Physics and Radiobiology of Nuclear Medicine

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