616
JOURNAL OF CHEMICAL EDUCATION
THENATURALOCCURRENCEOF SHORT-LIVED RADIOISOTOPES ISAAC ASIMOV Boston University School of Medicine, Boston, Massachusetts
IT
IS well known that seven elements, namely, polonium, astatine, radon, francium, radium, actinium, and protactinium (with atomic numbers of 84, 85, 86, 87, 88, 89, and 91 respectively), occur naturally, despite the fact that the half-lives of their isotopes are so short that none can reasonably he expected to have survived over the period of the earth's e~istence.~As an extreme example, the only naturally occurring francium isotope, F P 3 ,has a half-life cbf 21 minutes. The evanescence of such an isotope is illustrated dramatically when we consider that if the earth's entire substance were composed it would take less than 2.5 days to of nothing but BYz3, reduce that mighty quantity to a single atom. Francium and its sister elements nevertheless exist in the earth's crust because they are continually regenerated by the decay of certain long-lived precursors such as UZ38 and Th23=. They are therefore found in minute quantities in ores containing thorium and uranium. What these "minute quantities" amount to has not, t o the author's knowledge, been reported in the literature. Certainly, the average student of general chemistry gets a strong impression that radium, to take a glamorous example, is extremely rare and that only a few grams of it exist on the earth. That this is a false impression can be shown quite easily. In order to do so we must first consider the radioactive decav chains involvine the atoms with atomic
1Asnrov. I., J. CAEM.EDUC.,30, 398 (1953).
numbers higher than 80. Four distinct chains can exist, tbeoretieally, and of these, three occur in n a t u r e the uranium series, the thorium series, and the actinium series.l The fourth, the neptunium series, contains no member sufficiently long-lived for perceptible quantities still to exist, and so does not occur in nature. The chain has, however, been created in the laboratory and its characteristics studied. In dealing with the decay chains as usually presented in textbooks, two factorsexist which tend to confuse the student. One of these is the use of trivial names for the various isotopes in the series. For instance, there is a list of "radiums" from radium A to radium G in the Uzasseries, including radium C, radium C', and radium C". There are also various thoriums, mesothoriums, and actiniums in the other series, to say nothing of radium emanation, thorium emanation, and actinium emanation. These names have historical validity since they were first introduced at a time when the chemical nature of the members of the series was not known and the very concept of isotopes had not yet been estahlished. There is no reason except inertia, however, 'It is usually stated that the radiottctive decw chains are named after the longest-lived memher in the series. If that is so, the "xtinium" series is rtctually a. misnomer, since the longestlived member in it is not actinium but U2J9sometimes called xtinouranium. The author suggests that the most logical names series, the ThZ8'series, the U" aeries, for the series are the UPas and the NpPJ'sreies.
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DECEMBER, 1953
for the trivial names t o he perpetuated. The student certainly has a right to know that radium B, radium D, and radium G are all isotopes of lead, with all the chemical properties of lead. Under usual teaching conditions. it is much more natural for him t o think that they are isotopic (or perhaps allotropic) varieties of radium itself. The second element of confusion introduced into the radioactive decay chains, as usually presented, is that the half-lives of the constituent isotopes are given in varying units-in seconds, minutes, hours, days, or years according to the half-life's length. (The author is not aware of any exceptions to this statement.) The result is that where it is desired to obtain ratios of halfl i v e s a s , for instance, in the calculations introduced into this paper-preliminary conversions of one time unit into anokher are necessary. Table 1 The UZa8 Series Element
Nuclide
Uranium
dJ2S8
1.42 X 10''
Thorium 18 Protactinium
sTh2S4
2.08 X 108
,,Paza4
6.84 X 10
1
@ Uranmm
Half-life, seconds
w U " V . 4 1 X loLP
i? Thonum
2.52 X 1012
10 Radium la Radon
1
Polonium la L O P % Lead 14 /Astatine Bismuth a I! y . 0 4 % Polomum a l a /Thallium Lead 4
ssRsza6
5.11 X loLo
&n4"
3.30 X 10'
.4P0118
1 .83 X 102
ssBis'o
4.32 X 105
s,Pa210 8,T1"' 82Ph'oe
1.21 X 10' 2.54 X lo4 Stable
Tabla 2 The Th'" Se~eries Element
Nuclide
~Th""2
4.38 X 10"
Radium 1
J!
asRrt'*8
2.11 X 10'
Actmum 14 Thorium la Radium ia Radon 1P 99.986%Polonlum Le;da yb014%
r~Ac'2s .oTh428
2.21 x 19"
ssRaP" p6Ru2z0
3.14 x 106 5.45 X 10
.PosLe
1.6x
66.3%
Astatine ~ismuth~a
82Ph='~ ,AtsIe ssBi21'
Po,k~umv'7% l a Thallium Leadd8
a4PoP'2 8,Tlao8 azPh20~
I
3.63 X 10'
3 X lo-' 1.86 X 10% Stahle
TABLE 3 The Uza6Series Element
Nuclide
Urapium
plUsJs
2.23 X loL'
aThZSL
8.86 X 104
Q,P~"'
1.01 x 10"
spAc227
6.84 x lo8
aThZ2' saRa22S
1.63 X 106 1.26 X los 9.68 x lo6
s4PoP16
1.83 x 10-a
nPbPL1 .kAt216 ;&im
2.17 X 10' 1 x 10-4 1.30 x 10% 5 x lo-$ 2.86 X 10% Stahle
Thorium 16 Protrtctinium
radioactive decav chains in Tables 1., 2., 3. ~and> 4., ~wit,h ~ - these two elements of confusion eliminated. The Actmum +a actual name of the element and the actual isotope 98.8% la / l . z % Thorium a symbol is given for each member of the chain, and the l,a /Franoium half-life is presented uniformly in seconds. The data Rad~um 4 1 on which Tables 1 to 4 have been constructed are from Radon Glasstone's monoeraoh.3 *I = To determine 'the actual quantity of any of these Polonium 0.0005% radioactive isotopes in the earth's crust, it is necessary 99.9995% L k d 4 to make use of the principle that a t radioactive equilib18 ,Astatine Bi8muthd a rium the number of atoms present of each of the chain's constituent kotopes is directly proportional to 99.68% Polonium la y . 3 2 % ~
lo-' 3.82 x 10' 3 x lo-.
Thus, if the total quantity of existing uranium, thorium, and neptunium is known, the problem of the total quantity of the daughter isotopes becomes one of simple arithmetic. Neptunium may he dismissed immediately as not existing in nature. It has been sstimated, however,
la
It seems worth while, therefore, t o present the four
5.99 X 10'
the respective half-lives. Where there is a branch in the decay chain, the number of existing atoms of the branched product, as determined from half-life ratios, must he multiplied by the fraction of the total decay of its precursor which is given over to its own formation. Thus, in the Th232series the number of atoms of Atz1=is related to the number of atoms of Th232by multiplying the latter by the factor:
IR
*v
Bismuth 99.99999% 18 O.rnl% Polonium a l a /Thallium Lead 4
Half-life, seconds
Thorium
Half-life, s e c a d s
~~
~~
8drPPa
I
\
* GUSTONE, S., "Soureehaak on Atomic Enerm," D. Van Nostrsnd Co., New York, 1950.
/'l'hallium Lead 4 Ja
d'oy
d1'Ix0' nPh'"'
618
JOURNAL OF CHEMICAL EDUCATION
that the uranium content of the lithos~hereis 0.008 ~ e cenb4 while the corresponding figure for thorium is 0.002 per cent. If we restrict ourselves to the dry land area of the earth and take only the outermost mile as the only portion whose mineral content is likely to be useful t o mankind in the foreseeable future, we are left with a portion of the lithosphere which (assuming a deuaity of 2.7) has a mass of 6.70 X lozag. The mass of the constituent thorium, ThZ3%, is therefore 1.34 X 10'9 e.. while that of uranium is 5.36 X 1019 e. Since "ran& is composed of UZa8 and U235atoms iLthe ratio 9929:71, the mass of U" is 532 2 1019g., while that of
TABLE 4 The Np43' Seriea Element
Nuclide
Plutonium
,Pur41
3 X lo8
Amer~cium
rAmX4'
1 . 5 8 X 1O1O
Neptunium 1a Protactinium
~NP"'
6.94 X
1s 1a
Half-life, seconds
lox3
srPa'aa
2.37 X loa
Uranmm
~UZ5'
5.11 X loLa
1a Astatine
SSA~~"
1 . 8 X 10-%
-Bin'
2.82 X 10'
8,Poz'S aT1a09 82Pb40'
4 . 2 X 10-6 1.32 X 10' 1.19 X 10"
srBiP09
Stable
Lil
L Bismuth
96% ~ o lloan i u m / 4 ?
Ia
dThdium Lead p
IS
Biamuth
From these figures and the data in Tables 1 to 4, the information in Table 5 can be calculated. In the case of each of the seven elements listed in Table 5, the indicated isotope makes up a t least 99.99 Per Cent of the weight of the element in the earth's crust.
,
U I~ ~ ~of the ~ GUTENBERG, B., 2nd ed., Dover Publications, Inc., New York, 1951, p. 87.
~~
r
mxm.I2,T)Ur.
e
D
weight .,f s h o r t - ~ i v e dIsotopes Naturally Occurring in the Outermost Mile of the Earth's Land Araa M o d frequently occun-ing nuclide
Element
polanium Astatine ~ ~ Actinium
UPO'LO
d
i
81At2'8 ssRnPa' srFr'z' ssRaPse ~ ~ s~AcQ" ~,Ps"l
Total mass, gram
4.00 X 6.86 x 1.15 x 2.45 X 1.82 X 1.13 x 1.69 x
109
lo-=
lo8 10 10" loLo loLa
Thus, although six isotopes of polonium exist naturally in addition to the Po210of the table, their combined mass is only 6.28 X lo4 g., as compared with 4.00 X los for Po2l0 alone. I n the case of each element except astatine, the predominant naturally occurring isotope is also the most stable isotope. I n the case of astatine, i t is AtZlo,with a half-life of 8.3 hours, which is most stable but it occurs in none of the radioactive series and is completely artificial. Note that the most common of the seven elements is radium and that the mass of radium in the limited portion of the earth's crust being considered still exceeds 18 billion kilograms. While this is certainly a trace amount if considered to be distributed throughout the volume of crust under study (of which it forms only 2.7 X 10Wgper cent by wlght), it would prove to be a sizable quantity if gathered in one place. Assuming a density of 5, the radium in the earth's accessible crust would form a cube 1120 yards (12.7 city blocks) on each side. This would amount to over a quarter of a cubic mile--certainly a different picture from the *usual vision of radium as an almost non-cxistent material. Astatine and francium, to be sure, are trace elements even when collected in a single spot. In the three natural radioactive series, both elements occur onlv in branched portions of the chain, and bu the heavi1y"unfavored side of the branch a t that. As a final comment, it may be interesting t o note that such is the power of Avowdro's number that were the 70~ mn. - - - of - - exist - ~ - - - -in^ - -aasta& to be uniformly distributed through the upper mile of the earth's entire land surface, each kilogram of the would, nevertheless, contain 3.5 atoms of ~ lithosphere ~ ~ ~~ ~ i ~ ~ astatine. ~~~~
n~
~
