IONIZATION PRODUCED BY RADON I N SPHERICAL VESSELS BY GEORGE GLOCKLER AND G. B. HEISIG
Introduction The usual methods of calculating the ionization produced by the alphaparticles from Rn, RaA, and RaC in spherical vessels' assume the validity of Some evidence was obtained in Geiger's two-third power law (I = krz connection with other calculations made by the authors that the Geiger Law does not hold rigidly when the usual ranges of the alpha-particles are used. Since the publication of the above paper some question as to the validity of the law was also raised in the report of the International Radium Standards Committee.* I n the present paper a study is made of the assumption that Geiger's Law is applicable in the calculation of the ionization produced by the alphaparticles from Rn, RaA, and RaC which are used to cause the chemical effects studied by Lind,3 co-workers and others. The following terms are used in this paper: I T = Total ionization produced by an alpha-particle in its path. = Proportionality factor in Geiger two-thirds power law for Rn a t k '02 = 6.478 X 104 k' = Proportionalityfactorfor RaA = 6.417 X 1 0 4 ii ii " RaC = 6.253 X IO? k" r = Range of an alpha particle from Rn - ii 11 ii ii 'I for RaA r' ii li li for RaC rn = 3.45 cm = concordant range for alpha-particles from Rn a t oo ro and 76 cm. = Path traversed by an alpha particle P 1, = Ionization cm-1 a t the point p = r/R P I1 = Ionization from an alpha particle from Rn '' for alpha particles from RaA gas I* 11 " Ii " ii RaC gas IS 1L I1 ii 'I '' RaA on the wall I4 Li i, " " RaC on the wall 15 F, = Efficiency factor for Rn - ti '' RaA in the gas phase Fz - (i 'I RaC in the gas phase Fa " '' RaA on the wall F4 '' " RaC on the wall F, ").
11
'6
(1
I1
Glockler and Heisig: J. Phys. Chem., 35, 2478-2491 (1931) where other references will be found. 2 Rev. Mod. Phys., 3, 431 (1931); J. Am. Chem. SOC.,53, 2441 (1931). a "The Chemical Effects of Alpha Particles and Electrons" (1928).
GEORGE GLOCKLER AND G. B. HEISIG
770
A V
a, a N
k'/k = 0.99058; B = k"/k = 0.96527 velocity of an alpha particle constant in v3 = a,r r'/r = 1.16j; b = rs/r = 1.783 Number of alpha particles := E,(I-edt) X
3.70 2.097
x x
IO"
=
E,(I-e-Xt) X 1.764 X 1ot6
IO-6
R
Radius of the vessel Stopping power of a gas P Pressure of the gas Temperature in degrees C t Specific ionization of a gas g Efficiency factor based on decomposition of 70% of RaA and 9370 F' of RaC on the wall. I. T h e Geiger two-third power law. This important relation connects the ionization produced in the part of the path traversed by an alpha-particle and its range. The law is: IT = krZ5- k(r-p)" (1) S
If it is desired to calculate the ionization cm-1 a t a given distance from the origin of the alpha-particle equation (I) may be written:
IT=
dI - = dP
213
kr% r(I-p/r)H
Equation ( 2 ) permits the calculation of values which enable a theoretical ionization curve for alpha particles to be constructed similar to those obtained experimentally. The first question which arises has to do with the definition of the range of a single alpha-particle and with the average range of a group of such particles. 11. T h e range of a single alpha particle. I. Curie' has attempted to determine the ionization curve of a single alpha particle from the Bragg-curve obtained from a canalized beam. She states2 that the ionization curve of a single alpha-particle differs very little from the curve of Bragg. G. H. Briggs? calculated the "mean" range for a "group" of alpha-particles from the data of Curie for a single one and found that the mean range a t IS'C and 760 mm. in air is 6.90 cm. and the extrapolated range under the same conditions was 6.96 cm. I. Curie and Mercier' determined the mean range by the Wilson cloud method to be 6.92 cm. at ISOC and 760 mm. air uncorrected for pressure of water vapor. Geiger5determined the ranges of the alpha particles from many radioactive bodies for a canalized beam of such particles. These values for the Ann. Phys., (Io) 3, 299-401 (1925).
* LOC.cit. page 400.
P ~ o cRoy. . SOC.,114A, 341-354 (1927). 4
J. Phys., 7,289 (1926).
Z.Physik, 8, 45-57 (1922).
IONIZATION PRODUCED BY RADON I N SPHERICAL VESSELS
77=
ranges are determined fur a group of alpha-particles and give therefore the range for an average one. It is sLer- then that the range of a single alphaparticle and that of a group of them differs very little and no distinction is made in the following considerations between these two ranges since their numerical values are not greatly different. The various definitions of “range” will now be considered. 111. The eztrapolated range. The ionization curve for an alpha-particle of RaC has, towards the end of the range, a small tail which is due to straggling and a few particles of especially long ranges. This section of the ionization curve depends upon the sensitivity of the detecting apparatus and the intensity of the source and cannot be determined accurately. However, the descending portion of the curve after the maximum of ionization is a straight line and when extended cuts the abscissa a t a well defined point. This point determines the “extrapolated range.”’ Geiger states that this extrapolated range is a definitely reproducible quantity and attempted to state the two-third power law using this extrapolated range. However he found2 that the use of this range did not give a theoretical curve concordant with the experimental one. He used an average range and found that the two-third power law and experiment checked fairly well in the case of RaC. This average range is very nearly equal to the distance from the source to the point a t which maximum ionization occurs. Grieger did not study the detailed ionization curves for the alpha-particles from RaA and Rn. When it is attempted to apply the two-third power law (eq.2) to the case of RaA and Rn using the extrapolated ranges, the theoretical curves do not fit the experimental ones of Henderson3 as can be seen from Fig. I which is based on the data in Tables I and 11.
TABLE 1 Ionization per cm. path for RaC*. Experimental Values from Henderson (loc. cit.) IT = 2 . 2 0 X 1 0 5 Ion pairs Range 20’ 76 cm. air (cm.)
Ion pairs per cm.
3
2.09
I .07
2.25 2.48 2.77 3.23 4.01 4.83 5.89
2.15
3.22 4.29 5.37 5 90 6.33
x 10-4
* Note:
Range 20’ 76 cm.
Ion pairs per cm. X IO-^
6.44 6.55 6.59 6.6j 6.76 6.87 6.98 7.08 7.19
6.29 6.68 6.70 6.54 6.01 4.51 2.15 0.29 0.00
The experimental curves for ionization per cm. path for RaA and R n can be Clbtained from the curve for RaC by shifting the RaC curve a distance 2.29 cm. ( = 7.032 4 084 cm.) and 2.90 cm. ( = 7.072 - 4.193 cm.) to the left, respectively, for RaA and Rn. 1
Marsden and Perkins: Phil. Mag., 27, 690 (1914).
2
R o c . Roy. Soc., 82 A, 486 (1909); 83,505 (1910).
Phil. Mag., 42, 538-551 (1921).
GEORGE GLOCHLER AND G. B. HEISIG
772
6
T
2
2
4 RANGE FIG.I
6 c M . j
Geiger Law of Ionization per cm. ath as a function of the extra(0)experimental values; ( ). polated ranges for Rn, RaA and RaC! calculated values
TABLEI1 Ionization per cm. X IO-^ for alpha-particles from RaC, RaA and Rn, calculated by means of equation ( 2 ) on the basis of 2 . 2 x 104 ions pairs for RaC P
Extrapolated Ranges Fig. I RaC RaA Rn
Empirical Ranges Fig. 2 RaC RaA Rn
0.00
2.07
2.36
2.46
2.22
2.53
1.00
2.18 2.31 2.48 -
2.55
2.70
2.34
2.75
2.82
3.06 3.75 4.49
2.51
3.08 3.66
2.00
3 .oo 3.50 4.00 5.00
6.00 6.50 6.75
6.83 7.00
2.73
3.11 3.86 4.74 5.69 6.19 a .87
3.27
-
4.28
2.71
3.02
3.55 4.93 8.97
-
5.32
2.65 2.92 3.36 4.31 5.64
IONIZATION PRODUCED BY RADON I N SPHERICAL VESSELS
773
TABLE I1 (Continued) Concordant Ranges
Fia. 3 RaA same k
0.00
2.22
2.55
.oo 2 .oo 3.00 3.50 4.00
2.34
2.73 3.14 3.79
3.24 3.91
6.12
6.31
I
5.00
6.00 6.50 6.75 6.83 7.00 ’
Rn
RaC
D
2.51 2.71
-
3.02 3.55 4.93 8.97
-
diff. k
same k
2.63 2.87
2.70 3 .oo 3.50 4.70 7.13
-
diff. k 2 ’ 79 3.10 3.62 4.86 7.37
The extrapolated ranges a t 2ooC and 7 6 0 cm. air are 7.09 cm., 4.80 cm. and 4.19 cm. for RaC, RaA and Rn respectively. The total ionizations IT are: 2.2 X IO^, 1.70 X 1 0 5 and 1.55 x I O >ion pairs for RaC, RaA and Rn respectively. The values are taken from the report of the International Radium Standards Commission. In order to obtain concordant experimental and theoretical curves for the ionization as a function of the range, it is necessary to use an empirical range as was suggested by Geiger. IV. The empirical range. When the experimental ionization curves for RaC obtained by Henderson are used for a comparison with the Geiger law, it is found that an empirical range of 6.6 cm. (76 cm. air, 20’) will give a good fit between the experimental ionization curve and the curve obtained by the use of the theoretical two-thirds power law. This range is called the “empirical” range. Since this empirical range is made to fit the Geiger law, the constant k involved in the expression: IT = k” x rr’H (3 ) can be easily calculated. Since the International Radium Standards Commission recommends the value of 2.2 X 1 0 5 = IT obtained by FonovitsSmerekerl this value will be used in these calculations. Then from Eq.(3) : k“ = 6.253 X 104 The corresponding empirical ranges for RaA and Rn are defined as follows: The constant k is supposed to apply in all three cases and the total ionizations for RaA and R n are taken from the report cited above. Then For RaA: 1.70 X IO> = 6.253 x 104 x r’% For Rn: 1.55 X IO> = ” x r% Wien. Ber., 131, 355 (1922).
GEORGE GLOCKLER AND G. B. HEISIG
774
and the empirical ranges are found to have the values
r'
= 4.47
cm and r = 3.90 cm.
(zoo and 76
cm. air)
When, however, these ranges and values of the total ionizations are used to obtain the detailed ionization curves for Rn and RaA, it is again found that they do not produce a set of curves that fit the experimental ones satisfactorily as is seen from Fig. z which is obtained by the use of Tables I and 11.
1' 4
I,,X
i(r4
2
2
4 R A N G E CM.+ FIG.2
6
Geiger Law of Ionization er cm. path as a function of the empirical ranges for Rn, RaA and RaC? (01 experimental values; ( 0 ) calculated values
The difficulty is due to the attempt to produce a set of ionization curves which will give the proper total areas at ranges which are incompatible with the equations. V. The concordant range. A satisfactory set of ranges for RaC, RaA, and Rn may be defined by making the difference between them and the extrapolated ranges a constant. This procedure seems to be justified because the ionization curves for the three sets of alpha particles are treated in a like manner towards the end of the respective ranges.
775
IONIZATION PRODUCED BY RADON I N SPHERICAL VESSELS
TABLE I11 RaC
Extrapolated Range, zoo, 76 cm. air Constant difference:
7.092 cm. .492
Concordant range, 20°, 76 cm. air
6.60
Rn
RaA
4.193 cm.
4.804 cm.
11
492
cm.
11
.492
I1
3.701 cm.
4.312 cm
6
T 10096
4
iPx1cr4
2
)% 2
6
4
RANGE
CM.-
FIG.3 Geiger Law of Ionization per crn. path as a function of the concordant ranges for Rn, RaA and RaC. (0)experimental values;).( calculated values. S = the fractional decrease in scintillations near the end of the range for RaC
These ranges are again based on 6.6 cm. for RaC and are called “concordant” ranges. They give ionization curves which fit the experimental curves, as is seen in Fig. 3. The data are obtained from Tables I and 11. However, the total ionizations for RaA and Rn do not now agree with the accepted values obtained by the use of the extrapolated ranges, if the same constant k is used in the three cases:
k X r’’% = 6.253 X ’’ k x r f %= kXr% = 7,
104 X
6.60’~ = 2.2 X X 4.312” = 1.66 X X 3.701% = 1.50 X
105
105 105
(instead of 1.7 X (instead of 1 . 5 5 X
10~) 105)
GEORGE GLOCKLER AND G. B . HEISIG
776
VI. Empirical constants. Agreement in the total ionizations and closefitting detailed ionization curves can be obtained by the use of an empirical set of curves of the type of the Geiger N power law if the constant of the equation is taken to be different for each set. These empirical constants are obtained by using the total ionizations for RaA and Rn (secured by the use of the extrapolated ranges from RaC) and the concordant ranges. For RaC klrrtf% = 6.253 X 1 0 4 X 6.60% = 2.2 X 1 0 5
(4)
dI 2 2.2 X 1 0 5 OrI, = - = _ . dp 3 6.6 ( I - p/6.60)%
(5)
For RaA: 104 X
k’r‘% = 6.417X
4.312% =
1.70 X 105
(6)
For Rn k rH = 6.478 X
104
d1 2 OrI, = - = - . dp 3
X
3.701’
1.55 X 3.701 (1
=
1.55 X
(8)
105
105
(9)
- P/3.701)%
There is then possible a choice in method: Either the same value for k( = 6.253 X 104) may be used for the calculation, leading to total ionization values of 2.2 X 105, 1.66 X 105, 1.50 X 105for RaC, RaA and Rn respectively or different values of k may be used, namely, k” = 6.253 X
k’ = 6.417X
104,
104, and
k
=
6.478 X
104
for RaC, RaA and Rn respectively. These latter values give the total ionization 2.2 X 105, 1.70X 1 0 5 and 1 . 5 5 X 105respectively for RaC, RaA, and Rn, which values agree with the total ionization obtained graphically by the use of the extrapolated ranges and the experimental value for RaC. With either method close fitting detailed ionization curves are obtained. The graphs of Fig. 3 represent the situation in either case on the small scale used in preparing these curves. The reason that with the same value of k and the concordant ranges the total ionizations for RaA and Rn do not agree with the values obtained graphically from the extrapolated ranges and the experimental value of ionization for RaC, must lie in the fact that the concordant ranges are defined in an empirical manner. Since, however, the present considerations aim to calculate the ionization produced by Rn it seems logical to accept the values for the total ionizations for RaA and Rn as obtained from the extrapolated ranges from RaC. I n other words it appears proper to use different k values. This situation does not agree with the usual view that the alpha particle from different sources is the same but for its velocity of emission from the radioactive body. On this basis it would be expected that the quantity k is a constant for different alpha particles. However as far as is known experimentally the law v3 = aor is not
IONIZATION PRODUCED BY RADON IN SPHERICAL VESSELS
777
completely verified in as much as the constant a. varies for alpha particles from RaC, ThC and Po.' On this basis it does not seem impossible that k may also vary for different alpha particles. Ionization for the three sets of alpha particles for Rn shall then be calculated with the values of k as follows: RaC: k" = 6.253 X 104 RaA: k' = 6.417 X 1 0 4 Rn: k = 6.478 X 104 and the total Ionizations RaC: IT = 2.20 X 1 0 5 RaA: = 1.70 X 1 0 5 Rn: = 1.55 X 1 0 5 I t is quite necessary that the many definitions of range be kept clearly in mind and for this purpose Table IV gives the values for these ranges. For the purpose of calculating the ionization in chemical experiments with vessels of average size ( . 5 - 5 cm. radius) it is important that the proper range be used in these calculations. Evidently the range chosen should be the one that will give results closest to the theoretical Geiger ?.5 power law. This range is the concordant range defined above.
TABLE IV Ranges of Alpha Particles from Rn, RaA and RaC at zoo and 76 cm. air Extrapolated Ranges Empirical Ranges Concordant Ranges
Rn RaA RaC
4.19
3.90
4.80
4.47
7.09
6.60
3.70 4.3 1 6.60
While the concordant ranges will give the best fit to the ionization curves and for this reason their use is justified, there is also experimental justification for their use (curve S in Fig. 3). Geiger? has shown that the scintillations from RaC at the end of the range decrease in number. This shows that the alpha-particles straggle, i.e. that they have somewhat different ranges. In the case of RaC, I j"C, 76 cm. at about 6 cm. from the source, the number of scintillations begins to decrease. From these observations, it, is possible to deduce an average range as is shown in Fig. 3 of 6.76 cm. at zo°C, 76 cm. in air. The concordant range chosen to give the best fit for the theoretical and experimental ionization curves of alpha particles from RaC was 6.6 cm. If the Geiger equations 4-9 containing different constants for RaC, RaA and Rn are not used, it becomes necessary to establish completely empirical relations which would be more complicated. Such a procedure does not seem necessary or desirable for the present purpose.
' Report Int. Radium Standards Commission: loc. cit. page 431. * Proc. Roy.
Soc., 83 A, 51 I (1910).
GEORGE GLOCKLER AND G. B. H E I S I G
778
VII. Eficiency Factors. The use of the concordant ranges in the expression of the Geiger Law and the change from 2.37 x 105ion pairs for RaC to the value 2 . 2 X IOI' cause a small change in the efficiency factors. These factors have been recalculated for the case that 70% RaA and 93% RaC are decomposed on the wall and are given in Table V. The equations of Mundl have been used. The change from large to small spheres occurs at p = 2 , for Rn; at p = 1.72 for RaA and at p = 1 . 1 2 for RaC. The total ionization is given by IT 11 -k 1 2 f 13 f 1 4 f 1 s where I1 = N kr" F1 for decomposition in the gas phase.2 The ionization produced by RaA and RaC in the gas phase is respectively, I2 = .3 X N X k X r N X A X a N X Fg and Is = . o j X N X k X rN X B X b" X FB The factors Fz and Fa are obtained from the work of Mund. The ionization produced by RaA and RaC on the wall is obtained from I4 = .7 x N X k X r>6X A X a x X F4 I5 = .93 X N X k X r" X B X b% X Fs where the factor Fcand Fs are gott'en from Mund's equation (3). The concordant ranges were used (Table 111).
TABLE V Efficiency Factor l o be used in calculating Ionization produced by Alpha Particles from Radon in Spherical vessels P
F'
P
F'
0.0 .I .2
2,472 2.353 2.235
.3 .4
2.117 2.000
.5
I . 884 1.771 1.657 1 ' 546 1.437 1,331 I . 232 I . 140 1,053
1.4 1.5 1.6 1.7 1.8 1.9
0.974 ,901 ,836 ,777 '723 .676 ,636 '571 ,517 '494 ,473 '436 ' 404 .342
.6 '7 .8 .9 L O
1.1 1.2
1.3
2.0 2.2
2.4 2.5 2.6 2.8 3.0 3.5
P
4.0 5.0 10.0
15.0
20.0
F'
0.297 '235 ,116 ,077 .oj j
Table T' gives sufficient information so that a large scale plot of F' as a function of p can be made from which any corresponding set (F'p) can be 2
J. Phys Chern., 30, 890-894 (1926). M u n d : loc. ut., eq. ( I ) .
IONIZATION PRODUCED BY RADON I N SPHERICAL VESSEL8
779
obtained. Interpolation of the values given in Table V is not satisfactory because the relation between F’ and p approaches in shape a hyperbola. VIII. Calculation of Zonization. The calculation of ionization is to be made as follows: Consider a vessel of 2.232 cm. radius filled with acetylene a t 599 mm. at a temperature of z5OC. The concordant range of the alpha particles from Rn is calculated as follows:
where ro = 3.45 cm = concordant range of Rn a t s = stopping power = 1 . 1 2 for CsHt.
oo, 76
cm. air.
- 1.913 Then r = 4.27 cm. and p = __ 4’27 2.232
From a plot of F’ as a function of p it is found that the desired value of F’ is .671 which yields for the total ionization of N alpha particles: I T , C z H 2 = N X g X kr2I3 X F’ = N X 1.26 X I . j j X 105 X .671 = 1,3105 x N Summary: The assumption that the Geiger Law for ionization by the alpha particles from R n holds when using the extrapolated ranges is shown to be inadequate. I t is necessary to use empirically defined ranges as has been done by Geiger for RaC. While it is then possible to fit a N power law to t’he ionization curve for an alpha partlcle from RaC, the two other curves for RaA and Rn cannot be made to coincide with the known experimental curves. In order to obtain close-fitting two-third power curves for all three sets of alpha particles it is necessary to define empirically a set of three ranges called the concordant ranges. If now a fixed value of k ( = 6.2 j 3 X IO( = the constant in Geiger’s 9;power law) is used for all three sets of alpha particles, then the total ionizations for RaC, RaA and Rn are: 2 . 2 X IO^, 1.66 X IO^, and I . j o X 105which values do not agree with the total ionizations obtained from the extrapolated ranges which are: 2 . 2 X 105, I . j o X 105and.1. j j X IO^. These latter values can be used if different values of k are taken: 6.253 X IO^, 6.417 X io4 and 6.478 X IO(, respectively for RaC, R a h and Rn. With these changes it is possible to obtain three curves for RaC, RaA and Rn which fit the experimental ones: The efficiency factor for the calculation of ionization for the case that 70% RaA and 93YG RaC decompose on the wall have been calculated. The concordant ranges, and the proper constants giving the total ionizations as obtained graphically from the ionization curve for RaC and the experimentally determined extrapolated ranges have been used. The other method of calculation would demand the use of the same constant (k = 6.2 j 3 X IO?) and values for the total ionization for RaA and Rn which differ from the above. This last method would give efficiency factors differing from the adopted set by about I’?& University of Minnesota, Minneapolis, M i n n . October 1931.
