Biomedical Engineering Reference
In-Depth Information
Alternatively, we can use Eq. (4.24) with
T
= 5730 × 365 × 24 × 3600 = 1.81 × 10
11
s,
obtaining
4.17 × 10
23
10
11
Bq g
-1
SA
=
10
11
=
1.65
×
(4.29)
14
×
1.81
×
1.65
×
10
11
Bq g
-1
3.7
4.46 Ci g
-1
,
=
=
(4.30)
10
10
BqCi
-1
×
in agreement with (4.28).
Specific activity need not apply to a pure radionuclide. For example,
14
C produced
by the
14
N(n,p)
14
C reaction can be extracted chemically as a “carrier-free” radionu-
clide, that is, without the presence of nonradioactive carbon isotopes. Its specific
activity would be that calculated in the previous example. A different example is af-
forded by
60
Co, which is produced by neutron absorption in a sample of
59
Co (100%
abundant), the reaction being
59
Co(n,
γ
)
60
Co. The specific activity of the sample de-
pends on its radiation history, which determines the fraction of cobalt atoms that
are made radioactive. Specific activity is also used to express the concentration of
activity in solution; for example,
µ
Ci mL
-1
or Bq L
-1
.
4.4
Serial Radioactive Decay
In this section we describe the activity of a sample in which one radionuclide pro-
duces one or more radioactive offspring in a chain. Several important cases will be
discussed.
Secular Equilibrium (
T
1
T
2
)
First, we calculate the total activity present at any time when a long-lived parent (1)
decays into a relatively short-lived daughter (2), which, in turn, decays into a sta-
ble nuclide. The half-lives of the two radionuclides are such that
T
1
T
2
; and we
consider intervals of time that are short compared with
T
1
, so that the activity
A
1
of the parent can be treated as constant. The total activity at any time is
A
1
plus the
activity
A
2
of the daughter, on which we now focus. The rate of change, d
N
2
/d
t
,in
the number of daughter atoms
N
2
per unit time is equal to the rate at which they
are produced,
A
1
, minus their rate of decay,
λ
2
N
2
:
d
N
2
d
t
=
A
1
-
λ
2
N
2
.
(4.31)
To solve for
N
2
, we first separate variables by writing
d
N
2
A
1
-
(4.32)
λ
2
N
2
=
d
t
,
