Biomedical Engineering Reference
In-Depth Information
4
Radioactive Decay
4.1
Activity
The rate of decay, or transformation, of a radionuclide is described by its activity,
that is, by the number of atoms that decay per unit time. The unit of activity is
the becquerel (Bq), defined as one disintegration per second:
1
Bq
=
1
s
-1
.The
traditional unit of activity is the curie (Ci), which was originally the activity ascribed
to 1 g of
226
Ra. The curie is now defined as
1
Ci
=
10
10
Bq, exactly.
3.7
×
4.2
Exponential Decay
The activity of a pure radionuclide decreases exponentially with time, as we now
show. If
N
represents the number of atoms of a radionuclide in a sample at any
given time, then the change
d
N
in the number during a short time
d
t
is propor-
tional to
N
and to
d
t
. Letting
λ
be the constant of proportionality, we write
d
N
=
-
λ
N
d
t
.
(4.1)
The negative sign is needed because
N
decreases as the time
t
increases. The quan-
tity
λ
is called the decay, or transformation, constant; it has the dimensions of in-
verse time (e.g.,
s
-1
). The decay rate, or activity,
A
,isgivenby
A
= -
d
N
d
t
=
λ
N
.
(4.2)
We separate the variables in Eq. (4.1) by writing
d
N
N
=
-
d
t
.
(4.3)
λ
Integration of both sides gives
ln
N
=
-
t
+
c
,
(4.4)
λ
