biodex ATOMLAB 100 - Explanation: Calculator Method; Explanation: Decay Factor Method

EXPLANATION OF DECAY CALCULATION METHODS
The radioactivity of an isotope can be calculated as it
decays using the following expression:
A
f
= A
i
e
-λt
where
A
f
= final activity at the end of the decay time;
A
i
= initial activity measured at some starting time;
t = net decay time in units inverse to λ; and
λ = (lamda) decay constant specific to the radioisotope.
λ = ln (2) / T
1/2
= 0.693 / T
1/2
where
T
1/2
= half life specific to the radioisotope.
So, using a calculator with the e
x
function, decay calcula-
tions can easily be performed, as shown in the first section
of this appendix.
If you do not have a calculator with the e
x
function, the
above expression can be rewritten as follows:
A
f
= X A
i
where
X = X
n
(N) x X
r
(R)
N = integer number of half lives in time t; and
R = decimal remainder after dividing t by T
1/2
. To verify this,
remember three important relations regarding exponentials:
e
(A + B)
= e
A
x e
B
;
e
ln(A)
= A ; and
ATOMLAB Dose Calibrator Operation Manual Appendix C
Biodex Medical Systems C-6 Release 2.0
Calculator
Method
Decay Factor
Method