Using Eq. (3.4)
At= 150 ×e−0.1155×^5
= 150 ×e−0.5775
= 150 ×0.5613
=84.2 mCi (3.1 GBq) at 3 p.m.
Problem 3.3
If a radionuclide decays at a rate of 30%/hr, what is its half-life?
Answer
l=0.3 hr−^1
Problem 3.4
If 11% of 99mTc-labeled diisopropyliminodiacetic acid (DISIDA) is elimi-
nated via renal excretion, 35% by fecal excretion, and 3.5% by perspiration
in 5 hr from the human body, what is the effective half-life of the radio-
pharmaceutical (Tp=6 hr for 99mTc)?
Answer
Total biological elimination =11% +35% +3.5%
=49.5% in 5 hr
Therefore,Tb≈5hr
Tp=6hr
Successive Decay Equations
General Equation
In the preceding section, we derived equations for the activity of any
radionuclide that is decaying. Here we shall derive equations for the activ-
ity of a radionuclide that is growing from another radionuclide and at the
same time is itself decaying.
If a parent radionuclide pdecays to a daughter radionuclide d, which in
turn decays to another radionuclide (i.e.,p→d→), then the rate of growth
of dbecomes
T
TT
TT
e
bp
bp
=
×
+
=
×
+
==
56
56
30
11
27.hr
t 12
0 693 0 693
03
== = 231
..
.
.
l
hr hr
l=
0 693
12
.
t
Successive Decay Equations 29