book

1. Natural Radioactivity of the Crust and Mantle
W. R. Van Schmus
1. INTRODUCTION
Radioactive elements found in the crust and mantle
form the basis for several major applications in
geophysics and geochemistry. Direct use of natural
radionuclides and their decay products can be grouped
into three main categories: (1) geochronology and
cosmochronology, (2) understanding radiogenic heat
production and the thermal history of the Earth, and (3) as
tracers in various geologic processes, including
differentiation of the Earth. The information summarized
here focuses primarily on the four major, naturally
occurring, radioactive nuclides 4oK, 235U, 238U, and
232Th (Table l), selected intermediate daughter products,
and their applications in category 2. Geochronologic
applications are covered in a separate chapter, and both
geochronologic and geochemical tracer applications are
well covered by Faure [6].
2. ABUNDANCE OF NATURAL RADIONUCLIDES
Compilations of K, U, and Th abundances in rocks and
minerals are common, and that of Clark et al. [3] is an
excellent summary of knowledge to that time. The major
improvements in our understanding of these abundances
since 1966 have come about through development of
better analytical techniques for samples with low
abundances of these elements, better understanding of the
processes governing the distribution of these elements in
terrestrial and extraterrestial materials, and better
definition of bounding conditions (e.g., mean annual heat
W. R. Van Schmus, University of Kansas, Department of
Geology, Lawrence, KS 66045
Global Earth Physics
A Handbook of Physical Constants
AGU Reference Shelf 1
Copyright 1995 by the American Geophysical Union.
flow) that set limits on the abundances of these elements
in the Earth. Thus, in some respects this summary will
not differ significantly from earlier compilations, whereas
in other respects it will present our current best estimates
of the abundances involved.
Potassium is an important consitituent of the Earth. As
one of the alkali metals (Li, Na, K, Rb, and Cs), with an
ionic radius of ca. 1.6 angstroms, it is one of the so-called
large ion lithophile (LIL) elements and tends to be
concentrated in evolved crustal rocks such as granites and
shales, where it is an essential constituent of several
common rock-forming minerals (Table 2). Uranium, with
an ionic radius of ca. 1.Oangstroms, and thorium, with an
ionic radius of ca. 1.05 angstroms, are also LIL elements,
but their lower overall abundances (Table 3) mean that
minerals containing U or Th as essential constituents are
found only as trace minerals in common rocks or as
minerals in primary or secondary mineral deposits (Table
2).
In the broader context, it is not individual minerals that
are important, but their host rocks. Table 3 lists K, U, and
Th abundances for a variety of common crustal rock types
or rock suites. Rb and Sm are two other radioactive
nuclides used for geochronology, and representative
abundances for these two elements are also included in
Table 3, even though their contributions to general
radioactivity of the crust are negligible and are not
discussed further in this chapter. As is the case for
minerals, the abundances of a given trace element in rocks
can vary over a several orders of magnitude. The
abundances given in Table 3 should therefore be
considered as representative of crustal rocks and rock
types in general, but caution must be used in attaching too
much significance to a single example. For example, the
high Th contents for G-l and GSP-1 represent the higher
end of the abundance spectrum, and the mode is probably
about 10 to 20 ppm Th for felsic rocks (Table 3). Results
for average crustal rock types are probably more
283

2. TABLE 1. Isotopic Abundances of K, U, and Th
Potassium Thorium Uranium
Mass # At. % wt. % Mass # At. % Wt. % Mass # At. % wt. %
39 93.2581 92.937 1 232 100 100 234 0.0057 0.0056
40 0.01167 0.01193 235 0.7200 0.7110
41 6.7302 7.0510 238 99.2743 99.2834
Isotopic abundances: ref. [181 for 39K, 4oK, 41K; ref. [6] for 234U, 235U, and 238U.
TABLE 2. Some Typical K, U, Th - Bearing Minerals
Mineral Nominal Composition
Abundancesa
K U Th
Adularia KAISi308
Allanite (Ca,Ce,Y,Th)2(Al,Fe,Mg)3Si3012(OH)
Alunite KAk,(SO4)2(OH)6
Apatite Ca5(P04)3(F,CLOH)
Apophyllite KCa4(Sig02o)(OH,F).8H20
Autunite Ca(U02)2(P04)2’10-12H20
Baddeleyite ZrO2
Biotite K(MgPe)3(AlSi301o)(oH)2
Carnallite KMgQ6H20
Carnotite ESJW2WW2.3H20
Glauconite K(Fe,Mg,A1)2(Si4010)02
Hornblende NaCa2(Mg,Fe,Al,>s(Si,Al)s02202
Jarosite ~e3(S04)2(OH)6
Lepidolite KLi2Al(Si40to)(OH)2
Leucite KAISi206
Microcline KAlSi308
Monazite (Ce,La,Y,Th,)POq
Muscovite K(A1)2(AlSi3Olo)(OH)2
Nepheline (Na,K)AISi04
Orthoclase KAlSi308
Phlogopite KW,(AlSi30lo)Wh
Pitchblende Massive UO2
Polyhalite K2CazMg(S04)4.2H20
Sanidine KAISi3Og
Sphene (Titanite) CaTiSiO5
Sylvite KC1
Thorianite Th02
Thorite ThSiO4
Torbernite Cu(UO2)2(PO4)2.8-l2 Hz0
Tyuyamunite Ca(U02)2(V04)2.5-8.5 Hz0
Uraninite U02
Xenotime YPO4
Zircon ZrSiO4
14.0
8-9
14.1
7.2
4.6-6.2
***
7.8
7.1-8.3
17.9
14.0
9.8
3-10
14.0
9.4
13.0
14.0
52.4
*
-
*
-
48-50
**
-
53
-
-
-
-
-
-
**
-
-
-
-
88
-
*
-
-
***
32-36
45-48
88
***
**
a: Percents except as noted: *** = 0.5-3%; ** = O.l-0.5%; * = 0.001-O.1%. See also [4, Appendix].

3. VAN SCHMUS 285
TABLE 3. K, U, and Th Abundances in the Earth
Rock or System
U Th Rb Sm Ref.
(wm) (wm) (mm) (ppm)
USGS G-l granite 4.45 3.4 50 220
USGS G-2 granite 3.67 3.0 24 168
USGS RGM-1 rhyolite 3.49 5.8 13 154
USGS STM-1 nepheline syenite 3.54 9.1 27 113
USGS GSP- 1 granodiorite 4.50 2.0 104 254
USGS QLO-I quartz latite 2.90 5.8 13 68
USGS AGV- 1 andesite 2.35 1.9 6.4 67
USGS BCR-1 basalt 1.38 1.7 6.0 47
USGS W-l diabase 0.52 0.6 2.4 21
USGS BHVO- 1 basalt 0.43 0.5 0.9 9
USGS PCC-I peridotite 0.001 0.005 0.01 0.063
USGS DTS-1 dunite 0.001 0.004 0.01 0.053
USGS MAG- 1 marine mud 2.96 2.8 12.2 186
USGS SCo-1 shale 2.20 3.1 9.5 122
USGS SDC-1 mica schist 2.71 3.1 11.4 129
8
7
27
6
6.7
4
0.008
0.004
7
7
5,15
5,15
7
5,15
7
7
7
5,15
7
7
515
5,15
5,15
Avg Low-Ca granite 4.20 4.7 20 170 7.1 21
Avg. basalt 0.83 0.9 2.7 30 6.9 21
Avg. ultramafic rocks 0.003 0.001 0.004 0.13 1.1 21
Avg. shale 2.66 3.7 12 140 7.0 21
Avg. sandstone 1.07 1.7 5.5 60 1.9 21
Avg. carbonate 0.27 2.2 1.7 3 0.6 21
Avg. upper continental crust
0 ,r 1, 0
Lower continental crust
Avg. continental crust
0 11 ,,
Oceanic crust (basaltic layer)
2.7 2.5 10.5
2.8 2.80 10.7
0.28 0.28 1.06
1.27 1.25 4.8
0.91 0.91 3.5
0.1250 0.10 0.22
5.6 19
4.5 20, Table 2.15
3.17 20, Table 4.4
3.7 20, Table 3.3
3.5 20, Table 3.5
3.3 20, Table 11.6
Bulk Silicate Earth (BSE)
( = primitive mantle)
0.0240 0.021
0.023 1 0.021
0.0258 0.0203
0.0180 0.018
0.0266 0.0208
0.0235 0.0202
0.084
110
112
5.3
42
32
2.2
0.635
0.742
0.535
0.55
0.444
0.52
0.387
0.347
0.380
0.416
14, Table 1
23, Table 2
10, Table 1
20, Table 1I.3
9
Average BSE
Bulk Earth
Cl Chondrites (volatile free) 0.0854
0.0200
0.0159
0.020
0.014
0.0122
0.08 13
0.064
0.0764
0.074
0.052
0.0425
0.616
3.45
22, Table 7
BSE x 0.675
0.23 1 I, recal. in 20
representative, but even in some of these cases
uncertainties of a factor of 2 or more are possible for trace
constituents.
Even though K, U, and Th are chemically dissimilar
from each other, their LIL character means that all three
elements tend to follow one another on average when bulk
components of the Earth are considered. These
relationships have been used extensively in estimating the
bulk composition of the Earth and its major sub-units
(Table 3). Thus, the K/U ratio for the bulk Earth,
primitive mantle, and continental crust is estimated at ca.
1.Oto 1.3 x IO4 [24, 111,and the Th/U ratio is about 3.7 to
4.0. These relationships can, in turn, be used with other
geochemical or geophysical constraints to put realistic
limits on the abundances of these elements in the bulk
Earth. The three main ways of doing so are (a)
cosmochemical arguments [e.g., 23, 161,(b) assuming that
most (ca. 75 + 25%) of the Earth’s radiogenic 40Ar is now

4. 286 NATURAL RADIOACTIVITY
in the atmosphere and was produced by the decay of 4oK,
and (c) comparison with mean annual terrestrial heat flow
[e.g., 91. All of these have significant uncertainties
associated with them, but they nontheless yield
comparable and consistent results, giving substantial
confidence in the values for bulk Earth given in Table 3.
3. DECAY MODES
3.1. 4oK Decay.
4oK undergoes branching decay to 40Ca (via p-) and
40Ar (via electron capture), both of which are stable; the
decay scheme for 4oK is shown in Figure 1. The total
decay constant, h, is 5.543 x lo-lo yr-l [18], with a 10.5
percent probability of decaying primarily by electron
capture to 40Ar @EC = 0.581 x lo-lo yr-1) and an 89.5
percent probability of decaying to 40Ca via p- emission
(hp = 4.962 x IO-lo yr-1). All of the decay to 40Ca is
directly to the ground state, but most of the decay to 40Ar
is to an excited state, followed by subsequent isomeric
decay to stable 4oAr with emission of 1.46 MeV y-rays.
Kelley et al. [121 determined the spectrum of p- particles
emitted in the decay to 40Ca, obtaining a mean energy of
0.60 MeV (Fig. 2), or about 45% of the total (1.32 MeV);
the remainder, 0.72 MeV (55%), is carried away by
neutrinos. This spectrum is significantly different from
the average for p- decay, in which about 213 of the energy
is carried away by neutrinos [8].
Energy (MeV)
Fig. 1: Simplified decay scheme for 4oK based on decay
constants used for geochronology [ 181and energy (mass)
differences between 4oK and 40Ca, 4oAr.
3.2. U and Th Decay Series
The isotopes 232Th, 235U, and 238U do not decay
directly to a stable product, but achieve ultimate stability
through a succession of et and p- decays, including several
minor closed branches (e.g., branches that converge a step
later to the same subsequent product). Figure 3 and
Tables 4-6 summarize the principal steps in the uranium
and thorium decay series; full details on each series can be
derived from more detailed references [e.g., 131. The
exact (geochronologic) decay constants for the parent
isotopes are: h23g = 1.55125 x IO-lo yr-l; h235 = 9.8485
x lo-lo yr-l; and 1232 = 4.9475 x 10-l 1yr ml [18].
Within the 238U decay series there are significant
intermediate decay products that exist naturally in secular
equilibrium. The more notable are 234U, 230Th, and
231Pa, which are useful in geochronology [6], 226Ra,
which has a variety of uses, and 222Rn, which has
potentially serious environmental consequences [4, ch.
121.
I
- 1.51 MeV 1
“OAr
(stable)
- 1.32 MeV
40Ca
(stable)
3.3. Gamma Radiation
The major penetrative natural radioactivity is ‘y- Fig. 2: Spectrum of beta-particle energies for the decay of
radiation that accompanies many a and p- transitions. 4oK to 4oCa [121.

5. 234,-h - 2381
I
234Pa
I
214pb c218po +222Rn t226Ra +23oTh + 2341
I
214Bi
I
2lOpb tz’4Po + a Decay
I
2loBi pm Decay
I
206pbd’oPo
231Th 4-2351
I
227~~t231 pa
I
2llpb+215p,, t2lgRnc223Rat227Th
I
!07TI-2llBi
I
*07Pb
228Ra -232Th
I
228~~
I
21 Zpb 416po c220Rn +*24Ra +-*28Th
I
!08~1 -212Bi
136% 164%
208pb b-21 2Po
Fig. 3: Chart showing the principal steps in the decay
series for 238U, 235U, and 232Th (Tables 4 through 6).
Minor branching steps have been omitted.
TABLE 4. Principal Steps in the 238U Decay Series
Step Parent Half-life Decay Daughter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
4.47 x 109 y Alpha
24.1 d Beta
1.17 m Beta
2.44 x lo5 y Alpha
7.7 x 104 y Alpha
1.60 x lo3 y Alpha
3.82 d Alpha
3.05 m Alpha
26.8 m Beta
19.8 m Beta
1.64 x 1O-4s Alpha
22.3 y Beta
5.01 d Beta
138.4 d Alpha
234Th
234Pa
234~
230Th
226Ra
222Rn
2’8Po
214Pb
214Bi
2’4Po
2’oPb
2IOBi
2’OPo
206Pb
(stable)
VAN SCHMUS 287
TABLE 5. Principal Steps in the 235U Decay Series
Step Parent Half-life Decay Daughter
1 235~ 7.04 x lo* y Alpha 231Th
2 231Th 25.52 h Beta 231Pa
3 231Pa 3.28 x lo4 y Alpha 227Ac
4 227Ac 21.77 y Beta 227Th
5 227Th 18.72 d Alpha 223Ra
6 223Ra 11.43 d Alpha 219Rn
7 219Rn 3.96 s Alpha 2’5Po
8 215Po 1.78 x low3 s Alpha 2’1Pb
9 211Pb 36.1 m Beta 21IBi
10 211Bi 2.14 m Alpha 207Tl
11 207Tl 4.77 m Beta 207Pb
(stable)
Table 6. Principal Steps in the 232Th Decay Series
Step Parent Half-life Decay Daughter
1 232Th 1.40 x IO’O y Alpha 228Ra
2 228Ra 5.75 y Beta 228Ac
3 228Ac 6.13 h Beta 228Th
4 228Th 1.913 y Alpha 224Ra
5 224Ra 3.66 d Alpha 220Rn
6 220Rn 55.6 s Alpha 2’6Po
7 2’6Po 0.15 s Alpha 212Pb
8 2’2Pb 10.64 h Beta 2I2Bi
9a 212Bi 60.6 m Beta 212Po
(64%)
9b 212Bi 60.6 m Alpha 2O8Tl
(36%)
10a 2’2Po 2.98 x 10W7s Alpha 208Pb
10b 208Tl 3.053 m Beta (%?
(stable)
This radiation is widely used in geophysical and
geochemical prospecting, including well logging. The
major y-radiations from K, U and Th are summarized in
Table 7 and Figure 4. No y-rays for 235U are given
because its low natural abundance (238U/235U = 137.88
[18]) means that the intensity of its major y-rays would
still be minor compared to those from 238U, and hence are
not detectable for all practical purposes. Of the y-rays
shown in Table 7, the main ones used as diagnostic
radiations are 1.461 MeV (40K), 1.765 MeV (238U), and
2.615 MeV (232Th); most of the others are either too low
in abundance for easy measurement by routine methods or

6. 288 NATURAL RADIOACTIVITY
TABLE 7. Gamma Rays from Major Natural Nuclidesa
Energy
Parent Nuclides (MeV) Freq.b
4OK 4OK 1.461 11
232Th 228Ac 0.210 4
212Pb 0.239 43
224Ra 0.241 5
208Tl 0.277 3
212Pb 0.300 3
228Ac 0.339 12
228Ac 0.463 5
208Tl 0.511 8
208Tl 0.583 31
212Bi 0.727 6
208Tl 0.860 4
228Ac 0.911 27
228Ac 0.964 5
228Ac 0.969 16
228Ac 1.588 3
208Tl 2.615 36
238~ 0.186 3
0.242 6
0.295 19
0.352 37
0.609 46
0.768 5
0.934 3
1.120 15
1.238 6
1.378 4
1.408 3
1.730 3
1.765 16
2.204 5
aCompiled from [131;only energies > 0.100 MeV
tabulated.
bEvents per 100 decays of primary parent; secular
equilibrium assumed.
overlap radiations from another element (e.g., 0.58 and
0.61 MeV), although in certain applications they can be
used. Durrance [4, ch. 91 gives a detailed review of
geochemical applications for y-ray spectra.
4. RADIOGENIC HEAT PRODUCTION
In terms of the geophysical behavior of the earth, one
of the most important applications of radionuclides is in
40
1 40K
0.0 1 .o
232Th
Lc
z
c-i
_I.
2.0 3.0
Energy (MeV)
Fig. 4: Principal gamma-rays emitted during the decay of
4oK, 238U, and 232Th (Table 7). Spectra include gamma-
rays from intermediate daughter products in secular
equilibrium with parent for 238U and 232Th.
modeling the thermal state and thermal history of the
earth and planets. In this context it is necessary to know
the specific heat production of the major heat-producing
radionuclides: 4oK, 232Th, 235U, and 238U.
In the radioactive decay process, a portion of the
mass of each decaying nuclide is converted to energy.
Most of this is the kinetic energy of emitted alpha or beta
particles or of electromagnetic radiation (‘y-rays), which is
fully absorbed by rocks within the Earth and converted
quantitatively to heat. For p- decays, however, part of the
energy is carried by emitted neutrinos. Because neutrinos
are not easily captured, they pass completely out of the
earth, and that portion of the decay energy is lost to space.
In determining the radiogenic heat production of a
particular radionuclide, it is therefore necessary to correct
for the loss of neutrino energy by p- emitters.
All four of the major heat producing isotopes involve
p- decay. For 4oK there is the p- decay branch to 40Ca.
Evaluation of the mean p- energy for this decay branch
was based on the p- spectrum measured by Kelly et al.

7. TABLE 8. Specific Heat Production for Major Natural Radionuclides
Element: Potassium
Isotope: 4OK
Thorium
232Th
Uranium
235~ 238u
Isotopic abundance (weight percent)
Decay constant, h (year-l)
Total decay energy (MeVldecay)
Beta decay energy (MeVldecay)
Beta energy lost as neutrinos (MeV/decay)
Total energy retained in Earth (MeV/decay)
Specific isotopic heat production (Cal/g-year)
(1 I, 1, !f
WW/kg)
Specific elemental heat production (Cal/g-year)
1, 0 0 ,!
#W/kg)
0.0119
5.54 x 10-10
I.340 a
1.181 a
0.650 c
0.690
0.220
29.17
2.6 x 1O-5
3.45 x 10-3
100.00 0.71 99.28
4.95 x 10-l’ 9.85 x 10-10 1.551 x 10-10
42.66 b 46.40 b 51.70b
3.5 b 3.0 ‘J 6.3 b
2.3 d 2.0 d 4.2 d
40.4 44.4 47.5
0.199 4.29 0.714
26.38 568.7 94.65
0.199 0.740
26.38 98.10
aAveraged for branching decay: 89.5% p- @ 1.32 MeV + 10.5% E.C. @ 1.51 MeV.
bSummed for entire decay series.
CBasedon mean decay energy for p- of 0.60 MeV; 55% of total p- energy lost as neutrinos [ 121.
dAssumed average neutrino loss = 2/3 of total B- energy [8, p. 521.
TABLE 9. Present Radiogenic Heat Production in Selected Rock Units
Annual heat productiona
Rock unitb Due to K Due to Th Due to U Total
GSP- 1 “granodiorite” 1.17 20.70 1.48 23.35c
G- 1 “granite” 1.16 9.95 2.52 13.63
Av upper continental crust 0.7 2.09 1.85 4.64
AGV- 1 “andesite” 0.61 1.27 1.41 3.29
Av continental crust 0.33 0.50 0.74 1.56
BHVO- 1 “oceanic basalt” 0.11 0.18 0.37 0.66
PCC- 1 “peridotite” 0.0003 0.0020 0.0037 0.0060
Bulk Earth 0.0052 0.0147 0.0148 0.0347
aIn peal/g-year; multiply x 0.004184 for J/kg-year.
bElemental abundances from Table 7.
CNot a typical granodiorite, but it illustrates natural range due to granitic rocks high in Th or U.
[ 121. The p- emitters in the 232Th, 235U, and 238U decay
series (Tables 4 to 6) constitute only a small fraction of
their total decay energy, so individual determinations of
p- spectra were not used to determine neutrino energy
loss. Instead, the general relationship that, on average,
neutrinos represent 213 of the decay energy for B- decay
[8 p. 521 was used. Table 8 [after 221 summarizes the
information needed to determine specific heat production
and the resulting values; this compilation was based on
the data of Lederer and Shirley [131 for individual
nuclides except that the ratio of electron capture to beta
decay for 4oK is based on the recommended
geochronological decay constants for that isotope [18].
Total decay energies were based on the mass differences
between the starting radionuclides and their stable end
products (A E = Amc*). Perhaps one of the most
interesting results of this determination of specific heat
production is that the refined values listed in Table 8 do
not differ significantly from those reported nearly 40
years ago [2; see also 17, ch. 71 and Stein [this volume].
The results are given in both the traditional c.g.s. units
@Cal/g-yr) as well as in SI units @W/kg).
Table 9 represents some typical ranges of specific
heat production for various rock types, ranging from U,

8. 290 NATURAL RADIOACTIVITY
TABLE 10. Past Heat Production in the Bulk Eartha
Timeb
Pa)
Due to K Due to Th Due to U Total
Abs.C Rel.d Abs. Rel. Abs. Rel. Abs. Rel.
0.0 5.2 0.15 14.7 0.42 14.8 0.43 34.7 1.00
0.5 6.9 0.20 15.1 0.44 16.3 0.47 38.3 1.10
1.0 9.1 0.26 15.5 0.45 18.2 0.52 42.8 1.23
1.5 12.0 0.35 15.9 0.46 20.6 0.59 48.5 1.40
2.0 15.9 0.46 16.3 0.47 23.7 0.68 55.9 1.61
2.5 20.9 0.60 16.7 0.48 28.0 0.81 65.6 1.89
3.0 27.6 0.80 17.1 0.49 34.3 0.99 79.0 2.28
3.5 36.4 1.05 17.5 0.50 43.5 1.25 97.4 2.81
4.0 48. I 1.39 17.9 0.52 57.7 1.66 123.7 3.56
4.5 63.4 1.83 18.4 0.53 79.7 2.30 161.5 4.65
aAssumed present abundances: K = 200 ppm, Th = 74 ppb, U = 20 ppb (K: U : Th = 10,000 : 1 : 3.7).
bBillions of years ago.
CAbs. = absolute in 10m9Cal/g-year; multiply x 0.004184 for J/kg-year.
dRel. = relative to present total.
Th-rich granite (atypical) through intermediate to mafic 75 I I I I I I I I I
and ultramafic rock types. One should keep in mind, with
II
regard to Tables 3 and 9, that attempts to model the
E
P 4-
thermal history of terrestrial components are only 2
approximations; the abundances of K, U, and Th for any 5
specific case (e.g., “continental crust”) are not known well
= 3-
B
enough to permit precise interpretations.
Table 10 and Figure 5 summarize past heat 2 2-
production in the whole earth for one assumed buIk
a
v
composition [22]. For the model used, the Th/U ratio is
probably accurate to better than IO%, but the K/U ratio
21
9
may be somewhat low (cf. Table 3), and the absolute
.-
i;r
concentrations for some elements could also be uncertain 30
= 0 1 2 3 4 5
to a factor of 50% or more. Thus, the data in Table 10
and Figure 5 should only be considered as representative
Time (Billion Years Ago)
of possible past histories and not accepted as the best
model. However, they do give a good indication of the Fig. 5. Relative heat production within the Earth during
relative contributions of K, U, Th to heat production in the the past. Projected back in time using data from Tables 9
earth now and in the past. and 10.
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