differences in the ionization due to an a particle from the various products, the results indicate that uranium expels two a particles for one from each of the other a ray products in the series of transformations. This indicates either that two particles are expelled during the transformation of the atom of uranium, or that another a ray product is present which has so far not been separated from the uranium.

Although thorium is nearly always present in old uranium minerals and uranium in thorium minerals, there does not appear to be any radioactive connexion between these two elements. Uranium and thorium are to be regarded as two distinct radioactive elements. With regard to actinium, there is still no definite information of its place in the scheme of transformations. Boltwood has shown that the amount of actinium in uranium minerals is proportional to the content of uranium. This indicates that actinium, like radium, is in genetic connexion with uranium. On the other hand, the activity of actinium with its series of a ray products is less than that of radium itself or uranium. In order to explain this anomaly, Rutherford has suggested that at a certain stage of disintegration of the uranium-radium series, the disintegration is complex, and two distinct kinds of matter appear, one in much larger quantity than the other. On this view, the smaller fraction is actinium, so that the latter is a branch descendant of the main uranium-radium series.

End Products of Transformation

It is now definitely established that the a particle expelled from any type of radioactive matter is an atom of helium, so that helium is a necessary accompaniment of radioactive changes involving the expulsion of a particles. After the radioactive transformations have come to an end, each of the elements uranium and thorium and actinium should give rise to an end or final product, which may be either a known element or some unknown element of very slow period of transformation. Supposing, as seems probable, that the expulsion of an a particle lowers the atomic weight of an element by four units - the atomic weight of helium - the atomic weights of each of the products in the uranium and radium series can be simply calculated. Since uranium expels two a particles, the atomic weight of the next ray product, ionium, is 238.5-8 or 230.5. The atomic weight of radium comes out to be 266.5, a number in good agreement with the experimental value. Similarly the atomic weight of polonium is 210.5, and that of the final product after the transformation of polonium should be 206.5. This value is very close to the atomic weight of lead, and indicates that this substance is the final product of the transformation of radium.

This suggestion was first put forward by Bolt wood (40), who has collected a large amount of evidence bearing on this subject. Since in old minerals the transformations have been in progress for periods of time, in some cases measured by hundreds of millions of years, it is obvious that the end product, if a stable element, should be an invariable companion of the radioelement and be present in considerable quantity. Boltwood has shown that lead always occurs in radioactive minerals, and in many cases in amount about that to be expected from their uranium content and age. It is difficult to settle definitely this very important problem until it can be experimentally shown that radium is transformed into lead, or, what should prove simpler in practice, that polonium changes into helium and lead. Unfortunately for a solution of this problem within a reasonable time, a very large quantity of polonium would be necessary. Mme. Curie and Debierne have obtained a very active preparacion of polonium containing about f i oth milligram of pure polonium. Rutherford and Boltwood and Curie and Debierne have both independently shown that polonium produces helium - a result to be expected, since it emits a particles.

Production of Helium

In 1902 Rutherford and Soddy suggested that the helium which is invariably found in radioactive minerals was derived from the disintegration of radioactive matter. In 1903 Ramsay and Soddy definitely showed that helium was produced by radium and also by its emanation. From the observed mass of the a particle, it seemed probable from the first that the a particle was an atom of helium. This conclusion was confirmed by the work of Rutherford and Geiger (41), who showed that the a particle was an atom of helium carrying two unit charges of electricity. In order to prove definitely this relation, it was necessary to show that the a particles, quite independently of the active matter from which they were expelled, gave rise to helium. This was done by Rutherford and Royds (42), who allowed the a particles from a large quantity of emanation to be fired through the very thin glass walls of the containing tube. The collected particle gave the spectrum of helium, showing, without doubt, that the a particle must be a helium atom.

Since the a particle is an atom of helium, all radioactive matter which expels a particles must give rise to helium. In agreement with this, Debierne and Giesel have shown that actinium as well as radium produces helium. Observations of the production of helium by radium have been made by Ramsay and Soddy, Curie and Dewar, Himstedt and others. The rate of production of helium per gram of radium was first definitely measured by Dewar (43). His preliminary measurements gave a value of 134 cubic mms. of helium per year per gram of radium and its products. Later observations extending over a larger interval give a rate of production about 168 cubic mms. per year. As a result of preliminary measurements, Boltwood and Rutherford (44) have found a growth of 163 cubic mms. per year. It is of interest to note that the rate of production of helium by radium is in excellent agreement with the value calculated theoretically. From their work of counting the particles and measuring their charge, Rutherford and Geiger showed that the rate of production of helium should be 158 cubic mms. per year.

Properties of the a Rays. - We have seen that the rays are positively charged atoms of helium projected at a high velocity, which are capable of penetrating through thin metal sheets and several centimetres of air. Early observations indicated that the ionization due to a layer of radioactive matter decreased approximately according to an exponential law with the thickness of the absorbing matter placed over the active matter. The true nature of the absorption of the a rays was first shown by Bragg and by Bragg and Kleeman (45). The active particles projected from a thin film of active matter of one kind have identical velocities, and are able to ionize the air for a definite distance, termed the "range" of the a particle. It was found that the ionization per centimetre of path due to a narrow pencil of a rays increases with the distance from the active matter, at first slowly, then more rapidly, near the end of the range. After passing through a maximum value the ionization falls off rapidly to zero. The range of an a particle in air has a definite value which can be accurately measured. If a uniform screen of matter is placed in the path of the pencil of rays the range is reduced by a definite amount proportional to the thickness of the screen. All the a particles have their velocity reduced by the same amount in their passage through the screen. The ranges in air of the a rays from the various products of the radioelements have been measured. The ranges for the different products vary between 2.8 cms. and 8.6 cms.

Bragg has shown that the range of an a particle in different elements is nearly proportional to the square roots of their atomic weights. Using the photographic method, Rutherford (46) showed that the velocity V of an a particle of range R cms. in air is given by V 2 =K(R+I. 25), where K is a constant. In his experiments he was unable to detect particles which had a velocity lower than 8.8 X io $ cms. per second. Geiger (47), using the scintillation method, has recently found that a particles of still lower velocity can be detected under suitable conditions by the scintillations produced on a zinc sulphide screen. He has found that the connexion between velocity and range can be closely expressed by V 3 = KR, where K is a constant.

On account of the great energy of motion of the a particle, it was at first thought that it pursued a rectilinear path in the gas without appreciable deflection due to its encounters with the molecules. Geiger (48) has, however, shown by the scintillation method that the a particles are scattered to a marked extent in passing through matter. The scattering increases with the atomic weight of the substance traversed, and becomes more marked with decreasing velocity of the a particle. A small fraction of the a particles falling on a thick screen are deflected through more than a right angle, and emerge again on the side of incidence.

of some important radioactive data. The calculated and observed values are given below: - Calculated. Observed. Volume of the emanation in cubic milli-
metres per gram of radium. .	585	6
Volume of helium in cubic millimetres pro- duced per year per gram of radium.	158	169
Heating effect of radium per gram per hour in gram calories .	113	118
Half-period of transformation of radium in year	1760	2000

Rutherford and Geiger (49) have devised an electrical method of counting the a particles expelled from radioactive matter. The a particle enters through a small opening into a metal tube containing a gas at a reduced pressure. The ionization produced by the a particle in its passage through the gas is magnified several thousand times by the movement of the ions in a strong electric field. In this way, the entrance of an a particle into the detecting vessel is shown by a sudden and large deflection of the measuring instrument. By this method, they determined that 3.4 X 10 10 a particles are ejected per second from one gram of radium itself and from each of its a ray products in equilibrium with it. By measuring the charge on a counted number of a particles, it was found that the a particle carries a positive charge of 9.3 X io 1° electrostatic units. From other evidence, it is known that this must be twice the fundamental unit of charge carried by the hydrogen atom. It follows that this unit charge is 4.65 X io 10 units. This value is in good agreement with numerous recent determinations of this fundamental quantity by other methods. With this data, it is possible to calculate directly the values The calculated values are in all cases in good agreement with the experimental numbers.

It is well known from the experiments of Sir William Crookes (50) that the a rays produce visible scintillations when they fall on a screen of phosphorescent zinc sulphide. This is shown in the instrument called the spinthariscope. By means of a suitable microscope, the number of these scintillations on a given area in a given time can be counted. The number so obtained is practically identical with the number of a particles incident on the screen, determined by the electrical method of counting. This shows that each a particle produces a visible flash of light when it falls on a suitable zinc sulphide screen. The scintillations produced by a rays are observed in certain diamonds, and their number has been counted by Regener (51) and the charge on each particle has been deduced. The latter was the first to employ the scintillation method for actual counting of a particles. Kinoshita has shown that the number of a particles can also be counted by the photographic method, and that each particle must produce a detectable effect.

Absorption of l3 Rays

We have seen that the /3 particles, which are emitted from a number of radioactive products, carry a negative charge and have the same small mass as the particles constituting the cathode rays. The velocity of expulsion and penetrating power of the /3 rays varies widely for different products. For example, the rays from radium B are very easily absorbed, while some of the rays from radium C are of a very penetrating type. It has been found that for a single /3 ray product, the particles are absorbed according to an exponential law with the thickness of matter traversed, and Hahn has made use of this fact to isolate a number of new products. It has been generally assumed that the exponential law of absorption is a criterion that the /3 rays are all expelled at the same speed. In addition, it has been supposed that the /3 particles do not decrease much in velocity in passing through matter. Wilson has recently made experiments upon homogeneous /3 rays, and finds that the intensity.of the radiation falls off in some cases according to a linear rather than to an exponential law, and that there is undoubted evidence that the /3 particles decrease in velocity in traversing matter. Experiments upon the absorption of /3 rays are greatly complicated by the scattering of the /3 rays in their encounters with the molecules. For example, if a pencil of /3 rays falls on a metal, a large fraction of the rays are scattered XXII. 26 sufficiently to emerge on the side of incidence. This scattering of the [3 rays has been investigated by Eve, McLennan, Schmidt, Crowther and others. It has been found that the scattering for different chemical elements is connected with their atomic weight and their position in the periodic table. McCelland and Schmidt have given theories to account for the absorption of (3 rays by matter. The whole problem of absorption and scattering of particles by substances is very complicated, and the question is still under active examination and discussion. The negative charge carried by the j3 rays has been measured by a number of observers. It has been shown by Rutherford and Makower that the number of J3 particles expelled per second from one gram of radium in equilibrium is about that to be expected if each atom of the (3 ray products in breaking up emits one $ particle.

Heat Emission of Radioactive Matter

In 1903 it was shown by Curie and Laborde (52) that a radium compound was always hotter than the surrounding medium, and radiated heat at a constant rate of about 100 gram calories per hour per gram of radium. The rate of evolution of heat by radium has been measured subsequently by a number of observers. The latest and most accurate determination by Schweidler and Hess, using about half a gram of radium, gave 118 gram calories per gram per hour (53). There is now no doubt that the evolution of heat by radium and other radioactive matter is mainly a secondary phenomenon, resulting mainly from the expulsion of a particles. Since the latter have a large kinetic energy and are easily absorbed by matter, all of these particles are stopped in the radium itself or in the envelope surrounding it, and their energy of motion is transformed into heat. On this view, the evolution of heat from any type of radioactive matter is proportional to the kinetic energy of the expelled a particles. The view that the heating effect of radium was a measure of the kinetic energy of the a particles was strongly confirmed by the experiments of Rutherford and Barnes (54). They showed that the emanation and its products when removed from radium were responsible for about three-quarters of the heating effect of radium in equilibrium. The heating effect of the radium emanation decayed at the same rate as its activity. In addition, it was found that the ray products, viz. the emanation radium A and radium C, each gave a heating effect approximately proportional to their activity. Measurements have been made on the heating effect of uranium and thorium and of pitchblende and polonium. In each case, the evolution of heat has been shown to be approximately a measure of the kinetic energy of the a particles.

Experiments on the evolution of heat from radium and its emanation have brought to light the enormous amount of energy accompanying the transformation of radioactive matter where a particles are emitted. For example, the emanation from one gram of radium in equilibrium with its products emits heat initially at the rate of about 90 gram calories per hour. The total heat emitted during its transformation is about 12 ,000 gram calories. Now the initial volume of the emanation from one gram of radium is 6 cubic millimetres. Consequently one cubic centimetre of emanation during its life emits 2 X 10' gram calories. Taking the atomic weight of the emanation as 222, one gram of the emanation emits during its life 2 X 109 gram calories of heat. This evolution of heat is enormous compared with that emitted in any known chemical reaction. There is every reason to believe that the total emission of energy from any type of radioactive matter during its transformation is of the same order of magnitude as for the emanation. The atoms of matter must consequently be regarded as containing enormous stores of energy which are only released by the disintegration of the atom.

A large amount of work has been done in measuring the amount of the thorium and radium emanation in the atmosphere, and in determining the quantity of radium and thorium distributed on the surface of the earth. The information already obtained has an important bearing on geology and atmospheric electricity.

References.-1. H. Becquerel, Comptes Rendus, 1896, pp. 420, 501, 559, 689, 762, 1086; 2. Rutherford, Phil. Mag., Jan. 1899; 3. Mme Curie, Comptes Rendus, 1898, 126. p. t ioi; M and Mme Curie and G. Bemont, ib., 1898, 127. p. 1215; 4. Mme Curie, ib., 1907, 1 45. p. 422; 5. Thorpe, Proc. Roy. Soc., 1908, 80. p. 298; 6. Giesel, Phys. Zeit., 1902, 3. p. 578; 7. Giesel, Annal. d. Phys., 18 99, 6 9. p. 91; Ber., 1902, p. 3608; 8. Rutherford and Boltwood, Amer. Journ. Sci., July 1906; 9. Debierne, Comptes Rendus, 18 99, 12 9. p. 593; 1900, 130. p. 206; io. Giesel, Ber., 1902, p. 3608; 1903, p. 342; II. Marckwald, ib., 1903, p. 2662; 12. Mme Curie and Debierne, Comptes Rendus, 1910, 150. p. 386; 13. Boltwood, Amer. Journ. Sci., May 1908; 14. Rutherford, Phil. Mag., Feb. 1903, Oct. 1906; 15. Rutherford, ib., Jan. 1900; 16. Rutherford and Soddy, ib., May 1903; 17. Rutherford and Soddy, ib., Nov. 1902; 18. M and Mme Curie, Comptes Rendus, 18 99, 12 9. p. 714; 19. Rutherford, Phil. Mag., Jan. and Feb. 1900; 20. Rutherford and Soddy, ib., Sept. and Nov. 1902, April and May 1903; Rutherford, Phil. Trans., 1904, 204A. p. 169; 21. Russ and Makower, Proc. Roy. Soc., 1909, 82A. p. 205; 22. Hahn, Phys. Zeit., 1909, 10. p. 81; 23. Rutherford, Phil. Mag., Nov. 1904, Sept. 1905; 24. Meyer and Schweidler, Wien. Ber., July 1905; 25. Antonoff, Phil. Mag., June 1910; 26. Cameron and Ramsay, Trans. Chem. Soc., 1907, p. 1266; Rutherford, Phil. Mag., Aug. 1908; 27. Cameron and Ramsay, Proc. Roy. Soc., 1908, 81A. p. 210; Rutherford and Royds, Phil. Mag., 1908, 16. p. 313; Royds, Proc. Roy. Soc., 1909, 82A. p. 22; Watson, ib., 1910, 83A. p. 50; 28. Rutherford, Phil. Mag., 1909; 29. Gray and Ramsay, Trans. Chem. Soc., 1909, PP. 354, 1073; 30. Rutherford and Soddy, Phil. Mag., Sept. and Nov. 1902; 31. Hahn, Proc. Roy. Soc., March 1905; Phil. Mag., June 1906; Ber., 4 0. pp. 1462, 3304; Phys. Zeit., 1908, 9PP. 245, 246; 32. Hahn, Phil. Mag., Sept. 1906; 33. Godlewski, ib., July 1905; 34. Boltwood, ib., April 1905; 35. Strutt, Trans. Roy. Soc., 1905A.; 36. McCoy, Ber., 1904, p. 2641; 37. Soddy, Phil. Mag., June 1905, Aug. 1907, Oct. 1908, Jan. 1909; 38. Boltwood, Amer. Journ. Sci., Dec. 1906, Oct. 1907, May 1908, June 1908; 39. Boltwood, ib., April 1908; 40. Boltwood, lb., Oct. 1905, Feb. 1907; 41. Rutherford and Geiger, Proc. Roy. Soc., 1908, 81A. p. 141; 42. Rutherford and Royds, Phil. Mag., Feb. 1909; 43. Dewar, Proc. Roy. Soc., 1908, 81A. p. 280; 1910, 8 3. p. 404; 44. Boltwood and Rutherford, Manch. Lit. and Phil. Soc., 1909, 54. No. 6; 45. Bragg and Kleeman, Phil. Mag., Dec. 1904, Sept. 1905; 46. Rutherford, ib., Aug..1906; 47. Geiger, Proc. Roy. Soc., 1910, 83A. p. 505; 48. Geiger, ib., 1910, 8 3 A. p. 492; 49. Rutherford and Geiger, ib., 1908, 81 A. pp. 141, 163; 50. Crookes, lb., 1903; 51. Regener, Verhandl. d. D. Phys. Ges., 1908, 10. p. 28; 52. Curie and Laborde, Comptes Rendus, 1904, 136. p. 673; 53. Schweidler and Hess, Wien. Ber., June 1908, 117; 54. Rutherford and. Barnes, Phil. Mag., Feb. 1904.

General treatises are: P. Curie, Ouvres, 1908; E. Rutherford, Radioactive Transformations, 1906; F. Soddy, Interpretation of Radium, 1909; R. J. Strutt, Becquerel Rays and Radium, 1904; W. Makower, Radioactive Substances, 1908; J. Joly, Radioactivity and Geology, 1909. See also Annual Reports of the Chemical Society. (E. Ru.)