Specific activity is at times expressed as radioactivity per mole of a
labeled compound, for example, mCi/mole (MBq/mole) or mCi/mmole
(MBq/mmole) for^3 H-,^14 C-, and^35 S-labeled compounds.
The specific activity of a carrier-free (see Chapter 5) radionuclide sample
is related to its half-life: the shorter the half-life, the higher the specific activ-
ity. The specific activity of a carrier-free radionuclide with mass number A
and half-life t1/2in hours can be calculated as follows:
Suppose 1 mg of a carrier-free radionuclide is present in the sample.
Number of atoms in the sample
Decay constant
Thus, disintegration rate D=lN
Thus, specific activity (mCi/mg)
(3.13)
where Ais the mass number of the radionuclide, and t1/2is the half-life of
the radionuclide in hours.
From Eq. (3.13), specific activities of carrier-free 99mTc and^131 I can be cal-
culated as 5.27 × 106 mCi/mg (1.95 × 105 GBq/mg) and 1.25 × 105 mCi/mg
(4.6 × 103 GBq/mg), respectively.
Calculation
Some examples related to the calculation of radioactivity and its decay
follow:
Problem 3.1
Calculate the total number of atoms and total mass of^201 Tl present in
10 mCi (370 MBq) of^201 Tl (t1/2=3.04 d).
=
×
×
313 10^9
12
.
At
=
×
×× ×
1 1589 10
37 10
17
12 7
.
At.
=
×
×
1 1589 10^17
12
.
At
dps
=
××
×× ×
0 693 6 02 10
60 60
20
12
..
tA
l=
××
0 693 −
12 60 60
. sec 1
t
=
602 10. ×^20
A
=
×
××
110 −
602 10
3
23
A
.
Calculation 27