10.5 Using Equation 10.10 for δ 18 O = −1.2, −1.3 and −1.4‰,
the temperatures obtained are 21.8, 22.3 and 22.8 °C.
The best estimate is therefore 22.3 ± 0.5 °C.
11.2 (a) The integrated rate equation for radioactive
decay (Equation 3.2.4 in Box 3.2) is:
/ ( ) = λ
where n 26 represents the changing amount of
26 Al (e.g. in a planetary body), and n 2 0 is the
value when t = 0, and λ 26 is the decay constant of
26 Al. After one half-life ( t = 0.7 million years):
ln nn t
Calcite δ 18 O
Seawater δ 18 O
/ ( ) =×λ
Therefore λ 26 = 0.99 × 10 −6 year −1 .
(b) Heat output is proportional to the rate of decay
of 26 Al and therefore to its abundance. When
26 Al has decayed to 1% of original value:
The δ 18 O of seawater is believed to vary by about
1‰ (±0.5‰) between glacial maximum and inter-
glacial conditions owing to variation in the amount
of 'light' (low-δ 18 O) water locked up in polar
ice-sheets. Potentially this factor introduces an
uncertainty of ±2.3 °C in the temperature estimate.
) =× −
1001 09910 6
Calcite δ 18 O
Seawater δ 18 O
Therefore t = ln(100) × 1.01 × 10 6 years = 4.6 mil-
lion years. For this heat source to have been
significant during planet formation, planets
must have formed within a few million years
of nucleosynthesis of 26 Al.
11.3 From their atomic numbers, they are xenon Xe
( Z = 54, inert gas), caesium Cs ( Z = 55, subgroup
Ia), barium Ba ( Z = 56, IIa), hafnium Hf ( Z = 72,
IVa), tantalum Ta ( Z = 73, Va) and tungsten W
( Z = 74, VIa).
11.4 In the giant impact that is believed to have created
the Moon, it is likely that the impactor's mantle
completely vaporized before re-condensing to
form the Moon. Through taking longer to con-
dense, the volatile elements are more likely to
have been swept away by the solar wind before
incorporation into the solid Moon. Modelling
suggests that most of the metallic core of the
impactor became incorporated into the Earth's
core, rather than being available in orbit for incor-
poration in the Moon.
11.5 (a) Isotopes are nuclides that share the same
value of atomic number Z (i.e. have the same
number of protons and form part of the
same element) but possess different numbers
(b) Only the elements from C to Fe are products of
nuclear fusion in stars (Figure 11.3). The ele-
ments H, He and Li are believed to be prod-
ucts of nucleosynthesis in the primordial Big
Bang , not in stars (Figure 11.2.1) The elements
Be and B are bypassed by stellar fusion reac-
tions and are mainly formed by spallation
of heavier nuclei. Elements heavier than Fe
10.6 (a) Correct.
(b) Incorrect: 87 Sr is a naturally occurring isotope;
some 87 Sr in the rock was already present at
the time of its formation (Figure 10.1b).
(d) Incorrect: 143 Nd/ 144 Nd grows more slowly in con-
tinental crust than in the mantle (Figure 10.6b).
(e) Partially incorrect: only artefacts and rocks that
(1) incorporate carbon of biological origin
(e.g. carbonized tree debris caught up in a
volcanic deposit) and (2) are young enough
(age < 40 ka) can be dated using 14 C.
(f) Incorrect: the mass-independent fractionation
of S isotopes in Archaean times illustrates one
instance where this statement does not apply
11.1 There are no naturally occurring nuclides (only
short-lived radionuclides) at N values 19, 35, 39,
45, 61, 89 and 123, nor at Z values 43 (technetium)
and 61 (promethium). These are all odd numbers.
Odd values of Z and N signify half-filled nuclear
orbitals, and such nuclei are more prone to trans-
mutation into other elements by fusion, neutron
capture or radioactive decay than even-valued