Geoscience Reference
In-Depth Information
Are the decay constants truly constant?
One may wonder how we can be so sure that decay constants (probability of decay per unit
time) remain constant throughout geological times. The answer is unambiguously that they
do and there are three strong lines of evidence for this:
1. The decay constants are measured by different techniques, counting of decay events and
accumulation of radiogenic isotopes, and give, within the errors of the measurements,
values with a typical precision of a fraction of a per mil to a few percent depending
on the nuclide. These values are very consistent for different laboratories throughout the
world.
2. The ages of any particular object, typically a meteorite, a lunar rock, or an ancient volcanic
sample are very consistent from one method to another, e.g.
238
U-
206
Pb,
40
K-
40
Ar, and
147
Sm-
143
Nd.
3. The interior of the Earth is kept hot by the decay of four radioactive nuclides,
238
U,
235
U,
232
Th, and
40
K. The energy liberated by the decay of each of these nuclides is dictated
by the equivalence of mass and energy discovered by Einstein and used every day to
produce energy in nuclear power plants. The decay energy is strictly a function of the
mass difference between the original nuclides and the decay products. Today, the rate at
which the Earth is heated by radioactivity is about 18 TW (1 TW
10
12
W), while the
Earth loses 42 TW through its surface (the rest is “fossil heat” inherited from accretion).
If instead the same amount of radioactive energy was released over a few thousand
years, the interior of the Earth would be hot enough for the planet to melt and even
evaporate entirely. The situation would be far worse than the thermal regime created
early on in the first millions of years of the Solar System history by the decay of
26
Al (see
below).
=
Although the decay constants can still be refined for dating purposes, it is very unlikely that
they could be very wrong or have substantially changed throughout geological time.
We assume that planetary material precipitates straight out of the nebular gas under
conditions of isotopic equilibrium and that the isotopic properties of the solar nebula
are those of the least differentiated material for which we have samples, the chondritic
meteorites. For
t
λ
−
1
,
P
becomes negligible and therefore the closed system condition
reads:
D
today
=
P
t
+
D
t
(12.10)
at all
t
, where
P
and
D
are the parent and daughter nuclides, respectively. Let us write this
equation for a sample (spl) and, as for the conventional isochron, let us divide it by the
number of atoms of a stable isotope
D
of
D
:
D
D
spl
today
=
D
D
spl
=
SN
P
P
spl
=
SN
P
D
spl
+
(12.11)
t
t
today
