Decay and Growth Tables for the Naturally Occurring Radioactive Series H. W. KIRBY M o u n d Laboratory, Monsanto Chemical Co., Miamisburg, Ohio
T
HE tables which follow are intended primarily for use by the analytical chemist. While in no sense complete, they have been compiled in an effort t o reduce or eliminate much of the tedious and duplirative labor involved in the analysis of radioactive materials. The tables are divided into three sections devoted to the three naturallv occurring radioactive series. The nuclear data are those compiled by the Sational Bureau of Standards ( 2 ) . The decay of each radiosotope is given in one or more appropriate time units except \There the half life of a particular nuclide is either too lone - or too short to be of analvtical importance. The growth of families is given in relative disintegration rates, which are readily determined by standard counting methods, rather than in 'numbers of atoms. The criterion throughout has been utility to the analyst. Thus, where the growth of a family is either too slow to be useful, or is effectively complete in a f e n hours, it has not been computed. hlthough the uncertainty of the half lives and the precision of
Table 11. Thorium Series (4n) I
Min. 0 1
2 3 4
5 A 7 8 9 10 20 30 40 50 Hours 1 2 3 4
5 A
present-day counting techniques do not warrant more than three significant figures in most cases, values have been computed to four or five significant figures to permit reasonably accurate interpolation. The equations used for calculating growth and decay were adapted from those originally proposed by Rutherford (3)and Bateman ( 1 ) .
7 8 9 10 11 12 13 14 15
SYMBOLS
18
-1-0
T,, T 2 , T,,
(Decay in minutes and hours)
1 ime, .
16 17 I9 20 21 22 23
= number of atoms of the parent (first member) of a family at an arbitrary time, 1 = 0 = half life of the first, second, nth member of a
family
24
Thz28
Ac228
1
1 .oooo
.oooo
0,9981 0.9962 0.9943 0,9925 0.9906 0.9888 0.9869 0.9851 0.9831 0.9814 0.9630 0.9451 0.9274 0.9101
Rn220 1 .oooo 0,9999 0.4662 0.9997 0.2174 0.9996 0.1013 0,9995 0.0472 0.9993 0.0220 0.9992 0.0103 0.9991 0,0048 0.9989 0,0022 0.9988 0,0010 0.9987 0,0005 0.0474 0,0000 0 . 9960 0.9947 Ra224
1 .oooo
0,9934
0.8931 0,7976 0,7123 0,6362 0.5681 0.5074 0.4532 0.4047 0.3614 0.3228 0,2883 0,2575 0,2299 0.2058 0.1834 0,1638 0.1463
0.1306 0.1167 0.1042 0.0931
0.0831
0.0752 0.0603
0,9999 0.9999 0,9999 0.9998 0.9998 0.9998 0.9997 0.9997 0,9996 0,9996 0.9995 0.9995 0.9995 0.9994 0.9994 0.9993 0.9993 0.9993 0.9992 0.9992 0 9991 0.9991 0.9990 0.9990
0 9921
0.9843 0.9765 0.9688 0.9611 0.9535 0.9460 0.9385 0.9311 0.9237 0.91B4 0.9092
0.90'20 0.8948 0.8878 0.8807 0.8738 0 8(i69 0 86300 0.8533 0.8465
0.8398 0.8332 0.82flO
PbZlz 1.0000
biz12 1 .oooo
0,9989 0.9978 0.9967 0,9956 0.9946 0.9935 0.9924 0.9913 0.9902 0,9892 0.9784 0.9678 0.9573 0.9470
0,9888 0,9774 0.9662 0.9552 0.9443 0.9336 0,9229 0 9124 0.9020 0.8917 0.7932 0.7091 0.6324 0,5639
0.9367 0.8774 0.8219 0.7698 0.7211 0.6755 0.6327 0.5927 0.5552 0.5200 0.4871 0.4663 0.4274 0.4003 0.3750 0.3512 0.3290 0.3082 0.2887 0.2704 0.2833 0.2373 0,2222 0,2082
0.5024 0.2529 0.1272 0.0639 0.0322 0.0162 0.0081 0.0041 0.0021 0.0010
TlZOS 1 . 0000 0.7996 0,0394 0.5113 0,4089 0.3269 0.2614 0.2090 0.1672 0.1337 0.1069 0.0114 0.0012 0.0001 0.0000
0,0005
0.0003 0.0001 0.0001 0.0000
Table 1. Thorium Series (4n) Synonym
Mode of Decay
Energies in Rlev.
A,, Half Life
x
...
a
4.0
1.39
1IsThr
8-
0.002
6.7 T
1IsThz
8-
1 6
613H
HdTh
Cl
TIiX
a
Tn
a
Th.4
[00 ..80604180Y-1 0D-~
93% 5 . 7 a%5 4
3.64 D
1904 D - I [00 0079 H-1
...
a
TliR
P-
6.3
54.59
6 8 (1)
0.1586
AI-' 0.0127 S-I [0.7631 2 6 3 . 2 11 [4,3870S-1
7.8
0.0003S
2300 s - 1
88'3 0 3
[1 2 ' 3 0 6
a
8 8
3 04 X 10-7s
TIiC"
P-
1 8
3 I11
ThD
81
GROWTH AND DECAY EQUATIONS
...
Relative activity of a single radioactive species:
1 2694 D - l 0 0654H-l
10 6 TI
ThC'
...
(disintegration rate) of the parent of a family a t t = 0 S,,h = activities of the first and nth members of a family at any time = alpha activity of the parent at t = 0 = total alpha activity of thc chain a t any time = total beta activity of the chain nt any time
-I
TIiC
Stable
010 Oif
1 SOY
[ -
1*,)
[
2 7138D-1 0 1131 H -
(lecav constant of the nth memher of a family (A,< = 0.69315/
= activity
0.1035T-I 0 000283 D - '
r
=
m \
5.oXlo-"Y-'
72q5.4
128% 5 . 3
[(0.64% 8 3
101"Y
Decay Constnnts
2 3 X 106S-1
r
13 416H-1 0 2236 31-1
...
Activity of the first decay product relative to the initial activity of a parent which was pure a t t = 0:
ANALYTICAL CHEMISTRY
1064
Time. Days
Table 111. Thorium Series (4n)
Table IV. Thorium Series (4n)
(Decay in days)
(Growth of decay products from initially pure pareut.' Parent, thorium-228)
Time, Days RaZ"
Th2"
Raza
AcZB
Th'n
Razz'
PbZl'
2 3 4 5
1,0000 0.9997 0.9994 0.9992 0.9989 0,9986
1.0000 0,0663 0,0044 0.0003 0,0000
1.0000 0,9990 0.9980 0.9970 0.9960 0.9950
1 ,0000 0.8266 0.6833 0,5648 0.4669 0 3859
1,0000 0.2082 0.0433 0,0090 0.0019 0.0004
50 51 52 53 54 55
6 7 8 9 10
0 9983 0.9980 0 9977 0.9975 0.9972
0.9940 0.9930 0.9920 0.9910 0.9901
0.3190 0.2637 0.2180 0.1802 0.1489
0.0001 0.0000
56 0.9843 0.9456 57 0.9840 0.9446 58 0.9837 0.9437 59 0.9834 0.9427 60 0.9831 0.9418
11 12 13 14 15
0.9969 0.9966 0.9963 0.9960 0.9958
0.9891 0,9881 0.9871 0,9861 0.9851
0.1231 0.1018 0.0841 0.0695 0.0575
61 62 63 64 65
0.9829 0.9826 0.9823 0.9820 0.9817
0.9409 0.9399 0.9390 0.9380 0.9371
16 17 18 19 20
0.9955 0.9952 0.9949 0.9946 0.9943
0.9841 0.9832 0.9822 0.9812 0.9802
0.0475 0.0393 0.0325 0.0268 0,0222
66 67 68 69 70
0.9815 0.9812 0.9809 0.9806 0.9804
0.9362 0.9352 0.9343 0.9334 0.9324
0
1
0.9859 0.9856 0.9854 0.9851 0.9848 0.9845
0.9513 0.9503 0.9494 0.9484 0.9475 0.9465
0.9315 0.9306 0.9296 0.9287 0.9278
??
(Thn28)
=
( ~ ~ ~ 2 4 = ) 1,00528 (,--it NoAi (RnZZO)
.VoAi
(PbP12)
e
\I
2v6k6 (Bi21Z) -.VOX,
-
e-M)
1.005?5
+
,--2i
0.00017 ,--ha'
E: h'di =
=
-
1.00592 ,-'It
NOXI
(T1208)
"1 =
.vlA7
-= A'oAI
5.02182
71 0.9801 72 0.9798 73 0.9795 74 0.9792 75 0.9790
26 27 28 29 30
0.9927 0.9924 0.9921 0.9918 0.9915
0.9743 0.9734 0.9724 0.9714 0.9705
0,0071 0.0058 0.0048 0.0040 0.0033
76 0.9787 0.9269 77 0.9784 0.9259 78 0.9781 0.9250 79 0.9779 0.9241 80 0.9776 0.9232
31 32 33 34 35
0.9913 0.9910 0.9907 0.9904 0.9901
0.9695 0.9685 0.9676 0.9666 0.9656
0.0027 0.0023 0.0019 0.0015 0.0013
81 82 83 84 85
0.9773 0.9770 0.9767 0.9765 0.9762
0.9222 0.9213 0.9204 0.9195 0.9186
36 37 38 39 40
0.9898 0.9896 0.9893 0.9890 0,9887
0.9647 0.9637 0.9627 0.9618 0.9608
0.0011 0.0009 0,0007 0.0006 0.0005
86 87 88 89 90
0.9759 0.9756 0.9754 0.9751 0 9748
0.9176 0.9167 0.9158 0.9149 0 9140
41 42 43 44 45
0.9884 0,9882 0.9879 0.9876 0.9873
0.9598 0.9589 0,9579 0.9570 0.9560
0.0004 0.0003 0.0003 0.0002 0.0002
91 92 93 94 95
0.9745 0.9743 0.9740 0.9737 0.9734
0.9131 0.9121 0.9112 0.9103 0.9094
2 3 4 5
46 47 48 49 50
0.9870 0.9868 0.9865 0.9862 0.9859
0.9551 0.9541 0.9532 0.9522 0.9513
0.0002 0.0001 0.0001 0.0001 0.0001
96 97 98 99 100
0.9732 0.9729 0.9726 0 9723 0 9721
0.9085 0.9076 0.9067 0.9058 0.9049
49
1.00598 e - A l t
-
(po211)A-7nA;a
0.0183 0.0152 0.0125 0.0104 0.0086
Fraction Remaining After a Given Time. EXAMPLE 1. What fraction of radium-223 remains after 15 days?
-
-k
1.14424
0.13833 e--hat
0.9792 0.9783 0.9773 0.9763 0.9753
USE OF THE TABLES
1.00528 g - A l t
0x1
0 9941 0.9938 0.9935 0.9932 0,9929
Activity of the lath member of the decay chain relative to the initial activity of a parent which was pure a t t = 0:
=
(pozls) E 4 Nohi
21 22 23 24 25
Activity of the second decay product relative to the initial activity of a parent which was pure a t t = 0:
(--Xif
NOXI
-
+
1.1575Y e - A z t 0.15287
e-Aet
-
0,00125
' E a Nohi
1.00598
- 1.15827 e - A 2 t
-t
0.163W ,-'st e--Xlt
a0
La = 2.67886 ,--If NoXi
-
4.17377 e - A 2 L t 0.00034 e - A a t 0.51287
-
- 0 00132 ,--hat
+
3,06999 e - A z L f 0,39330
- 0.00125 e F A 5 f 0.00215
Valid 1 hour after purification, assuming 100% retention of radon-220. b Assumes 100% counting yield of all betas.
0
Table V.
Thorium Series (4n)
(Growth of decay products from initially pure parent. Parent, thorium-228) Time, Day0 0 1
6
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 3% 40 41 42 43 44 45 46 47 48 49 50
Razz4 0.0000 0.1733 0.3165 0,4345 0.5319 0.6123 0.6786 0.7332 0.7781 0.8151 0.8456 0,8705 0.8910 0.9078 0.9214 0.9325 0.9416 0.9488 0.9547 0.9594 0.9631 0,9660 0.9682 0.9698 0.9710 0.9719 0.9724 0.9726 0.9727 0.9725 0.9723 0.9719 0.9714 0.9708 0.9701 0.9694 0.9687 0.9679 0.9671 0.9663 0.9654 0.9645 0.9636 0.9627 0.9618 0.9609 0.9899 0.9590 0.9581 0.9571 0.9562
Pb212
at/NoAl
,t?t/.Y,Al
0.0000 0.0878 0.2280 0.3578 0.4679 0.5593 0.6349 0.6972 0.7485 0.1907 0,8256 0.8540 0.8775 0.8967 0.9124 0.9252 0.9356 0.9440 0.9508 0.9563 0.9606 0.9640 0.9667 0.9687 0.9702 0.9713 0.9720 0.9724 0.9726 0.9726 0.9724 0.9721 0.9717 0.9711 0.9705 0.9699 0.9692 0.9684 0.9676 0.9668 0.9659 0.9651 0.9642 0.9633 0.9624 0.9615 0.9605 0.9596 0.9587 0.9577 0.9568
1 0000 1.5986 2.1666 2.6508 3.0535 3.3861 3.6603 3.8861 4.0718 4.2245 4.3503 4.4533 4.5372 4.6060 4.6619 4,7072 4.7437 4.7729 4.7968 4.8156 4.829Y 4.8410 4.8493 4.8554 4.8596 4.8622 4,8035 4,8637 4.8631 4.8617 4.8597 4.8572 4.8543 4.8511 4.8476: 4.8439 4.8399 4.8359 4.8317 4.8274 4.8230 4.8185 4.8140 4.8094 4.8048 4.8002 4.7955 4.7908 4.7861 4.7814 4.7767
0.0000 0.2204 0,5929 0.9404 1.2356 1 ,4809 1.6835 1 ,8506 1 ,9882 2.1015 2.1950 2.2717 2.3345 2.3861 2.4283 2.4626 2,4905 2.5130 2.5314 2.5462 2.5577 2.5669 2.5741 2.5795 2.5836 2.5865 2.5884 2.5896 2.5901 2,5901 2.5896 2.5888 2.5876 2.5862 2.5846 2.5829 2.5810 2.5789 2.5768 2,5746 2.5724 2.5701 2.5677 2.5653 2.5629 2.5605 2.5580 2.5556 2.5530 2.5506 2,5481
.
V O L U M E 26, N O . 6, J U N E 1 9 5 4
1065 -
Table VI.
EXAMPLE 3. What fraction of thorium-228 will remain after 1 year? Since the tables do not give decay values beyond 100 days, it is necessary either to make use of the decay constant given in Table I or to use Equation 5, thus:
Thorium Series (4n)
(Growth of decay products from initially pure parent.a Parent, radium- 224) ( R a m ) 2!3. = e-Xd &VOX,
(~~220)
=
1.00017 ( e - ~ l t
(P021')
=
1.00017 e-X1t
'* .vox1
Nohi
e4 1.13823 KOA1
-
1.00308 e - - X 2 t
+ 0.00291 e--XBt
+ 0.00143 e - x x z t - 1.13966
=
(Pb212)
- ,--~zt)
( ~ i z i 2 )'$3 = 1.15151 e - ~ i l A OX1
\I
s, Nflv,xi
0x1
=
+ 0.10798
+ 0,00001 e - - x 2 L -
1 .I8219
1.26564 2.00327
=
4.15185 e - & l t
-
-
3 05387
+ 0.00143 e - X z t
+- 0.11381 e - X s t - 0.00037 ~
+ 0.00291 e - X 3 t
1.25947 e - - d t
-
3.24033 e - - X 4 t
-
-
+ 0.10798 +
e-Xbt
- 0.0003i
0.18540
0 Valid 1 hour after purification, assuming 100% retention of radon-220 and its decay products. b Assumes 100% counting yield of all betas.
--~ .~
0.2721 0.3155 0.3557 0.3928
3 . 085fi 8.1098 3.1315 3.1505
0.6044 0.7262 0.8402 0.9464
18 21 24
0.4271 0.4588 0.4880 0.5149 0.5832 0.6355 0.6749 0.7036
3.1667 3.1803 3.1914 3.2002 3.2137 3.2111 3.1956 3.1698
1 ,0449 1.1361 1,2203 1.2981 1.4962 1 ,6488 1 ,7644 1 ,8498
30 36 42 48 54 60 66 72
0.7369 0.7472 0.7425 0.7284 0.7082 0.6846 0.6590 0.6326
3.0953 3.0006 2.8944 2,7823 2.6681 2.5543 2.4425 2.3336
1.9514 1 ,9873 1 ,9805 1.9462 1 ,8948 1,8331 1.7657 1 ,6966
78 84 90 96 102 108 114 120
0.6061 0.5798 0.5542 0.5293 0.5053 0.4822 0,4600 0.4388
2.2283 2.1268 2,0294 1 ,9360 1 ,8467 1.7613 1.6797 1.6018
1,6249 1.5549 1,4863 1.4197 1.3554 1.2935 1 ,2341 1,1773
126 132 138 144
0.4185 0.3992 0.3807 0.3630
1 ,5275
1,1229 1 ,0709 1.0213 0.9739
n
10 11 12
15
Fraction remaining after 100 days
=
Fraction remaining after 65 days
= 0.9371 (Table
0.9049 (Table 111)
111)
~
Differential Decay. Mixtures of nuclides are sometimes encountered which cannot conveniently be resolved by chemical methods. Various means have been employed to determine the e ~ amount of each species present, but one of the most generally useful is the technique of differential decay.
Exmpm 4. A mixture is known to contain only radium-223 and radium-224 in equilibrium with their decay products. When counted, the activity of the mixture is found to have decayed to half its original value in 5 days. What fraction of the original activity was due to radium-224 and its decay produrts? Table VIII.
(Growth of decay products from initially pure parent. Parent, radium-224) Time, BIINoXI Hours PbQ12 Ut/.VOXl 0.0000 1 . 0000 0 0,0000 0.0878 2.9936 1 0.0617 0.2096 3.0087 0.1204 2 0.3425 3.0328 0.1748 3 0,4758 3.0594 0.2253 4
7 8
= 0.6943, or,
. - ~ - ~ - ~ _ _ _
~
Table VII. Thorium Series (4n)
5 ti
=
Fraction remaining after 365 days = (0.9049)3(0.9371) = 0.6043
- o.oooo2 ,-M 1.25947
NsXs
(T1108)
Fraction remaining after 1 year
1 ,4565 1.3889 1.3244
Synonym UI
Uranium-Radium Series (4n
Mode of Decay a
Energies, MeV. 4 2
56% 0 . 2
UXl
[44%
uxz [(O. I:%
IT)
0.1
90% 0 6 10% 1 2 (0 4)
[
0.02876 D -1
24.10 D
0.0012 H-1 1 14x1
0.6080 11 - 1
UZ
8-
2.3
6.7H
a
4.8
267,OOOY
0,0000026 Y -1
a
75% 4 . 7 [25% 4 . 6
80,000 Y
0,0000087 Y
1,620 Y
0.000428
Io
93% 4 . 8
... E 111
7% 4 . 6 5.5
a
3.825 D
0 . 1035 €1-1
T-1
0.1812 D -1 0.00755H-1 0,2273 M
0.7
26.811
6.7
c
-1
0.02586 M - 1 1,5518 H-1
2.0s
0 3466 S-1
0.019s
36 5 s - 1
(1)
7.1
U
23% 3 . 2 [77% 1 . 7 5.5
2.1111 H-1
0.000164S
4,227 S - 1
1.8
1.32 M
0.5251 31-1
22Y
0.03151
0.03
ponintials
4.85 D
(5.0)
(5)
5.3 138.4 D
the decay of bismuth-210 for the desired time is the product of its decay in 7 days (0.3677 from Table X ) , in 3 hours (0.9823 from Table IX), in 10 minutes (0.9990 from Table IX), and in 4 minutes (0.9996 from Table 1X)-i.e.,
Stable a
(0.3677) (0.9823) (0,9990) (0.9996) = 0.3607
1.5
B-
Isomer.
...
0.0351911-1
19.7M
7.7
92y0 1.1 8% 1 . 2 eaeb
Decay Constants 1.54 x 10-1OY-1
UII
a
,(a+b)
Half Life 4 . 5 1 X lO9Y
4- 2)
4.23M
...
T-1
0 1429 D-1
[
0,00595 Hi-
0 005008 D -1
[1 8279 Y-1 0.1639 M
...
-1
-1
A N A L Y T I C A L CHEMISTRY
1066 Table IX. Time,
Min. 0
Uranium-Radium Series (4n
1.oOoo
1 2 3 4 5 6 7 8 9 10 20 30 40 50
0,9999
0,9998 0.9996 0.9994 0.9992 0,9990
Hours 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1.0000 0.5444 0.2964 0.1614 0.0879 0.0478 0.0260 0.0142 0.0077 0.0042 0.0023 0.0000
~
1.0000 0.9999 0.9997 0.9996 0.9995 0.9994 0.9992 0.9991 0.9990 0.9989 0.9987 0.9975 0.9962 0.9950 0.9937
1.0000 0.7967 0,6348 0.5057 0.4029 0.3210 0.2557 0.2038 0.1623 0.1293 0.1030 0.0106 0.0011 0,0001 0,0000
0.9924 0,9850 0,9776 0,9703 0.9629 0.9557 0.9485 0.9414 0.9343 0.9273 0.9203 0.9134 0.9065 0.8997 0.8929 0.8862 0.8795 0,8729 0.8663 0.8598 0.8533 0.8470 0.8405 0.8343
0,9988 0.9976 0.9964 0.9952 0,9940 0.9928 0.9916 0.9904 0.9893 0.9881 0.9869 0.9857 0.9845 0,9833 0.9822 0,9810 0.9798 0,9786 0.9775 0.9763 0.9731 0.9739 0.9728 0.9716 ~~
1.0000 0.9744 0,9496 0.9253 0.9017 0.8787 0.8562 0.8344 0.8131 0.7923 0.7721 0.5962 0.4603 0.3554 0.2744
1.0000 0.9654 0.9320 0.8998 0.8687 0.8387 0.8097 0.7817 0,7547 0.7285 0,7034 0.4948 0,3480 0.2448 0.1722
0,2119 0,0449 0.0095 0.0020 0.0004 0.0001 0.0000
0.1211 0.0148 0.0018 0,0002 0,0000
~
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Th'ak 1.0000 0.9716 0.9441 0.9173 0.8913 0.8661 0.8415 0.8176 0.7945 0.7719 0,7501 0.7288 0.7081 0.6880 0.6685 0.6496 0.6312 0.6133 0.5959 0.5790 0.5626 0.5466 0.5311 0.5161 0,5014 0.4872 0,4734 0,4600 0.4469 0.4343 0.4220 0.4100 0.3984 0 3871 0.3761 0,3654 0.3551 0.3450 0.3352 0.3257 0.3165 0.3075 0.2988 0 2903 0.2821 0.2741 0.2663 0.2588 0.2514 0 2443 0.2374
1.0000 0.5915 0.3499 0.2069 0.1224 0.0724 0.0428 0.0253 0.0150 0,0089 0.0052 0.0000
1~0000 0.9999 0.9998 0.9997 0.9996 0.9995 0.9994 0.9993 0.9992 0,9991 0.9990 0.9980 0.9970 0.9960 0.9950 0.9940 0,9882 0,9823 0.9765 0.9706 0.9649 0.9692 0.9535 0.9478 0.9422 0.9366 0.9310 0.9255 0.9200 0.9146 0.9091 0.9038 0.8983 0.8931 0.8877 0.8824 0.8772 0.8720 0.8668
~
Table X. Lranium-Radium Series (4n Time, Days 0
+ 2)
Bill4
Th214
1,0000 0.9999 0.9998 0.9997 0.9997 0,9996 0,9995 0,9994 0.9993 0.9992 0.9991 0.9991 0.9990 0 9989 0,9988 0.9987 0.9986 0.9985 0,9984 0.9984 0.9983 0.9982 0.9981 0.9980 0,9979 0,9978 0.9978 0,9977 0,9976 0.9975 0.9974 0.9973 0.9972 0.9972 0.9971 0,9970 0.9969 0.9968 0.9967 0.9966 0.9966 0.9965 0.9964 0.9963 0.9962 0.9961 0.9960 0.9960 0 9959 0.0001 0 9958 0.0001 0,9957
1.0000 0.8343 0.6960 0.5806 0.4844 0.4041 0.3371 0,2813 0.2346 0.1967 0.1633 0.1362 0.1137 0.0948 0.0791 0,0660 0.0551 0.0459 0.0383 0,0320 0,0267 0.0222 0.0186 0.0155 0.0129 0.0108 0.0090 0.0075 0.0063 0.0052 0.0044 0,0036 0.0030 0,0025 0.0021 0,0018 0.0015 0.0012 0.0010 0.0009 0 0007 0.0006 0 0005 0.0004 0.0003 0 0003 0 . 0,002 0.0002 0.0002
1.0000 0.8668 0.7514 0.6513 0.5646 0,4894 0,4242 0.3677 0.3188 0.2763 0.2395 0.2076 0.1800 0.1560 0 1352 0.1172 0 1016 0.0881 0,0763 0,0662 0.0574 0 0497 0.0431 0.0374 0,0324 0 0281 0.0243 0.0211 0.0183 0.0158 0.0137 0.0119 0.0103 0,0089 0.0078 0,0067 0.0058 0 0051 0.0044 0.0038 0.0033 0.0029 0.0025 0 0021 0,0019 0 0016 0.0014 0 0012 0.0010 0.0009 0,0008
1.0000 0.9950 0.9900 0.9851 0.9802 0.9753 0,9704 0,9655 0.9607 0,9559 0.9512 0.9464 0.9417 0.9370 0.9323 0.9276 0,9230 0.9184 0.9138 0.9092 0.9047 0,9002 0,8957 0.8912 0.8867 0.8823 0.8779 0.8735 0.8692 0.8648 0.8605 0.8562 0.8519 0 8477 0.8434 0 8392 0.8350 0.8308 0.8267 0.8226 0.8185 0.8144 0.8103 0.8063 0.8022 0.7982 0.7942 0,7603 0.7863 0,7824 0.7785
Time, Days 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
92 93 94 95 96 97 98 99 100
+ 2)
Thlak 0.2374 0.2307 0.2241 0.2178 0.2116 0,2056 0.1998 0.1941 0.1886 0.1832 0.1781 0.1730 0.1681 0.1633 0.1587 0,1542 0.1498 0.1456 0.1415 0.1374 0.1335 0.1298 0.1261 0.1225 0.1190 0.1157 0.1124 0.1092 0.1061 0 . IO31 0.1002 0.0973 0 0946 0.0919 0 0893 0.0868 0 0843 0,0819 0.0796 0.0773 0.0751 0.0730 0.0709 0.0689 0.0670 0.0651 0.0632 0.0614 0.0697 0.0680 0.0564
Pb210
0.9957 0.9956 0.9955 0.9954 0.9953 0.9953 0.9952 0.9951 0,9950 0.9949 0.9948 0.9947 0.9947 0.9946 0.9945 0,9944 0,9943 0.9942 0.9941 0.9941 0.9940 0,9939 0.9938 0.9937 0.9936 0.9935 0.9935 0.9934 0.9933 0.9932 0.9931 0.9930 0.9929 0.9929 0.9928 0,9927 0.9926 0.9925 0.9924 0.9923 0.9923 0.9922 0.9921 0,9920 0.9919 0.9918 0.9917 0.9917 0.9916 0.9915 0.9914
Bill0
p0210
0.0008 0,0007 0.0006 0,0005 0,0004 0,0004 0.0003 0.0003 0,0003 0.0002 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000
0.7785 0.7746 0.7707 0.7669 0.7630 0,7593 0.7554 0.7517 0.7479 0.7442 0.7404 0.7368 0.7331 0.7294 0.7258 0.7221 0.7185 0.7149 0.7114 0.7078 0.7043 0,7008 0.6973 0.6938 0.6903 0.6869 0.6834 0.6800 0,6766 0.6732 0.6699 0.6665 0.6632 0.6599 0.6566 0,6533 0.6600
0.6468 0.6436 0 6404 0,6372 0.6340 0.6308 0.6277 0,6245 0.6214 0.6183 0.6152 0.6121 0.6091 0.6060
V O L U M E 2 6 , N O . 6, J U N E 1 9 5 4
1067 __
Table XI.
Uranium-Radium Series (4n
(Growth of decay products from initially pure parent." (Ra22B) >>kl =
+ 2)
= .vox1
1,00001 e - x ? t
-
1.00056
-
1.00545 e - X 2 t
(BiZLO)
1.00001
e--X2t
f 0,00055 e-xx3f (1'0210)
-
0.00007 e--Xat
. E6 = I.OOOOI SOX, =
o\'.h1
(Bizlo)
-m sox, SOX,
(po?in)
e--Xlt
&! .\-OX1
.vox1 1.01378 ,--Ii
+ 0.00048 e--Zt
-
1.01428
=
1.01379 e P x l t
-
-
1,01489
=
1,01402
+ 0.00005
-
1,03267 e - x d
0.00179 e - x 2 t
0.00286 e -
4.02759
-
3.00958 e - x 2 t
-
+ 0.00056 e--13f
1.03267 e--Xit 0.01179 e--Xsf
-
f 0.02084
f 0.01868e-X9t
- 0.00010 e - x B t
- 2,01582 e - - h 2 t - 0.00006 e--X3t
-
+ 0.01868
O.OOOIO e--hBt
0,01179 =
+
=
,j.01405 e - - X l t
- a' =
+
O.OOOO~ 0.02084 e--X4t - 0.01179 e--Xat
- i.00906 e - x z f
ssxs
.\'OX1
sox1
+ 0.02636
- 2.02917 e - x 7 f
-
f 0.00286 e - x h s t
yalid 1 hour after purification, assuming 100% retention of radon-222 and its decay products. b Assumes 100% counting yield of all betas. a
-
Table XII.
Uranium-Radium Series
(Growth of decay products from initially pure parent Time Days
Rn22?
Pb2Io
Biz10
Po210
0.0000
0.0000
5
0.0000 0.1657 0.3040 0.4193 0.5156 0,5959
0.0000
6 7 8 9 10
0.6628 0.7187 0.7653 0.8042 0.8367
0,0002 0.0003 0.0003 0.0004 0.0005
11 12 13
0.8637 0.8863 0,9052 0,9209 0.9340
Parent, radium-226) W'\'O'oXI
.
&/.\'OX
1 0000 1.4892 1.9054 2.2525 2.5422 2.7838
0.0000 0.3194 0.5979 0.8304 1 ,0243 1,1861
0.0000 0.0001 0.0001 0.0002 0.0002
2,9853 3.1536 3.2939 3.4110 3.5086
1.3211 1 ,4337 1.5277 1 ,6062 1.6710
0.0005 0.0006 0.0007 0.0008 0.0009
0.0002 0.0002 0.0003 0.0004 0.0004
3,5901 3.6580 3.7147 3.7619 3.8014
1 ,7263 1.7719 1.8100 1.8417 1 ,8683
20
0,9449 0,9541 0.9617 0.9680 0.9733
0.0010 0.0010 0.0011 0.0011 0.0012
0.0005 0.0006 0.0007 0.0007 0.0007
3.8344 3.8618 3.8847 3.9038 3.9197
1 ,8905 1 ,9090 1 ,9245 1 ,9374 1 ,9482
21 22 23 24 25
0,9777 0.9814 0.9845 0.9871 0,9892
0.0013 0.0014 0.0015 0.0016 0.0017
0.0008 0.0009 0.0010 0.0011 0.0011
0.0000 0.0001 0.0001 0,0001
3.9331 3.9442 3.9535 3.9612 3.9675
1,9573 1 ,9649 1.9712 1.9766 1.9810
2G 27 28 29 30
0.9910 0.9926 0.9937 0.9948 0.9956
0.0018 0,0018 0.0019 0.0020 0,0021
0.0012 0.0013 0.0014 0.0015 0.0015
0.0001 0.0001 0.0001 0.0001 0,0001
3.9728 3.9774 3.9811 3.9842 3.9868
1 ,9848
31 32 33 34 35
0.9963 0.9969 0.9974 0.9979 0,9982
0,0022 0.0023 0 002.4 0.0024 0,0025
0.0016 0.0017 0.0018 0.0019 0.0019
0.0001 0.0001 0.0001 0.0001 0.0001
3.9890 3.9908 3.9923 3.9936 3.9947
1.9964 1 ,9978 1.9990 2.0000 2.0009
36 37 38 39 40
0,9985 0.9987 0,9989 0.9991 0.9993
0.0026 0.0027 0,0028 0.0029 0.0030
0,0020 0.0021 0.0022 0.0023 0.0024
0,0001 0.0001 0.0001 0.0001 0.0002
3.9956 3.9963 3.9969 3.9974 3.9978
2.0016 2.0023 2.0028 2,0034 2.0038
45 50 60 70 80 90 100
0.9997 0.9998 0,9999 0 I9999 0,9999 0,9999 0.9999
0.0034 0.0038 0.0047 0.0055 0.0064 0.0072 0.0081
0,0028 0,0032 0.0041 0.0049 0.0058 0.0067 0,0075
0,0002 0,0003 0.0005 0.0006 0,0009 0.0012 0.0015
3.9992 3.9997 4,0001 4.0003 4.0006 4.0007 4.0010
2.0055 2.0067 2.0086 2.0103 2.0120 2.0137 2.0154
0 1
2 3 4
14
15 16
17 18 19
_
_
~
Uranium-Radium Series (4n
+ 2)
Parent, lead-210)
= e-hlt
- E 2
= 1,00060 ( , - A d
-
e-X?t)
0.0000 0.0001
z53= 1,01815 e - x l t + 0.03034 e - x z t sox1
+
0.005.i~e--4t
(Pb?10)
_
x o x 1
* 'k? = 1,00001 e - - l t SOXI
(POZ,()
~
A\TOToxl
-
sox1
( ~ i 2 1 1 )
_
( C r o n t h of decay products froin initially pure parent. (I'hZ10) slxl
.\-ox1
(Pb21')
_
Table XIII.
Parent, radiuin-226)
,-Alf
(RnZ22) s?x2 = 1,00001 e - x d (1'0218)
_
1 ,9880 1.9906 1.9929 1 ,9948
-
1.05449
Time. Days
Biz10
Po210
Time, Days
Bizlo
0 1 2 3
0.0000 0.0003 0.0013 0.0027 0.0047 0.0071
40 41 42 43
?
0.0000 0.1332 0.2485 0,3484 0.4364 0.5105
44 45
0.9939 0.9942 0.9946 0.9947 0.9950 0.99.51
6 7 8 9 10
0.5755 0 6320 0.6809 0 7233 0 7601
0.0098 0.0128 0 0160 0.0194 0.0230
46 47 48 49 50
0.9952 0.9953 0.9954 0.9956 0.9955
0,1889 0,1929
11 12 13 14 15
0.7919 0.8195 0.8434 0.8640 0,8820
0,0268 0.0306 0.0346 0.0387 0,0429
51 52 53 54 65
0.9956 0,9955 0.9955 0.9955 0.9955
0.1969 0.2009 0.2049 0.2088 0.2127
I6 17 18 19 20
0.8975 0,9109 0,9226 0.9328 0.9415
0.0471 0.0514 0,0557 0.0601 0.0645
56 57 58 59 60
0.9954 0.9954 0.9953 0.9953 0.9952
0.2167 0.2205 0.2244 0.2283 0.2321
21 22 23 24 25
0.9491 0.9556 0.9612 0.9661 0.9704
0.0089 0.0733 0.0777 0.0821 0.0866
61 62 63 64 65
0.9952 0.9951 0.9950 0.9950 0.9949
0.2359 0.2397 0.2435 0.2472 0.2510
26 27 28 29 30
0.9740 0.9772 0.9799 0.9822 0.9843
0.0910 0.0984 0,0998 0.1042 0.1086
6f1
67 68 69 70
0.9948 0,9948 0.9947 0.9946 0.9945
0.2547 0.2584 0.2621 0.2657 0.2694
31 32 33 34 35
0,9860 0.9875 0.9888 0.9899 0.9909
0.1130 0.1174 0.1217 0.1261 0.1304
71 72 73 74 75
0 9944 0,9944 0.9943 0.9942 0,9941
0.2730 0.2766 0.2802 0.2837 0,2873
36 37 38 39 40
0.9916 0.9924 0.9929 0,9934 0.9939
0.1347 0.1390 0.1432 0,1475 0.1517
76 77 78 79 80
0.9940 0.9940 0.9939 0.9938 0.9937
0,2908 0.2943 0,2978 0.3013 0.3049
Po2lQ
0.1537 0.1559 0.1601
0.1643 0.1684 0.1726 0.1767 0.1808
0.1848
Let Corepresent the oiiginal count obtained, let R1 be the fraction of Co due to radium-223 and its decay products, and let R2 be the fraction due to radium-224 and its decay products. In 5 days, radium-223 decays to 0.7339 of its original value (Table SVI)and radium-224 decays to 0.3859 of its original value (Table 111). Therefore,
+ I ,0000 Rr 0 . 5 CO = 0 . i 3 3 9 RI + 0 3859 Rt CO = 1,0000 R,
The two equations are solved simultaneously, and it is found that R, = 0.3279 COand R, = 0.6721 CO. The results give a measure of the relative activity of each isotope and its decay products in the mixture a t the time of the first measurement. rl determination of the absolute amount of each isotope depends upon the radioactive equilibrium constant (see below), the nature and energy of the radiation counted, the self-absorption of the sample. and the geometry of the counter, subjects which are beyond the scope of this discussion. Radioactive Equilibrium. \\-hen a radioisotope decays to a radioactive daughter whose half life is shorter than that of its parent, a condition of radioactive equilibrium will eventually be attained in which the daughter product is decaying as rapidly as it is being produced. The mixture then decays with the half life of the parent. The ratio of daughter activity to parent activity is given by the expression
ANALYTICAL CHEMISTRY
1068 Table XIV. Uranium-Actinium Series (4n Synonyni
Mode of Decay
BCU
a
Energies, MeV. 20% 4 . 6
80% 4 . 4 CY
...
...
5?% 20?& 3% 13%
[(1.2ia)
a
-4n
a
AcB
x
10-10Y-1
25.65H
0.0000202 Y -1
34,300y
0.0315 Y - 1
22.0 Y
0.0000863 D -1 0.0373D-1
[
18.6D
0 00155 H-1
1.9804 H-1
[
41% 35% 17% 7%
5.7 5.6 5.5 5.4
11.2D
69% 15% 12% 4%
6.8 6.6 6.4 6.2
3'92S
10.61 hl-1
0.00183 S
22.800M-1
7.4
p-)
0 0330 XI -1 0.0619 D-1 0 00258 H-1
:::
0,0192 M-1
8.0
1O-dS
416,000M-1
7.4
0.529
79 98 M-1
(?)
[i-:
8-
...
7.9
0.6486 D-1
21 M
r a L(0.0005%
88XlOeY
1.2
8-
.4OX
5.0 4.9 4.8 4.7 0.02
(4.9) 24% 6 . 1 22% 6 . 0 7% 5 9 25% 5 . 8 22% 5 . 7
a
ACK
Decay Constants
0.0270H-1
a
KdAc
AC.4
0.2
8-
Half Life
+ 3)
a
1.1520H-1
36.lhI
ACC
AcC"
8-
ACC'
a
AcD
...
...
Stable
...
Table XV. Uranium-Actinium Series (4n TI1227
FrZza
Time, Min.
Thlal
0 1 2 3 4 5 6 7 8 9 10 20 30 40 50
1.0000 0.9995 0,9991 0.9986 0.9982 0.9977 0.9973 0.9968 0.9964 0.9959 0.9955 0.9910 0.9866 0.9822 0.9778
1.0000 1.0000 0.9675 0.9361 0.9057 0,8763 0.9999 0.8479 0.8204 0.7937 0.7679 0.7430 0.9997 0.7189 0.9995 0.5168 0,9992 0,3715 0.9990 0.2671 0.9987 0.1920
0.9734
0.9984 0.9969 0.9954 0.9938 0.9923
Hours 1 2
3 4 5
0 9474
0.9221 0.8975 0.8736
jy--=e Xp
X2
- XI
(Decay in minutes and hours) Razz3 Pbz" Bill1 Time, Hours 1.0000 1.0000 0.9810 0.9623 0,9440 0.9261 0.9998 0.9085 0.8912 0.8742 0.8576 0.8413 0.9996 0.8253 0.9991 0.6811 0.9987 0.5621 0.9983 0.4639 0.9979 0.3829
0.1380 0.9974 0,0190 0.9949 0.0026 0.9923 0.0004 0.9897 0.0001 0.9872
Ti
Ti - Tz
1.0000 0.7255 0.5263 0,3819 0.2770 0.2010 0.1458 0.1058 0.0767 0.0557 0.0404 0.0016 0,0001 0.0000
0.3160 0.0998 0.0316 0.0100 0.0032
(6)
or, for a three-member chain, the ratio of the activity of the third member to that of the first member is (sa)
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
+ 3)
Ti1931 0.8504 0.8276 0.8056 0.7841 0.7632 0.7428 0.7230 0.7038 0.6850 0.6668 0.6489 0.6317 0.6148 0.5985 0.5825 0.5689 0.5518 0.5371 0.5228
Tti221
Frn:
Ra22:
0.9907 0.0000 0.9846 0.9892 0.9821 0.9877 0.9796 0.9861 0.9771 0.9846 0.9745 0,9831 0,9720 0,9815 0.9695 0.9800 0.9670 0.9785 0.9645 0.9170 0.9621 0.9755 0.9596 0,9739 0.9571 0.9724 0.9546 0.9709 0.9622 0.9694 0.9497 0.9679 0.9473 0.9664 0.9448 0.9649 0,9424 0.9634 0,9400
Pb211
0.0010 0.0003 0.0001 0,0000
If the half lives of the decay products are very much smaller than that of the parent, K , is very nearly equal to unity. The time required for the first decay product to reach 99.9% of equilibrium is approximately 10 KST2. EXAMPLE 5 . How long does it take for thorium-234 to reach 99.9% of equilibrium in a sample of uranium-238? How much thorium-234 is present in a microcurie of uranium-238 30 dayr after purification?
1069
V O L U M E 26, NO. 6, J U N E 1 9 5 4 -
Table XYI.
Uranium-Actinium Series (4n f 3) (Decay in days)
Time, Days
Th2al
0 1 2 3 4 5
1.0000 0.5228 0.2733 0.1429 0.0747 0.0391
6
0.0204 0.0107 0.0056 0.0029 0.0015
0.9995 0.9994 0.9993 0.9992 0.9991
0.7996 0.7704 0.7422 0.7151 0.6889
0,0008 0.0004 0.0002 0.0001 0.0001
0.9991 0.9990 0.9989 0.9988 0.9987
0,0000
Th227
Razz1
50 51 52 53 54 55
0 0 0 0 0 0
9957 9956 9955 9954 9953 9953
0 1552 0 1495 0 1440 0 1387 0 1337 0 1288
0 0453 0 0426 0 0400 0 0376 0 0354 0 0332
0.6898 0.6484 0.6095 0.5729 0.5385
36
57 58 59 60
0 9952 0 9951 0 9950 0 9949 0 9948
0 1241 0 1195 0 1182 0 1109 0 1069
0 0312 0 0294 0 0276 0 0260 0 0244
0.6637 0.6394 0.6160 0.5935 0.5718
0.5062 0.4758 0.4473 0.4204 0.3952
61 62 63 64 65
0 0 0 0
9947 9947 9946 9945 0 9944
0 1030 0 0 0992 0 0 0956 0 0 0921 0 0 0887 0
0.9986 0.9985 0.9984 0.9984 0.9983
0.5509 0.5307 0.5113 0.4926 0.4746
0.3715 0.3492 0.3282 0.3085 0.2900
66 67 68 69 70
0 0 0 0 0
21 22 23 24 25
0 9982 0 9981 0 9980 0.9979 0 9978
0 4572 0 4405 0 4244 0 4089 0 3939
0 2726 0 2563 0 2409 0 2264 0 2128
71 72 73 74 75
0.9939 0,9938 0.9937 0.9936 0.9935
0.0709 0.0683 0.0658 0.0634 0.0611
26 27 28 29 30
0.9978 0 9977 0.9976 0.9975 0.9974
0.3795 0,3656 0.3522 0.3394 0.3269
0 2001 0 1881 0.1768 0 1662 0.1562
76 77 78 79
so
0 9935 0 9934 0 9933 0 9932 0 9931
0 0 0 0 0
31 32 33 34 35
0 9973 0 9972 0.9972 0.9971 0.9970
0.3150 0.1468 0.3035 0.1380 0.2924 0.1297 0.2817 0.1219 0.2714 0.1146
81 82 83 84 85
0 0 0 0 0
9930 0 0489 0 0067 9929 0 0471 0 0063 9929 0 0454 0 0059 9928 0 0437 0 0055 9927 0 0421 0 0052
36 37 38 39 40
0.9969 0.9968 0.9967 0.9966 0.9966
0.2614 0.2519 0.2427 0.2338 0,2252
0.1077 0.1013 0.0952 0.0896 0.0841
86 87 88 89 90
0 0 0 0 0
9926 9925 9924 9923 9923
0 0 0 0 0
41 42 43 44 45
0.9965 0.9964 0.9963 0.9962 0.9961
0.2170 0.2091 0.2014 0.1940 0.1869
0.0791 0.0743 0.0699 0.0657 0.0617
91 92 93 94 95
0 9922 0 9921 0 9920 0 9919 0 9918
0 0 0 0
46 47 48 49 50
0.9960 0.9960 0 9959 0 9958 0 9957
0,1801 0.1735 0.1672 0.1611 0.1552
0 0580 0.0545 0.0513 0 0482 0.0453
96 97 98 99 100
7 8 9 10 11
12 13 14 15 16 17 18 19 20
Ac22i
Table XVII. (A4c227j55
=
,-Ad
-\!x2
=
0,9QO20 ( e - k l t
-
0,012 i e - X i t
-
.YoA I
(T)iZ2i)
0 0856 0 0168 0 0823 0 0158 0 0793 0 0149 0 0764 0 0140 0 0736 0 0131
0589 0567 0547 0527 0507
0 0124 0 0116 0 0109 0 0103 0 0096
n
0091 0 0085 0 0080 0 0075 0 0071
0406 0 0049 0391 0 0046 0377 0 0043 0363 0 0041 0349 0 0038
0337 0324 0312 0301 0 0290
0 9917 0 0279 9917 0 0269 9916 0 0259 9915 0 0250 9914 0 0241
0 0 0 0
Uranium-Actinium Series (4n
(Growth of decay products from initially pure parent.a
9943 9942 9941 9941 9940
0229 0216 0203 0190 0179
0 0036 0 0034 0 0032 0 0030 0 0028
0026 0025 0023 0022 0 0021 0 0 0 0
+ 3)
Parent, actinium-227)
,-Ad)
.\TOXI
(Frz2?) ?-2aA2Q
SOA,
rd.3
(Razz9 NOXI
=
iRn"g) X,h, = NoAi (po21j)3 x 5= SOXI
=
1.00309
e-Azoi)
-
2.48912
f 0.00002
+
-
2.49248 e-'?'
-
0.00002
f 1.48875 e-Xat
+ 0.00006
f 1.48895 ,--st
+ 0,00007 ,--Et
SOXI
-53 9OAI
.VEX6 = 1.00370 e - A 1 ' (Pb2ll) XOXI , (Bi211)
%* = 1.00370 e - x 1 f
- 2,49268 e-Az'
-
0.00002
e-A2at
(T1207j
'xp = 1.00370 .\-ox,
-
-
0.00003
e
~~
.vox1
=
ut
.VOX1
2 U"
=
N
A, a
b
-
5.01707 e - - X ~ '
418.089 =
1.48541e-X31
.\-A3
2.01939
10.95034 , - A I f
- 912.529 ePAlt
2.49313 e - A z f
+ O . O O O Oe - ~x z a t + 6.94518
f 0.002 e-AnaL
- 4.98561 e - - x z '
f 1.48939 e - A 3 t
-
0.01205
f 0,00008 e--xflt
+ 0.00007 , - A d
+ 495.432 e - A d + 0,005 f 2.97813 e--Xat
+ 0,00014
,--Ef
Valid 1 hour after purification, assuming 100% retention of radon-219 and its decay products, Assumes 25 kev threshold and 100% counting yield for all countable betas.
__
ANALYTICAL CHEMISTRY
1070 Table XVIII.
+ 3)
Uranium-Actinium Series (4n
(Growth of decay products from initially pure parent.
Parent, actinium-227)
0 1 2 3 4
0.0000 0.0361 0.0710 0.1045 0.1368 0.1679
0.0000 0,0018 0.0057 0.0113 0.0186 0.0274
0.0120 0.0553 0.1054 0.1615 0.2229 0.2890
1.0000 4.6052 8.7808 13.457 18.577 24.087
0.0000 0.0154 0.0229 0.0341 0.0486 0.0660
50 51 52 53
0.8324 0.6804 0.8379 0.6905 0.8432 0.7002 0.8484 0.7096 0.8533 0.7188 0.8581 0.7278
3.5657 3.6113 3.6556 3.6985 3.7403 3.7807
297.15 300.94 304.63 308.21 311.69 315.06
1.3720 1.3921 1.4116 1,4305 1.4489 1.4668
6 7
0,0374 0,0487 0,0609 0.0741 0.0880
0.3593 0.4330 0.5098 0.5892 0.6708
29.938 36.084 42.485 49.103 55.901
0.0860 0.1084 0.1328 0.1591 0.1869
56
9 10
0.1979 0.2268 0.2546 0.2814 0.3072
57 58 59 60
0.8627 0.7364 0.8671 0.7449 0.8713 0.7530 0.8754 0.7610 0.8793 0.7687
3.8201 3.8582 3.8951 3.9310 3.9657
318.34 321.51 324.59 327.58 330.48
1.6842 1,5010 1.5174 1.5333 1.5487
11 12 13 14 15
0,3321 0,3561 0.3791 0.4014 0,4228
0.1027 0.1179 0.1336 0.1497 0,1662
0.7542 0.8390 0.9249 1.0117 1.0990
62.849 0.2161 69.917 0.2465 77.077 0.2779 84.305 0.3102 91.580 0.3431
61 62 63 64 65
0.8831 0.8868 0.8903 0.8936 0.8969
0.7762 0.7834 0.7901 0.7972 0.8038
3.9994 4.0320 4.0637 4.0943 4.1240
333.28 336.00 338.64 341.19 343.66
1.5637 1.5782 1.5923 1,6059 1.6191
16 17 18 19 20
0,4434 0.4633 0,4824 0,5009 0.5186
0,1829 0,1999 0,2170 0,2342 0.2515
1.1866 1.2742 1.3618 1.4491 1.5359
98.880 106.19 113.48 120.76 127.99
0.3766 0.4105 0.4447 0.4791 0.5136
66 67 68 69 70
0.9000 0.8102 0.9030 0.8164 0.9059 0.8224 0.9087 0.8282 0.9114 0.8338
4.1527 4.1803 4.2074 4.2334 4.2586
346.06 348.37 350.62 352.79 354.89
1.6319 1.6443 1.6563 1.6679 1.6792
21 22 23 24 25
0,5357 0.5522 0,5681 0,5834 0,5981
0,2688 0.2860 0,3032 0.3203 0,3372
1.6221 1.7075 1.7921 1.8757 1.9583
135.17 142.29 149.34 156.31 163.19
0.5481
0.5826 0.6170 0.6512 0.6851
71 72 73 74 75
0.9140 0.8393 0.9165 0.8446 0.9189 0.8497 0.9212 0.8546 0.9234 0.8694
4.2830 4.3066 4.3294 4.3514 4.3728
356.92 358.88 360.78 362.62 364.40
1.6901 1.7007 1,7109 1,7208 1,7304
26 27 28 29 30
0,6123 0.6259 0,6391 0.6518 0.6640
0.3540 0.3706 0,3871 0.4033 0.4193
2.0397 2.1199 2.1988 2.2764 2.3526
169.97 176.66 183.23 189.70 196.05
0.7187 0.7520 0.7849 0.8174 0.8494
76 77 78 79 80
0.9255 0.9276 0.9295 0.9314 0.9332
0.8640 0.8685 0.8727 0.8770 0.8810
4.3934 4.4133 4.4326 3.4512 4.4691
366.11 367.77 369.38 370.93 372.43
1.7396 1.7485 1.7572 1.7656 1.7737
31 32 33 34 35
0,6757 0.4351 0,6871 0,4506 0,6980 0.4808 0.7086 0.4658 0.7186 0.4955
2.4274 2.5008 2.5727 2.6430 2.7119
202.28 0.8809 208.40 0.9119 214.39 220.25 0.9424 0.9724 225.99 1.0018
81 82 83 84 85
0.9350 0.9367 0.9383 0.9399 0.9414
0.8849 0.8887 0.8923 0.8959 0.8993
4.4866 4.5030 4.5195 4.5351 4.5502
373.87 375,25 376.62 377.93 379.18
1.7816 1,7890 1.7963 1,8034 1.8102
36 37 38 39
0,7283 0,7377 0.7468 0.7555 0,7638
0.5099 0,5240 0,5378 0,5513 0.5846
2.7793 2.8451 2.9095 2.9723 3.0336
231.61 237.10 242.46 247.69 252.80
1.0306 1.0688 1.0865 1.1136 1.1041
86 87 89 90
0.9428 0.9442 0.9455 0.9468 0.9480
0.9026 0.9057 0.9088 0.9117 0.9156
4,5648 4.5789 4.5925 4.6056 4.6182
380.40 381.57 382.71 383.80 384.85
1.8168 1,8232 1.8294 1,8352 1.8409
0,7719 0.7797 0,7872 0.7944 0.8013
0.5776 0,5901 0.8024 0,6144 0.8262
3.0933 3.1516 3.2084 3.2637 3.3176
257.78 262.63 267.37 271.98 276.46
1.1660 1.1912 1.2158 1.2399 1.2634
91 92 93 94 95
0.9492 0.9174 0.9503 0.9200 0.9514 0.9226 0.9525 0.9251 0.9535 0.9275
4.6304 4.6422 4.6536 4.6648 4.6751
385.87 386.85 387.80 388.71 389.59
1.8464 1.8517 1,8568 1.8618 1 8666
0,8080 0,8145 0.8207 0.8266 0,8324
0.6376 0,6487 0,6596 0,6702 0,6804
3.3700 3.4210 3.4706 3.5189 3.5657
280.83 1.2863 285.08 1.3086 289.22 1.3303 293.24 1.3514 2 9 7 , l 5 1.3720
96 97 98 99 100
0.9544 0.9554 0.9563 0.9511 0.9579
4.6853 4.6951 4.7046 4.7137 4,7225
390.44 391.26 392.05 392.81 393.54
1.8712 1.8757 1.8800 1.8841 1 8881
5
8
40
41 42 43 44
45 46 47 48
49 50
Table XIX. Uranium-Actinium Series (4n -k 3)
54 55
88
K, =
(Growth of decay products from initially pure parent Parent, thorium-227)
0.9298 0.9320 0.9341 0.9362 0.9382
4.51 X IO9 4.51 X 109
-
365
= 1.0000 (data from Table
VIII)
Time for 99.9% equilibrium = (IO) (1.0000)(24.1) = 241 days Because of its extremely long half life, the decay of uranium238 is negligible. Since Ke = 1.0000 and the decay of thorium234 in 30 days is 0.4220 (Table X), solution of Equation 2 yields
- 2.52024 e-XZt + 0.00276 e - X s t +
(TI207) % = 2.61756
.YOXI
2=
11.05767
-
10.06006 e--Zt
Noh
+
o,oo239 e - - X s t
@e 5.03448 e--X1t - 5.03941 'VOX1
O.OOOOI e-'& - 0.00008 e - - X 7 t 0.00001 e--Xst 4-
=
e-X2t
- oooool
+ 0.00601 e - X s t +
e--Xst
p,ooool e - ~ B t - o , ~ o ,o- -~~ ~ t Valid 1 hour after purification assuming 100% retention of radon-219 and its decay products. b Assumes 25-kev. threshold and 100% counting yield for all countable betas. 0
Growth of Decay Products. EXAMPLE 6. How much polonium-210 is present in a sample of lead-210 15 days after purification? The answer is read directly from Table XIII. The activity of polonium-210 will be 4.29% of the initial activity of the lend-210 . .. - - - - -. EXAMPLE 7. Assuming 100% retention of radon-219, how much will the alpha activity of the actinium-227 chain increase during the first 36 hours after purification? From Table S X I the ratio of the alpha activity a t 36 hours to the initial a1ph.a activity iS 0.0795/0.0120 = 6.625. EXAMPLE 8. Assuming 100% radon retention, what is the beta activity of the radium-226 chain relative to the activity of
V O L U M E 26, N O . 6, J U N E 1 9 5 4 Table XX.
Uranium-Actinium Series (4n
(Growth of decay products from initially pure parent. Time, Days
.
1071
+ 3)
Parent, thorium-227)
Time, Days
0 1 2 3 4 5
0.0000 0.0589 0.1121 0.1600 0.2031 0.2417
1.0000 1.1968 1.3746 1.5326 1.6724 1.7952
0.0000 0.1133 0.2202 0.3165 0.4030 0.4804
50 51 52 53
6 7
8 9 10
0.2760 0.3066 0.3335 0.3572 0.3779
1.9025 1.9955 2.0754 2.1432 2.1998
11 12 13 14 15
0.3958 0.4111 0.4241 0.4350 0.4438
10 17 18 19 20
Hours 0 1 2 3
1 0000 1.0160 1.0363 1.0580 1.0798 1.1021 1.1238
0.0000 0.0048 0.0167 0.0308 0,0454 0.0601 0.0747
0,0120 0.0136 0.0153 0.0169 0.0186 0.0203 0.0221
0.0000
6
0.0000 0.0003 0.0015 0.0037 0.0070 0.0113 0.0165
7 8 9 10 11 12
1.1688 1.1937 1.2187 1.2438 1.2690 1,2943
0.0228 0.0299 0.0378 0.0464 0.0558 0.0658
1.1454 1.1668 1.1881 1.2092 1.2302 1.2511
0,0892 0.1035 0.1178 0.1320 0.1460 0.1600
0.0238 0.0256 0.0273 0.0291 0.0309 0.0327
0.0125 0.0126 0.0127 0.0129 0,0130 0.0131
13 14 13 16 17 18
1.3197 0.0764 1.3451 0.0875 1.3706 0.0992 1.3960 0.1112 1.4214 0.1238 1.4469 0.1367
1.2718 1.2924 1.3128 1.3330 1.3530 1.3729
0.1738 0.1876 0,2012 0.2147 0.2282 0.2415
19 20 21 22 23 24
1.4723 1.4977 1.5230 1.5482 1.5734 1.5986
0.1499 0.1635 0,1773 0,1915 0.2058 0.2204
1.3927 1.4124 1.4319 1.4512 1.4703 1.4892
0.2547 0.2679 0,2809 0,2938 0.3067 0.3194
0.0456 0.0143 0.0475 0.0145 0.0495 0.0147 0.0514 0.0149 0.0533 0.0152 0.0553 0.01 54
0.2508 0.2427 0.2348 0.2271 0.2197
26 28 30 32 34 36
1.6486 1.6982 1.7474 1.7961 1.8443 1.8921
0,2501 0.2803 0.3111 0.3422 0,3735 0.4050
1.5268 1.5639 1.6004 1.6364 1.6718 1.7067
0.3446 0.3694 0,3938 0.4179 0.4416 0.4650
0.0592 0,0159 0.0632 0,0164 0.0672 0.0169 0.0713 0.0175 0.0754 0,0181 0.0795 0.0187
0.2125 0.2055 0.1988 0.1922 0.1858
38 40 42
1.9393 1.9859 2.0319 2.0774 2.1223 2.1666
0.4365 0.4680 0.4995 0,5308 0,5619 0.5929
1.7411 1.7749 1.8083 1.8411 1.8735 1.9084
0.4880 0.5106 0.5330
0.0837 0.0880 0.0923 0,0966 0.1010 0.1054
04
68 7%
2.2533 2.3376 2.4195 2.4989 2.5761 2.6508
0.6541 0.7141 0.7728 0.8301 0.8860 0.9404
1.9677 0.6397 2,0281 0.6801 2.0868 0.7194 2.1437 0,7575 2.1990 0,7944 2.2525 0,8304
0.1143 0.0246 0.1234 0.0263 0.1327 0.0281 0.1422 0.0300 0.1518 0.0320 0.1615 0.0341
80 88 96
2.7936 2.9276 3.0535
1.0448 1.1481 1.2356
2.3550 2.4514 2.5422
0.8989 0.9635 1.0243
0.1814 0.2019 0,2229
0.0386 0.0434 0.0486
108 120
3.2278 3.3861
1.3641 1.4809
2.6685 2.7838
1.1088 1.1861
0.2564 0.2890
0.0569 0.0660
55
1.2600 1.2245 1.1898 1.1557 1.1223 1 ,0896
0.5529 0.5380 0.5233 0.5089 0.4947 0.4808
0.5495 0.6109 0.6651 0.7127 0.7543
56 57 58 59 60
0.2333 1.0576 0.2266 1.0262 0,2201 0.9956 0.2136 0.9657 0.2073 0.9365
0.4672 0.4538 0.4406 0.4278 0.4152
2.2463 2.2835 2.3121 2.3330 2.3467
0.7903 0.8212 0.8473 0.8691 0.8870
61 62 63 64 65
0,2012 0.1952 0.1893 0.1836 0.1780
0.9080 0.8802 0.8531 0.8266 0.8009
0.4029 0.3909 0.3791 0.3670 0.3564
0.4509 0.4562 0.4601 0.4626 0.4639
2.3540 2.3556 2.3517 2.3430 2.3300
0.9012 0’.9121 0.9200 0.9251 0.9277
66 67 68 69 70
0.1725 0.1672 0.1620 0.1570 0.1521
0.7758 0.7514 0.7276 0.7045 0.6821
0.3455 0.3349 0.3245 0.3144 0.3045
21 22 23 24 25
0.4640 0.4631 0.4612 0.4585 0.4551
2.3132 2.2928 2.2694 2.2431 2.2144
0.9280 0.9262 0.9226 0.9173 0.9105
71 72 73 74 75
0.1473 0.1426 0.1381 0.1337 0,1294
0.6602 0.2949 0.6390 0.2856 0.6183 0.2765 0.5983 0.2677 0.5788 0.2591
26 27 28 29 30
0.4510 0.4463 0.4410 0.4353 0.4292
2.1836 2.1509 2.1165 2.0808 2.0438
0.9023 0.8929 0.8825 0.8711 0.8588
76 77 78 79 80
0,1252 0,1212 0.1172 0.1134 0.1097
0.5599 0.5416 0.5238 0.5065 0.4897
31 32 33 34 35
0,4227 2.0059 0.4159 1.9671 0.4088 1.9277 0.4015 1.8878 0.3940 1.8475
0.8459 0.8323 0.8181 0.8035 0.7885
81 82 83 84 85
0.1061 0.1026 0,0992 0.0960 0.0928
0.4735 0.4577 0.4425 0.4277 0.4133
?
44 46
48 36 37 38 39 40
0.3863 0.3785 0.3706 0.3627 0.3547
1.8069 1.7662 1 ,7255 1.6848 1.6443
0.7732 0.7576 0,7419 0.7260 0.7100
86 87 88 89 90
0.0897 0.0867 0.0838 0.0810 0.0783
0.3994 0.3860 0.3729 0.3603 0.3481
0.1796 0.1736 0.1678 0.1622 0.1567
41 42 43 44 45
0.3467 0.3386 0.3306 0.3226 0.3147
1.6039 1.5639 1.5242 1.4849 1.4461
0.6940 0.6779 0.6619 0.6459 0.6301
91 92 93 94 95
0.0756 0.0731 0.0706 0.0682 0.0659
0.3363 0.3248 0.3137 0.3030 0.2926
0.1514 0.1463 0.1414 0.1366 0.1319
46 47 48 49 50
0.3068 1.4077 0.6143 0.2990 1.3699 0.5987 0.2913 1.3328 0.5832 0.2837 1.2960 0.5679 0.2761 1.2600 0.5529
96 97 98 99 100
0.0636
0.2826 0.1274 0.0615 0.2728 0.1231 0.0394 0.2634 0.1189 0.0573 0.2543 0.1148 0.05.54 0.2456 0,1109
pure radium-226 6 days, 6 hours after purification? Although the growth factors are not given for fractional days after the first 5 days, a linear interpolation will produce an answer which is correct to better than 0.5%. From Table XII, the beta growth factors of radium-226, 6 and 7 days after purification, are 1.3211 and 1.4337, respectively. The average increase between these two times is 0.0047 Der hour, so the increase in 6 hours is 0.0282. The beta growt,h factor for 6 days, 6 hours is 1.3211 0.0282 = 1.3493. E x A i r P m 9. A mixture of thorium-227 and thorium-228 is purified and a sample is alpha-counted periodically. At 24 and 120 hours the counts are 10,000 and 20,000 counts per minute, respectively. Assuming 100% retention of the radon isotopes, calculate the counts due to each thorium isotope a t the time of purification. This problem is treated in the same manner as in Example 4. The growth factors are found in Tables V and XX. Let A be the number of counts a t zero time from thorium-227 and B the nJmher of counts from thorium-228, a t zero time.
+
.
1.0000 1.0234 1.0472 1.0711 1.0952 1.1195 1.1441
0.2761 0.2687 0.2614 0.2542 0.2471 0,2401
54
Table XXI. Growth of Alpha and Beta Activities from Initially Pure Parents during First 120 Hours
52 56
60
0.5550
0.5766 0.5979
0.0104 0.0118 0.0121 0.0122 0.0123 0.0124
0.0193 0.0200 0.0207 0.0214 0.0222 0,0229
+ 1.5986 B 20,000 = 1.7952 A + 3.3861 B 10,000 = 1.1968 A
A = 1597 counts per minute from thorium-227 at zero time
B
=
5060 counts per minute from thorium-228 at zero time LITERATURE C I T E D
(1) Bateman, H., Proc. CamSridge Phil. Soc.. 15, 423 (1910). (2) Natl. Bur. Standards (E. S.),Circ. 499 (September 1950). (3) Rut.herford, E., Chadwick, J., and Ellis, C . D., “Radiations from Radioactive Substances,” p. 13, London, Cambridge
University Press, 1951.
RECEIVED f o r review September 17, 1953. Accepted December 24, 1953. hlound Laboratory is operated by Monsanto Chemical Co. for the United States Atomic Energy Commission under Contract Xumher AT-33-1-GES53.
