Geochronology and radiogenic tracers - Geochemistry: An Introduction - page 67

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Geochronology and radiogenic tracers

We have seen that radioactivity is not dependent on the chemical bonding of atoms, or on
temperature, or on pressure. Radioactivity can be described as an event whose probability
of occurrence per unit time is invariant. The probability that a radioactive nuclide will
decay per unit of time is denoted . This probability, better known as the decay constant,

is specific to the radioactive nuclide under consideration. Radioactive decay, like incoming
calls at a telephone exchange, is a prime example of a Poisson process, in which the number
of events is proportional to the time over which the observation is made. In the absence of
any other loss or gain, the proportion of parent atoms (or radioactive nuclides) disappearing
per unit of time t is constant:

λ

d P
P d t =− λ

(4.1)

For a number of parent atoms P = P 0 at time t = 0, this equation integrates as:

P 0 e − λ t

= =

P P ( t ) (4.2)

In this form, Eq. 4.2 is not generally useful for measuring ages. The half-life T 1 / 2 , which
is the time it takes for half of the parent nuclides to decay, is ln 2/ .Afterfive

half-lives, 97% of the radioactive isotopes have decayed away, and 99.6% have decayed
after eight half-lives. The product

λ ≈ 0.69 /λ

P measures the number of decay events per unit time.
It is commonly referred to as the activity of the radioactive nuclide P and denoted [ P ]. The
becquerel (Bq) is a unit equal to one decay event (count) per second. A liter of seawater has
an activity of 12 Bq, mostly because of the potassium-40 and uranium naturally dissolved
in it. The human body contains enough potassium-40 and carbon-14 to register an activity

λ