EXCHANGE 
 
EXCHANGE 
 NGv' IS 
 
 Ufoe mni\?erstt ot Gbtcago 
 
 THE RELATION BETWEEN THE ALPHA- 
 
 RAY ACTIVITIES AND RANGES OF 
 
 RADIOACTIVE SUBSTANCES 
 
 A DISSERTATION 
 
 SUBMITTED TO THE FACULTY 
 
 OF THE OGDEN GRADUATE SCHOOL OF SCIENCE 
 
 IN 'CANDIDACY FOR THE DEGREE OF 
 
 DOCTOR OF PHILOSOPHY 
 
 DEPARTMENT OF CHEMISTRY 
 
 BY 
 
 EDWIN DANIEL LEMAN 
 
 Private Edition, Distributed By 
 
 THE UNIVERSITY OF CHICAGO LIBRARIES 
 
 CHICAGO, ILLINOIS 
 
 1918 
 
Ube *Cinix>ersft ot Gbfcaao 
 
 THE RELATION BETWEEN THE ALPHA. 
 
 RAY ACTIVITIES AND RANGES OF 
 
 RADIOACTIVE SUBSTANCES 
 
 A DISSERTATION 
 SUBMITTED TO THE FACULTY 
 
 OF THE OGDEN GRADUATE SCHOOL OF SCIENCE 
 
 IN CANDIDACY FOR THE DEGREE OF 
 
 DOCTOR OF PHILOSOPHY 
 
 DEPARTMENT OF CHEMISTRY 
 
 BY 
 
 EDWIN DANIEL LEMAN 
 
 Private Edition, Distributed By 
 THE UNIVERSITY OF CHICAGO LIBRARIES 
 CHICAGO, ILLINOIS 
 1918 
 
Qc 
 
 i-5 
 
CONTENTS 
 
 PAGE 
 
 INTRODUCTION i 
 
 CHAPTER 
 
 I. THE RELATION BETWEEN THE a-RAY ACTIVITIES AND RANGES or 
 
 RADIUM AND ITS SHORT-LIVED PRODUCTS 
 
 II. THE RELATION BETWEEN a-RAY ACTIVITIES AND RANGES OF 
 
 RADIOACTINIUM AND ITS SUBSEQUENT PRODUCTS . . .,.,.' 9 
 
 III. NOTES . ,. ^_^ '1 v J . . 14 
 
 Note i . The Period of Radioactinium 14 
 
 Note 2. Determination of the Range of Radioactinium ... : * . 17 
 
 Notes. The Period of Actinium X .''"._ , .. . . . . ; . . 18 
 
 404734 
 
f t 
 
INTRODUCTION 
 
 At the present time all previous work tends to indicate that the 
 number of ions, and therefore the ionization current in air due to a single 
 particle of range R, is very closely proportional to the two- thirds power 
 of R. 1 This can be represented by the equation, I = kR%, where / is 
 the ionization current, R the range, and k a constant for particles of all 
 ranges. McCoy and Viol 2 have shown that the relative a-ray activities 
 in the thorium series, as calculated from this equation, are in good accord 
 with experimental values. The purpose of this paper is to show that the 
 relative activities of radium and its short-lived products and of radio- 
 actinium and its subsequent products are also in good agreement with 
 those calculated from the known ranges. Notes on the period and range 
 of radioactinium and the period of actinium X are also included. The 
 subject-matter of this thesis has been published in three papers. 3 
 
 1 Geiger, Proc. Roy. Soc., A, 82, 486, 1909; Taylor, Phil. Mag., 21, 371, 1911; 
 McCoy, Phys. Rev., i, 393, 1913. 
 
 2 Phil. Mag., 25, 333, 1913. 
 
 3 McCoy and Leman, Phys. Zeit., 14, 1280 (1913); Phys. Rev., 4, 409 (1914); 
 ibid., 6, 184 (1915). 
 
CHAPTER I 
 
 THE RELATION BETWEEN THE d-RAY ACTIVITIES AND RANGES OF 
 RADIUM AND ITS SHORT-LIVED PRODUCTS 
 
 The latest available data on the radium series 1 which are used in this 
 paper are given in Table I. 
 
 TABLE I 
 
 THE RADIUM SERIES 
 
 
 Symbols 
 
 Period 
 
 Rays 
 
 Ranges (Cm. at 
 15 C.) 
 
 Radium 
 
 Ra 
 
 i 730 years 
 
 a, /3 
 
 3 3O 
 
 Emanation 
 
 Em 
 
 3 . 8 ^ days 
 
 a 
 
 4 16 
 
 Radium A 
 
 Ra.A 
 
 3 oo minutes 
 
 a. 
 
 47^ 
 
 Radium B 
 
 R&B 
 
 26 . 7 minutes 
 
 /3 
 
 
 Radium Ci 
 
 RaCi 
 
 19 5 minutes 
 
 a(?) 13 
 
 
 Radium C 2 
 
 RaC 2 
 
 i 4 minutes 
 
 /3 
 
 
 Radium C" 
 
 RaC' 
 
 io-6 seconds(?) 
 
 a 
 
 6.94 
 
 The accepted scheme of disintegration in this series, according to 
 Fajans, 2 is as follows: 
 
 a , 
 
 According to this view, the product formerly called radium C is 
 complex: d, which is the product of B, disintegrates in two ways: the 
 first (principal) with the production of a /3-particle giving C'; the second 
 (subordinate) with the expulsion of an a-particle, giving C 2 . The prod- 
 uct C' also gives a-rays, and of every 10,000 a-par tides produced by the 
 C components all but three are due to the change of C' into Z), the balance 
 being due to the change of d into C 2 . 3 If we assume that these conclu- 
 sions are essentially correct, we see that the effect on the activity caused 
 by a minute fraction of the a-particles of radium C, having a different 
 range from those of the main fraction, would be negligibly small. I shall 
 
 1 Kolowrat, Le Radium', n, i, 1914. 
 
 2 Phys. Zeit., 13, 699, 1912. 3 Fajans, loc. cit. 
 
a-RAY ACTIVITIES AND RANGES OF RADIUM 3 
 
 neglect the complexity of C in the discussions in this paper, merely point- 
 ing out that the present work furnishes no data regarding this important 
 question. 
 
 The method of determining the relative a-ray activities of Ra and 
 its short-lived products consisted in preparing a Ra-BaSO 4 film free 
 from all of the subsequent products of Ra and measuring its initial and 
 final activities. The activities of such films increased for about six 
 weeks after the preparation of the film and then remained practically con- 
 stant during several months of observation, the constant activity in each 
 case being taken as the final. The Ra-BaSO 4 film, free from its sub- 
 sequent products, was prepared in the following manner: One c.c. 
 of a solution of pure radium chloride in dilute hydrochloric acid was 
 diluted to 10 c.c.; the solution was heated to its boiling-point, and a 
 current of air was bubbled through it for thirty minutes, the solu- 
 tion being kept near its boiling-point and a few cubic centimeters of 
 water being added from time to time to replace that lost by evaporation. 
 This procedure kept the solution free from emanation, and allowed Ra^l 
 to decay practically completely. A few drops of lead acetate solution 
 were then added and hydrogen sulphide passed in. The lead sulphide, 
 which was precipitated, removed B, C, D, E, and F. 1 The precipitate 
 was rapidly filtered off, and a current of air was again bubbled through 
 the filtrate for ten minutes, keeping it near its boiling-point and the 
 volume constant. Lead sulphide was again precipitated in the solution, 
 the precipitate filtered off, and the filtrate again treated in the manner 
 just described, making a total of three precipitations of lead sulphide 
 and removing practically every trace of the products of radium. The 
 various operations to this point had taken about fifty minutes. The 
 filtrate from the last treatment was put into a 15 c.c. centrifuge tube, 
 i c.c. of N/ioo barium chloride solution added, then a few drops of dilute 
 sulphuric acid. The solution was well shaken and then centrifuged. 
 The supernatant solution was decanted from the precipitate, and the 
 latter was well washed, by decantation, with water acidified with a few 
 drops of HC1, and finally with alcohol. A small portion of this precipi- 
 tate was spread as uniformly as possible, with the aid of a glass rod and a 
 little alcohol, over a flat polished brass plate, about 7 cm. in diameter. 
 When the alcohol had evaporated, the less firmly adhering particles were 
 brushed off, care being taken to guard the edges and back of the plate 
 from radioactive contamination. The films so prepared were so thin 
 
 1 Compare the work of McCoy and Viol, loc. cit., on the separation of Th B, C, 
 and D from Th X. 
 
4 a-RAY ACTIVITIES 
 
 as to be almost invisible; the differential absorption of a-rays in such 
 films was therefore negligibly small. 
 
 The time of precipitation of the sulphate was taken as zero time, as 
 at this moment the precipitate was free from all of the subsequent 
 products of radium. That the foregoing method completely freed the 
 radium from all of its active products was shown both by control experi- 
 ments and by the fact that the activity increased at a regular rate from 
 the start. About thirty minutes elapsed between the time when the 
 sulphates were precipitated and the time of making the first measure- 
 ments. The activity measurements were made in a gold-leaf electro- 
 scope, as previously described, 1 the active films being placed 7 cm. below 
 the charged electrode, thus allowing all rays to reach their full ranges. 
 Sufficient potential (about 600 volts) was used to insure practically 
 complete saturation currents for the weak ionization produced. All 
 activities were measured in comparison with a standard film of uranium 
 oxide, the activities given being in terms of this standard. All measure- 
 ments were made with the greatest care, and corrections were made for 
 the accurately determined natural leak, which in every case was less than 
 i per cent of the standard. The initial activity of each film was less than, 
 the final activity greater than, the standard. The activity increased 
 nearly linearly for the first six hours, so that by a small extrapolation 
 the activity at time zero could be determined with a high degree of accu- 
 racy. The activities in terms of the standard are given in Table II for 
 two films. 
 
 TABLE II 
 THE INITIAL AND FINAL ACTIVITIES OF RADIUM (UNCORRECTED) 
 
 Film 
 
 Initial Activity 
 
 Final Activity 8 
 
 Ratio Uncorrected 
 
 I 
 
 0.858 
 
 4. -12< 
 
 c .043 
 
 2 
 
 O S^S 
 
 2 8^2 
 
 ir Q7 1 ? 
 
 
 
 
 
 But these results are subject to three corrections, viz.: the activity 
 due to the /3-rays, the escape of emanation from the film either by 
 diffusion or by recoil, and the loss of other products by recoil. 
 
 The activity due to /3-rays was determined by placing consecutive 
 layers of aluminium foil over the Ra-BaSO 4 film, the first layer being of 
 sufficient thickness to absorb all a-rays and measuring the activity 
 with each additional layer in the same electroscope as was used for the 
 
 1 McCoy and Ashman, Am. Jour. Sci., 26, 521, 1908. 
 
i< 
 
 FTE: 
 
 a-RAY ACTIVITIES AND RANGES OF RADIUM 5 
 
 a-ray measurements. By plotting the activities against the thickness 
 of covering, and extrapolating to the axis of the activities, the /3-ray 
 activity could be ascertained with a fair degree of accuracy. This 
 activity must be subtracted from the final activity of the film. 
 
 Since Kolowrat 1 has shown that the /3-ray activity of radium free 
 from its products is only 2 per cent of the /3-ray activity of radium in 
 equilibrium with its short-lived products, and since the /3-ray activity of 
 the latter as measured in the electroscope used in this work was only 
 about o . 5 per cent of the a-ray activity, it follows that it is not neces- 
 sary to apply any correction for /3-ray activity of the radium itself. 
 
 The amount of emanation lost by the film was determined by the 
 use of a circular brass box, as shown in Fig. i. The cover A, fitted with 
 two small bore tubes E and G, was ground so as to fit very tightly over 
 the lower compartment B. In the lower 
 compartment was a recess about o . 2 cm. 
 in depth and 8 cm. in diameter. Small- 
 bore glass tubes drawn out at one end, C 
 and D, were attached to the tubes E and 
 G by means of short pieces of thick-walled 
 rubber tubing. The Ra-BaSO 4 film was 
 placed in B, the cover A fitted on, and 
 all joints sealed with wax. The ends of C Fig. i 
 
 and D were then sealed by fusion. After 
 
 an interval of 40 days or more the emanation which had accumulated 
 was drawn into an emanation electroscope by a stream of air, care 
 being taken to prevent any loss of the accumulated emanation and also 
 to prevent any appreciable diminution of pressure within the box which 
 might withdraw some of the Em from the film. The rate of discharge 
 of the electroscope was measured after the emanation had stood in it 
 for three hours. 
 
 In order to find what fraction this quantity of Em was of the equi- 
 librium quantity in the Ra-BaSO 4 film, two additional determinations 
 were necessary. One c.c. of the original radium solution was diluted and 
 then freed from subsequent active products, as described in a preceding 
 paragraph. By means of a small weight-pipette, an accurately weighed 
 portion of this solution was taken and uniformly distributed over the 
 surface of a fiat platinum plate and evaporated to dryness. The activity 
 of the residue, which was entirely invisible, was measured within twenty 
 minutes, and the measurements extended over a short interval in order 
 
 1 Le Radium, 7, 269, 1910. 
 
6 a-RAY ACTIVITIES 
 
 to be able to get the initial activity by extrapolation. To find the activ- 
 ity of the emanation from this quantity of radium, a known portion of 
 the solution in the weight-pipette was run into a small round-bottom 
 flask containing about 10 c.c. of dilute hydrochloric acid. The flask 
 was well stopped with a two-hole rubber stopper fitted with delivering 
 tubes, one of which extended into the solution. A current of air was 
 bubbled through the solution for 30 minutes to drive off the accumulated 
 emanation, and the flask was then sealed by fusing the ends of the 
 delivery tubes. After an interval of a few days the emanation was drawn 
 into the emanation electroscope by allowing air to bubble through the 
 solution, which was heated near its boiling-point. After three hours the 
 rate of discharge of the electroscope was measured. 
 
 The corrections for loss of emanation by the film were made as 
 follows: 
 
 Initial activity of film No. i o. 858 
 
 Initial activity of Ra on the platinum plate 660 
 
 The radium on the platinum plate was obtained from i.4942gm. of 
 solution. After 3 days 21.5 hours 1.5738 gm. of the same solution 
 gave a quantity of Em which discharged the electroscope in 46.45 sec- 
 onds. Since for 3 days 21.5 hours, i e~= 0.5036, the equilibrium 
 amount of Em from the solution would have discharged the electroscope 
 in o . 5036 X 46 . 45 = 23 . 40 seconds. Therefore the equilibrium amount of 
 Em from i .4942 gm. of this solution would discharge the electroscope in 
 24 . 64 seconds. That is, a radium film, free from all subsequent products 
 of radium, having an initial a-ray activity of o . 660, produces an equi- 
 librium quantity of emanation which discharges the emanation electro- 
 scope in 24 . 64 seconds. It then follows that the equilibrium quantity of 
 emanation from film No. i, which has an initial activity of o .858, would 
 discharge the emanation electroscope in 18 .97 seconds. The emanation 
 which had escaped from film No. i, when the latter had been sealed up 
 40 days or more, discharged the emanation electroscope in 1,748 seconds; 
 therefore i .08 per cent of the equilibrium quantity of Em escaped from 
 the film. This means that the quantity of emanation and the short- 
 lived products in the film is i .08 per cent too low. In this film the activ- 
 ity of the subsequent products of Ra is 4.297 0.858 = 3.439, which 
 value is i . 08 per cent too low. Hence the true activity of the products, 
 if no Em had escaped, would be 3 .476. 
 
 To find the loss of activity due to recoil, a polished brass plate 7 cm. 
 in diameter was placed i mm. above, and completely insulated from, 
 film No. i. A potential of no volts was maintained for six weeks, the 
 
a-RAY ACTIVITIES AND RANGES OF RADIUM 
 
 upper plate being kept negatively charged. The activity of the plate 
 was measured as quickly as possible after removing the potential, four 
 minutes elapsing from the time the potential was removed to the mean 
 time of making the measurements. The activity of the active matter 
 which collected on the plate was o . 0374. Assuming that the active matter 
 on the plate at the instant the potential was removed was Ra^4 , Ra, 
 and RaC in equilibrium, the activity of the matter on this plate four 
 minute's after the potential is removed is approximately 70 per cent of its 
 initial value. 1 Therefore the initial activity of the matter on the plate 
 was o .0534. To find what quantity of the matter on the plate is due to 
 active deposit from escaped emanation and what quantity is due to 
 
 TABLE III 
 THE INITIAL AND FINAL ACTIVITIES OF RA (CORRECTED) 
 
 Film 
 
 Initial Activity I 
 
 Final Activity I 
 
 I./I 
 
 I 
 
 o 8^8 
 
 4. 363 
 
 r 08"? 
 
 2 
 
 o tx8 
 
 2 86^ 
 
 r J77 
 
 
 
 
 
 Mean 
 
 
 
 r IOQ 
 
 
 
 
 
 direct recoil, it is necessary to recall that the emanation lost by this film 
 was i . 08 per cent of the equilibrium quantity, or the activity of the prod- 
 ucts Em, Ra^4, and RaC lost was 0.037. Assuming that the activities 
 are proportional to the two- thirds powers of the ranges, the fraction 
 of the activity due to Ra^-fRaC is 65 per cent of the total activity due 
 to Em+Ra^4+RaC, or 0.0241, and that due to recoil is 0.0534 
 o. 0241 = 0. 0293^ 
 
 Table III gives the results of two determinations. The final activ- 
 ity is corrected for /3-ray activity, loss of emanation, and loss by recoil, 
 these corrections being determined separately for each film. 
 
 1 Rutherford, Radioactive Substances and Their Radiations (1913), p. 491. 
 
 2 It must be pointed out that this value is calculated on the assumption that at 
 the instant the potential is removed the active matter on the plate is Ra.4 -f-Ra+RaC 
 in equilibrium, and there is a decided drop in activity before the first measurement is 
 made, due to the rapid decay of Ra^4 . In the case of the active matter due to active 
 deposit we do have this equilibrium, but in the case of recoil atoms there is in all 
 probability an excess of RaC atoms over the equilibrium number of Ra^4 atoms. This 
 would mean that the percentage of the activity which decayed during the interval 
 between the time the potential was removed and the time of measurement would 
 not be so great as that calculated upon complete equilibrium, and the value of the loss 
 by recoil would be even less than that calculated above. However, the loss by recoil 
 is so small that the value calculated above is certainly correct within experimental 
 error, and it represents the maximum value. 
 
a-RAY ACTIVITIES 
 
 In the series Ra Em Ra^4 RaC it is very probable that each 
 member when present in equilibrium amount produces the same number 
 of a-particles per unit time; if this is so, the equation 
 
 leads to the theoretical results shown in Table IV. 
 
 TABLE IV 
 
 
 RANGES 
 
 pi 
 
 RELATIVE A 
 
 CTIVITIES 
 
 
 AT 15 
 
 
 Calculated 
 
 Found , 
 
 Ra 
 
 3 -2Q 
 
 2 217 
 
 I OO 
 
 (i oo) 
 
 Em 
 
 3-ov 
 
 A 10 
 
 2 586 
 
 I 17) 
 
 
 Ra4 
 
 A 7^ 
 
 2 826 
 
 I 28 r4 OO 
 
 4n 
 
 RaC 
 
 6 04. 
 
 2 6^0 
 
 i 64 
 
 
 
 
 
 
 
 The only previous determination of the relative activities of radium 
 and its products was made by Boltwood. 1 In these experiments the 
 films were made by the evaporation of a chloride solution. Since such 
 films gave off very large fractions of the emanation produced (in one 
 case as high as 65 per cent), it is not surprising that the results obtained 
 were not very accurate. Instead of a ratio of 4.11 given here (last 
 column, Table IV), Boltwood found 4.65. For several years this result 
 was looked upon as satisfactory, 2 since it was in good agreement with 
 that calculated upon the assumption that the number of ions produced 
 by an a-particle is proportional to the first power of its range 3 instead 
 of the two-thirds power. 
 
 The good agreement of this result with the theoretical value as 
 calculated by the equation I = kR*, the correctness of which may be 
 considered as already established, shows that only those members which 
 are here considered play significant parts in the a-ray activity of the 
 radium series, and that the accepted ranges are at least approximately 
 correct. 
 
 1 Phys. Zeit., 7, 489, 1906; Le Radium, 3, 170, 1906. 
 
 2 Rutherford, Radioactive Substances (1913), p. 447- 
 
 3 Boltwood, he. cit. 
 
CHAPTER II 
 
 THE RELATION BETWEEN a-RAY ACTIVITIES AND RANGES OF 
 RADIOACTINIUM AND ITS SUBSEQUENT PRODUCTS 
 
 A study of the actinium series was made along the same lines as in 
 the preceding part of this paper, and radioactinium, free from actinium 
 itself as well as actinium Xand subsequent products, was prepared, thin 
 films made, and the a-ray activities measured from time to time. The 
 activities, of course, increase to a certain interval, then decrease, owing 
 to the formation of actinium X and its products and the consequent 
 decay of the whole. 
 
 Table V gives the latest available data for this series. 
 
 TABLE V 
 
 THE ACTINIUM SERIES 
 
 
 Symbols 
 
 Periods 
 
 Rays 
 
 Ranges 
 (Centimeters) 
 
 Actinium 
 
 Ac 
 
 ? 
 
 
 
 Radioactinium 
 
 Rn 
 
 i 8 88 days* 
 
 a B 
 
 A 4.ot 
 
 Actinium X . 
 
 AcX 
 
 ii ^ days* 
 
 a 
 
 4 4.O 
 
 Emanation 
 
 Em 
 
 3 9 seconds 
 
 a 
 
 70 
 
 Actinium A . , 
 
 A 
 
 0.002 seconds 
 
 a 
 
 6 <o 
 
 Actinium B 
 
 B 
 
 36 minutes 
 
 /3 
 
 
 Actinium C 
 
 C 
 
 2 . i minutes 
 
 a 
 
 $ .40 
 
 Actinium D 
 
 D 
 
 4 71 minutes 
 
 B 7 
 
 
 
 
 
 
 
 *This paper. The previously accepted periods of radioactinium and actinium X were 19.5 days 
 and 10 . 2 days respectively. 
 
 t The range of radioactinium found by Geiger was 4.60 cm.; the value given above is that given 
 in this paper. 
 
 If /i is the fraction of the original Rn left after an interval of / days 
 and /,. is the fraction for AcZ, unit amount being the equilibrium quantity 
 corresponding to the initial amount of Rn, then the activity A , at time /, 
 resulting from unit initial quantity of Rn, is given by the equation: 
 
 (i) 
 
 where x is the a-ray activity of the equilibrium quantity of AcX plus 
 products for unit quantity of Rn. Strictly speaking, for intervals of less 
 than 3 or 4 days one should take into account the fact that the products 
 
10 a-RAY ACTIVITIES 
 
 of AcX are not in equilibrium with the latter; practically, however, for 
 longer intervals the simple equation (i) is entirely sufficient. If Xi 
 and X 2 are the decay constants of Rn and AcX, respectively, then 
 
 and 
 
 The periods being 18.8 days and 11.35 days, respectively, Xi= 0.0369 
 and X 2 = o.o6n. 
 
 The actinium used in this work had been found to be free from all 
 but negligible traces of radium and thorium and their active products, 
 emanation tests proving the absence of radium and active deposit 
 experiments proving that of thorium. It contained, however, an appre- 
 ciable amount of ionium. To the solution of the actinium-bearing 
 material in dilute hydrochloric acid a few milligrams of thorium nitrate 
 was added and the latter then precipitated with hydrogen peroxide. 
 The filtrate contained all the actinium and was apparently free from 
 Rn and lo; but, to be certain that no trace of the latter remained in the 
 Ac, the treatment with Th and hydrogen peroxide was repeated three 
 times. To the purified actinium solution i c.c. of 5 per cent aluminium 
 chloride solution was added and ammonia gas (free from carbon dioxide) 
 passed in. The aluminium hydroxide was filtered out, dissolved in 
 hydrochloric acid, and precipitated with ammonia once more. The 
 filtrate from the first aluminium precipitate contained two-thirds of the 
 AcX; that from the second the larger part of the balance; while 6 per 
 cent of the AcX remained in the third aluminium precipitate, which con- 
 tained practically all of the Ac. The precipitations with ammonia had 
 freed the Ac from the minute amount of mesothorium introduced with the 
 few milligrams of Th used. This Ac solution stood for several months, 
 during which time a large amount of Rn formed. The Rn was then 
 separated from this solution, which had a volume of 5 c.c. by adding 
 3 drops of a 2 per cent solution of thorium nitrate, which had just been 
 freed from mesothorium, and precipitating the Th by hydrogen peroxide. 
 The precipitate was filtered out, dissolved in dilute hydrochloric acid 
 and potassium iodide, and reprecipitated by hydrogen peroxide four 
 times more. The 10 c.c. of acid solution of the last Th precipitate which 
 contained all the Rn, but was entirely free from AcX and its products, was 
 treated with oxalic acid. The precipitate of 3 or 4 mg. of thorium 
 
a-RAY ACTIVITIES AND RANGES OF RADIOACTINIUM 
 
 II 
 
 oxalate contained all of the Rn. It was separated from the solution by 
 a centrifuge and washed thoroughly with water and then with alcohol. 
 A small portion was then spread on a metal plate in an exceedingly thin 
 film, the activity measurements of which are given in Table VI. In this 
 table x is the activity of AcX+Em+A+B+C+D in terms of the 
 activity of the equilibrium amount of Rn as unity. 
 
 TABLE VI. 
 
 THE a-RAY ACTIVITY CURVE OF RADIOACTINIUM INITIALLY 
 FREE FROM ITS PRODUCTS. FILM No. 4 
 
 Interval in Days 
 
 Activity 
 
 X 
 
 o ooo 
 
 I OOO 
 
 
 <? IOI . 
 
 I CH3 
 
 A ZA 
 
 6.O2^ . . 
 
 2 . O4< 
 
 A C5 
 
 I 1 ?. 76. . 
 
 2 . 5Q7 
 
 4 cc 
 
 16.08 
 
 2.62O 
 
 4. en 
 
 17.07 
 
 2.623 
 
 4- ^0 
 
 17.80 
 
 /- 
 
 2.620 
 
 4.60 
 
 20 o< 
 
 2 ^Q3 
 
 4 <?6 
 
 2-1 10 
 
 2 ^27 
 
 A CA 
 
 27 OQf 
 
 2. 3Q7 
 
 A CA 
 
 31 IO 
 
 2. 28l 
 
 4 63 
 
 36 OA 
 
 2 .O 1 ?'? 
 
 4.60 
 
 7Q Q7 . 
 
 1.881 
 
 4.61 
 
 2O6 .O 
 
 0.007 
 
 
 
 
 
 Mean 
 
 
 A 72 
 
 
 
 
 The activity at the end of 206 days (Table VI) was found to be 
 0.007; f this, o.ooi was calculated to be due to remaining Rn and 
 products; the balance, 0.006, represents the constant activity of the 
 minute amount of thorium present. The activities given in Table VI 
 have been corrected for this constant thorium activity. The activity 
 measurements were made in the a-ray electroscope previously described. 1 
 The active films were placed 6 . 5 cm. below the charged electrode, thus 
 allowing all rays to reach their full ranges. The activities of the films 
 varied between one-half and one and one-half that of the standard 
 film of uranium oxide. Sufficient potential, 500 to 600 volts, was used 
 to insure practically complete saturation currents for the weak ionization 
 measured. 
 
 Three other series of measurements like those represented by Table II 
 were made with films made from two additional lots of radioactinium, 
 
 1 McCoy and Ashman, loc. cit. 
 
12 a-RAY ACTIVITIES 
 
 each prepared and purified separately. The results for the four films are 
 summarized in Table VII. 
 
 The value of x thus found is subject to a correction, which was 
 estimated to be 2.5 per cent, due to the effects of /3-rays, recoil, and loss 
 of emanation. The corrected value is 4.68. By direct measurement 
 it was found that the /3-rays, largely from actinium D, increased the 
 value of x, 0.5 per cent for the a-ray electroscope used in our measure- 
 ments. To find the loss of activity due to recoil and loss of emanation 
 a brass plate charged to a negative potential of no volts was placed 
 i mm. above the radioactive film in a closed vessel, and the activity 
 which deposited on the plate during the first 16 days following the prepa- 
 ration of the radioactinium film was measured. Almost exactly half 
 of the activity of the deposit was due to AcC; the balance decayed with 
 the period of AcX, the presence of the latter substance being due to 
 
 TABLE VII 
 
 No. of Film 
 
 No. of Observations 
 
 X 
 
 I 
 
 18 
 
 A en 
 
 2 
 
 14. 
 
 A. f"7 
 
 2 . 
 
 1C 
 
 A. ff 
 
 4-. . 
 
 12 
 
 4-57 
 
 
 
 
 Mean 
 
 
 4-57 
 
 
 
 
 recoil. Assuming that all of the AcC lost by the film was deposited on 
 the plate, the correction to x on this account would amount to 2 per cent. 
 The correction to AcX, which is accompanied of course by Em and A, 
 is also apparently 2 per cent, but should be taken somewhat less by reason 
 of the probable extensive escape in the ionization chamber of the Em and 
 A from the surface of the brass plate into the space above, where they 
 would cause greater ionization than if they remained wholly on the plate. 
 The true correction, however, was taken to be 1.8 per cent instead of 
 2 per cent. A further correction should be made because of the volatili- 
 zation of Em and therefore of A from the principal film in the ionization 
 chamber of the electroscope. From the amount of C in the active 
 deposit, we estimate that 2 per cent of the whole Em is present in gas- 
 eous form in the electroscope, and that this would cause the value of x 
 as found to be 0.8 per cent too high. The combined effect of these 
 corrections is 2+1.80.5 0.8=2.5 per cent. Taking x uncorrected 
 as 4 . 57, the corrected value becomes 4 . 68. 
 
a-RAY ACTIVITIES AND RANGES OF RADIOACTINIUM 13 
 
 Table VIII shows the ranges, R, at 15 and 76 cm., R*, and the per- 
 centage activity of each a-ray member of the series; these percentages 
 are taken proportional to the corresponding values of R* } it being 
 assumed that the equilibrium amount of each member of the series pro- 
 duces the same number of a-par tides per second. 1 The values given in 
 the last column of Table VIII are those found by experiment : for radio- 
 actinium the "activity found" is i/(i+#)= 17 .6 per cent of the whole. 
 
 TABLE VIII 
 
 
 RANGES AT 15 
 
 V 
 
 PERCENTAGE ACTIVITY 
 
 Calculated 
 
 Found 
 
 Radioactinium 
 
 4.40 
 4.40 
 S-70 
 6.50 
 5-40 
 
 2.69 
 2.69 
 3-19 
 3-49 
 3-o8 
 
 17-8 
 I 7 .8 
 21. 1 
 23.0 
 20.3 
 
 82.2 
 
 I 7 .6 
 82.4 
 
 Actinium X 
 
 Emanation 
 
 Actinium A 
 
 Actinium C 
 
 
 IOO.O 
 
 The value of 2R* for AcX+Em+A+C divided by R* for Rn gives 4 .62, 
 which is therefore the theoretical value of x. The close agreement of 
 this result with that found by experiment, 4.68, is further evidence, if 
 such were necessary, that the roll of the a-ray members of the actinium 
 series is now complete and that the constants given in Tables V and 
 VIII may be accepted with considerable confidence as being at least 
 close approximates to the true values. 
 
 1 While it is probable that AcC is complex, the number of a-particles of longer 
 range than 5. 4 cm. compared with those of this range is so small 0.15 per cent 
 that we need not take them into account here. See Marsden and Perkins, Phil. Mag., 
 27, 700, 1914. 
 
CHAPTER III 
 NOTES 
 
 NOTE I. THE PERIOD OF RADIOACTINIUM 
 
 Hahn's early work 1 on radioactinium indicated a period of 19 . 5 days. 
 This value has been accepted during the past eight years and was thought 
 to be confirmed by Rothenbach, 2 working under the direction of 
 Professor Hahn. In determining the period of a radioactive substance, 
 which produces products of considerably shorter life, it is usually prac- 
 ticable to consider that the rate of decay is exponential after a sufficient 
 lapse of time. It was by this method of calculation that the period of 
 radioactinium was determined by Hahn and by Rothenbach. However, 
 in case the period of one or more of the products is the same order of 
 magnitude as that of the mother-substance, this simple treatment of 
 the problem is not accurate, and it becomes necessary to make the follow- 
 ing modification: 
 
 The familiar equation which has been previously used in the form 
 
 may be written 
 
 A.-Ai 711 
 
 if for i e~( A '- A ')' WQ write p. The equation 
 
 then becomes 
 
 Now the limiting value of / 2 is given by 
 
 1 Phil. Mag., 12, 244, 1906; 13, 165, 1907. 
 
 2 Dissertation (Berlin, 1913). 
 
 14 
 
NOTES 15 
 
 and to calculate the period of Rn by the simple exponential equation is 
 to assume that / 2 has approached this limitating value sufficiently 
 closely. But this is by no means the case, even after a much longer time 
 than that over which Hahn's and Rothenbach's observations were car- 
 ried. After 115 days the activity of a Rn film is about 6 per cent less 
 than it would be if the limiting ratio of AcX were present. Let us repre- 
 sent by A' the activity of the film if this limiting ratio of AcX (+ prod- 
 ucts) were present: then 
 
 and 
 
 A' X 2 -; 
 
 or we may write 
 
 A' = Aq. 
 
 In order to find the period of Rn, films were made as previously 
 described, and very careful measurements were made of their initial 
 activity, extrapolating from the first measurements made 45 minutes 
 after the precipitation of the Rn with the thorium oxalate to find the 
 true activity at time zero, which value was used in check calculations. 
 These films were allowed to decay a suitable length of time, and a 
 series of measurements was made on each at convenient intervals. The 
 films were then allowed to stand for nearly a year, and the activities 
 again measured over a short period. This activity, which was in each 
 case nearly constant, was due to the small amount of thorium present, 
 all Rn having decayed. All measurements on each film were then 
 respectively corrected. 
 
 Table IX gives the results of a series of measurements made on 
 one of the films, calculated on the basis that #=4.68. 
 
 Three other series of measurements of different films gave the results 
 found in Table X. The low result, 18.75 days, for the last series was 
 caused by three very low values, found on successive measurements on 
 the ninth, twelfth, and fourteenth days, viz., 18.56, 18.57, and 18.67. 
 On both the fifteenth and sixteenth days, however, the measurements 
 gave 18.84 days, and it is probable that these low results were caused 
 by some undiscovered error in the activity measurements. If these 
 low results are omitted from the mean, the figure for this series becomes 
 
i6 
 
 a-RAY ACTIVITIES 
 
 18.87 days, a value in good agreement with the means of the other 
 three series. 
 
 Further check calculations were made of the activities at various 
 times upon the assumption that the period of Rn is 19 .o and 19 . i days. 
 If the period of Rn is 19 . i days, the mean difference between the activ- 
 ities found and calculated is 5 .9 per cent; for a period of 19 .o days the 
 difference is 3 .7 per cent, while for a period of 18 .8 days the difference 
 is only o . 8 per cent. It is therefore perfectly clear that the old value, 
 19.5 days, is far from the true value and can no longer be supported. 
 
 TABLE IX 
 
 Age of Film 
 in Days 
 
 Interval since 
 92.21 Day 
 
 Activity 
 Corrected 
 
 Q 
 
 A' 
 
 Period 
 
 QI . 21 . . 
 
 O.O 
 
 A 
 1.658 
 
 no 
 
 I 840 
 
 
 IOO.Q7 . . 
 
 8.76 
 
 1 .227 
 
 .087 
 
 I 734. 
 
 18 86 
 
 103 08 
 
 II 77 
 
 i 106 
 
 080 
 
 I IOC 
 
 18 88 
 
 1 08 20 
 
 It 00 
 
 QC2 
 
 O72 
 
 I O2I 
 
 18 81 
 
 112.92 
 
 117-89 
 
 119 16 ... 
 
 20.71 
 25.68 
 26 Q<? 
 
 yo- 6 
 .809 
 .678 
 652 
 
 .064 
 .056 
 OCA 
 
 .861 
 .717 
 687 
 
 18.89 
 18.88 
 
 l8 Q7 
 
 
 
 
 
 
 
 Mean 
 
 
 
 
 
 18 88 
 
 
 
 
 
 
 
 TABLE X 
 
 Age of Film at First 
 Measurement 
 
 Age of Film at Last 
 Measurement 
 
 Number of 
 Measurements 
 
 Period 
 
 60, i days 
 60 . i days 
 104.0 days 
 
 109 . 2 days 
 118.0 days 
 120.0 days 
 
 II 
 12 
 
 7 
 
 18.88 
 18.88 
 18-75 
 
 The difference between the value 18.8 for the period of radioactinium 
 and that of Hahn and Rothenbach is wholly due to the fact that in the 
 latter case the formula used in the calculation was not sufficiently 
 accurate. The experimental results given here are in satisfactory 
 agreement with theirs and indicate also a period of 19.5 days if the cal- 
 culation is made by the simple exponential equation used by Hahn 
 and Rothenbach. The latter's calculations were based on measure- 
 ments made between the one hundred and fifteenth and one hundred and 
 seventy-fourth day. Now a simple calculation will show that, if the 
 period as found by the simple exponential equation is 19 .5 days for the 
 interval between 120 and 139 .5 days, then by use of the correct formula 
 used here the same data show the true period to be 18.89 days. 
 
NOTES 17 
 
 These measurements indicate that the period of radioactinium is a 
 little higher than 18.8 days, which value was used in finding the value 
 = 4 .68. If, as is very probable, the period is 18 .88 days, the previous 
 experimental results give # = 4.67; the difference is not great, and the 
 lower value of x is in even closer agreement with the value calculated 
 from the ranges, viz., 4.63. 
 
 NOTE 2. DETERMINATION OF THE RANGE OF RADIOACTINIUM 
 
 From the value found for the activity of the products of radioactinium 
 compared with radioactinium itself it was suspected that either the 
 accepted range of radioactinium was too great or that of AcX was too 
 small. The values found by Geiger 1 for Rn and AcX at 15 and 760 mm. 
 were 4.60 and 4. 40 cm., respectively. Furthermore, by Geiger 's law 
 relating ranges and decay constants, the range of Rn should be less than 
 that of AcX. As it was a comparatively easy task to determine the 
 range of Rn, this measurement was carried out with the use of a modifica- 
 tion of Geiger's spherical flask apparatus. The flask, which was chosen 
 from a large stock, was almost perfectly spherical, except in the region 
 near the neck. Its internal radius was 6 . 7 cm. 
 
 The radiothorium was prepared by the same method as that used in 
 preparing this substance for the activity measurements. A large quan- 
 tity of actinium was used, and but one drop of a 0.4 per cent thorium 
 nitrate solution, =0.1 mg., ThO 2 . The thorium was precipitated three 
 times with hydrogen peroxide and was converted into oxalate, which 
 was separated by means of a centrifuge and washed with dilute hydro- 
 chloric acid and finally with alcohol. A small portion of this oxalate 
 was made into a very thin film, about i mm. in diameter on the center 
 of the brass disk of the range apparatus. The range measurements were 
 completed within two or three hours from the time of the oxalate pre- 
 cipitation; from this it follows that the maximum amount of AcX 
 formed did not exceed 0.25 per cent of the equilibrium amount. The 
 temperature was read at frequent intervals during the measurement and 
 always remained constant within one degree. 
 
 The results of one determination are shown graphically in Fig. 2, 
 which is drawn to scale. The break comes at 504 mm. of mercury, and 
 as the temperature was 20, this gives as the range of radioactinium 
 4.17 cm. at 760 mm. and o, or 4 .40 cm., at 15. Two other determina- 
 tions were made, each with separately prepared samples of radioactinium. 
 
 1 Phil. Mag., 24, 653, 1912. 
 
i8 
 
 a-RAY ACTIVITIES 
 
 One gave 4.38 cm., the other 4.43 cm., at 15; the mean of the three 
 results is 4. 40 cm. for 15. This is 0.20 cm. lower than Geiger found 
 for radioactinium and is identical with Geiger's value of actinium X. 
 The periods of radioactinium and actinium X are 18.8 and n .35 days, 
 respectively, and if the range of the former is 4 . 40 cm. that of the latter 
 
 1.2 
 
 I i.o 
 
 . 
 x 
 '> 
 
 1 
 
 300 
 
 400 500 
 
 Pressure in mm. of mercury 
 Fig. 2 
 
 600 
 
 700 
 
 should by Geiger's law be 4.45 cm., which differs from the value found 
 by Geiger by scarcely more than the experimental error of the measure- 
 ments. 
 
 NOTE 3. THE PERIOD OF ACTINIUM X 
 
 Kolowrat 1 gives in his annual tables of radioactive constants the 
 value for the period of actinium X as 10 to n days. Goldewski 2 has 
 previously reported this figure to be 10.2 days. Hahn and Rothen- 
 bach 3 have recently given the value to be 1 1 . 6 =*= o . i days. In view 
 of the uncertainty of this figure, work along this line was undertaken 
 to ascertain its true value. 
 
 1 Le Radium, loc. cit. 
 
 3 Phil. Mag., 10, 35, 1905. 
 
 3 Phys. Zeit., 14, 409, 1913. 
 
NOTES IQ 
 
 Radioactinium free from actinium itself and all subsequent products 
 was prepared as previously described, except that the precipitation of the 
 thorium as oxalate was omitted. The solution was allowed to stand for 
 about two weeks; a portion of this solution was then nearly neutralized 
 with ammonia and the thorium precipitated by means of hydrogen 
 peroxide. The solution which contained the actinium X was filtered and 
 10 drops of 2 per cent thorium nitrate solution were added. ThO 2 was 
 again precipitated and the solution filtered. This treatment was repeated 
 three more times, insuring the complete removal of Rn. A portion of 
 the last filtrate was placed in a 15 c.c. centrifuged tube, i c.c. of o.oi N 
 BaCl 2 added, then a few drops of dilute H 2 SO 4 . The solution was allowed 
 to stand 15 minutes and then centrifuged. The BaSO 4 which carried 
 
 TABLE XI 
 
 Time in Days 
 
 Activity 
 
 Decay Constant 
 
 Time in Days 
 
 Activity 
 
 Decay Constant 
 
 O.OO 
 
 1 .000 
 
 
 O.OO 
 
 I .OOO 
 
 
 3 . 06 
 
 0.830 
 
 0.0610 
 
 3 . 71 . . 
 
 o. 708 
 
 o 0609 
 
 5 . 04 
 
 ~J~ 
 
 0.736 
 
 0.0610 
 
 4.71 
 
 o. 751 
 
 O 0609 
 
 6.77 
 
 f 
 0.659 
 
 0.0616 
 
 6.72 
 
 0.664 
 
 0.0610 
 
 9 . 83 
 
 0.546 
 
 0.0616 
 
 8.84 
 
 0.581 
 
 0.0614 
 
 II 00 
 
 o 480 
 
 o 0613 
 
 72 
 
 O ZZI 
 
 o 0613 
 
 12 72 
 
 o 4^8 
 
 o 0614 
 
 12 8l 
 
 O 4^7 
 
 o 0611 
 
 I s ; .02 . . 
 
 0.380 
 
 o 0610 
 
 i 7 . oo ... . 
 
 O 3^7 
 
 o 0607 
 
 19.08 
 
 0.318 
 
 0.0608 
 
 
 
 
 Mean 
 
 
 o 0612 
 
 Mean 
 
 
 o 0610 
 
 
 
 
 
 
 
 down the actinium X was then washed and made into films as previously 
 described in making the Ra'BaSO 4 films. Two films were prepared in 
 this manner. Each was allowed to stand for two days before the series 
 of measurements was begun. The measurements were made in the 
 a-ray electroscope used in the previous work, the active films being 
 placed 7 cm. below the charged electrode. All activities were measured 
 in comparison with a standard film of uranium oxide, and corrections 
 were made in every case for the natural leak. A small correction was 
 applied for the presence of thorium X, introduced by the thorium 
 nitrate solution. This correction was obtained by running a blank 
 experiment, and in every case it was less than o . 3 per cent of the total 
 activity. 
 
 Table XI gives the values obtained, the activities given being cor- 
 rected for all known factors. 
 
20 a-RAY ACTIVITIES 
 
 The mean of the values for the decayed constants is therefore 
 0.0611 day" 1 , corresponding to a period of 11.35 days. This value 
 is in close agreement with that of Hahn and Rothenback and disproves 
 that given by Godlewski. 
 
 In conclusion the author wishes to express his most sincere thanks 
 to Professor Herbert N. McCoy, whose interest, co-operation, and 
 encouragement have made the completion of this work possible. 
 
Syracuse N Y. 
 PAT. JAN. 21, 1908 
 
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 UNIVERSITY OF CALIFORNIA LIBRARY