The rate of decay of a radioactive material is proportional
to the number of undecayed atoms in the sample.
This may be expressed mathematically as shown:
dN/dt
N
which may be
written as
dN/dt = N
The negative sign tells us that N diminishes as time
passes.
of
the random nature of radioactivity
Applying calculus to the above equation leads to the result:
This is an exponential equation. We may interpret the
result in a number of ways:


Activity
Activity is the number of disintegrations per second which occur in
a radioactive sample. It is a measure of the strength of the source.
The SI unit of activity is the Bequerel (Bq).
Decay
constant
This is the probability per second that a nucleus will disintegrate.
Halflife
Although radioactivity is a random process, there is an
underlying order to it. It can be shown mathematically (and has been
verified by experiment) that the time taken for half the radioactive
nuclei in a sample to decay is a constant value. We call this time
interval the Halflife, denoted by T.
It can be shown that T = 0.693/
By analysing the formula it can be seen that the value of T depends
only on the decay constant
and is therefore independent of the number of atoms present N, or
the time t, at which the measurements were taken.