Page 135 - Environmental Control in Petroleum Engineering

122 Environmental Control in Petroleum Engineering

and a positron (antielectron). The neutron remains in the nucleus and
the positron is emitted. Gamma decay is the lowering of the energy
of a nucleus through the emission of a photon of electromagnetic
radiation. In most cases, gamma decay is of most concern in the
petroleum industry.
Radioactive decay is the spontaneous change of a nucleus of an
atom. Because it is a random process, there is no way to predict when
a particular nucleus will decay. The decay of large numbers of atoms
can be modeled through a decay probability, however. When a large
number of nuclei are considered, the number of radioactive decay
events is proportional to the number of nuclei present,

dN , XT / ,
_ = XN(t) (3-6)
dt
where \ is a constant of proportionality that depends on the type of
nucleus and is a measure of the probability of decay for the nucleus.
N is the number of nuclei present. If multiple decay modes are
possible for a given nucleus, X is the sum of the decay probabilities
of each decay mode.
This equation can be solved for the number of nuclei as a function
of time:

Xt
N(t) = N(0)e- (3-7)

The most common measure of the rate of decay of radioactive
nuclei is the time for half of the nuclei to decay. This time is called
the half-life and can be expressed as

1 XT
- XT (3-8)
N(0) 2

where T is the half-life. The decay probability can be expressed in
terms of the half-life, yielding the following equation for the number
of nuclei as a function of time:

(3-9)