Box 3.3 Kinetics of radioactive decay II: the U-Th-Pb system
each of the naturally occurring isotopes of the trace ele-
ments uranium ( 235 U and 238 U) and thorium ( 232 th) decays
through a complex series of intermediate radioactive
nuclides to an isotope of lead (pb). this is illustrated for
the decay of 238 U to 206 pb in Figure 3.3.1; similar flow dia-
grams can be drawn for the decay of 235 U to 207 pb and for
232 th to 208 pb. together these decay chains form the basis
of U-th-pb radiometric dating.
Despite its complexity, the overall decay process in
Figure 3.3.1 conforms to first-order kinetics, because the
first step in the process (to 234 th, a short-lived radioactive
isotope of thorium) happens to be the slowest. the kinetic
complexities of the subsequent branching decay series are
immaterial because the rate of the whole process is con-
trolled by this one rate-determining step , just as the flow of
water from the end of a hose can be controlled by adjusting
the tap supplying it. this phenomenon is not limited to radi-
oactive decay: the kinetics of some complex chemical reac-
tions are also controlled by a slow, rate-determining step.
For every uranium or thorium nucleus that decays to
lead within the earth, between 6 and 8 alpha particles are
released. By capturing electrons the α -particles become
4 he atoms, which form the bulk of the helium flux escaping
from the earth's interior.
all but one of the nuclides involved in Figure 3.3.1 are
radioactive solids, likely to be retained within the mineral
hosting the original U. the sole exception is 222 rn, one of
the isotopes of the inert gas radon, whose mobility pre-
sents an environmental hazard in areas underlain by high-
U-th rocks like granites, as discussed in Box 9.9.
α -decay step*
β -decay step*
*See Box 10.1
Figure 3.3.1 the chain of radioactive decay steps by which 238 U (also written 'uranium-238') decays to 206 pb (lead-206).
their reaction rates when the temperature is raised by
just 10°C (see Exercise 3.2 at the end of this chapter).
The temperature-dependence of reaction rates is par-
ticularly significant for geological processes, whose
environments can vary in temperature over many
hundreds of degrees.
Most reaction rates vary with temperature in the
manner shown in Figure 3.2a. The Swedish physical
chemist Svante August Arrhenius 1 showed in the
late 1880s that this behaviour could be represented
Arrhenius is also notable for being the first scientist to postu-
late (in 1896) a climatic 'greenhouse effect' arising from the
presence of CO 2 in the atmosphere, and for recognizing even
in the nineteenth century that mankind's burning of fossil car-
bon contributed to global warming.