is
a measure of this. We may write:
A Level Physics Notes: Nuclear Physics - Radioactive Decay and Half Life
Any radioactive atom of a particular element with a certain number
of protons and neutrons has a fixed and constant probability of
decaying in a certain time period, usually taken as one second. The
decay constant,is
a measure of this. We may write:
(1)
The expression on the left hand side is the proportion of the N
atoms at the start of the time period that decay in that time
period.
is
the probability that an individual atom decays in the that second and
the negative sign means that
is
decreasing, or that atoms are decaying. We can show exponential decay
in more than one way. We can show a graph of mass of undecayed
substance – illustrated below, number of mols,
(the
activity), or N against t. All these graphs will show exponential
decay.
We can integrate (1) to find N in terms of t.
N in the equation above could be replaced by
(for
mass),(or
activity),
(number
of mols) and would still exhibit radioactive decay.
Half Life
The half life of a radioactive substance is the time take for half
of the material to decay. We can find an equation for the half
life
in
terms of
When
half the material has decayed,
