e
AB
= (e
A
)
B
.
Now t / T
1/2
= N + R
where N is an integer, and R is the remainder less than 1.
For t = 32.5 hours and T
1/2
= 6.007 hours,
t / T
1/2
= 32.5 / 6.007 = 5.410
so that N = 5 and R = 0.410.
Now, to simplify calculations, we can write the above rela-
tion as:
A
f
= A
i
e
-λt
= A
i
e
-ln (2)t / T
1/2
A
f
= A
i
e
-ln (2)(N + R)
= A
i
e
-ln (2)N
x e
-ln (2)R
= A
i
x X
n
(N) x X
r
(R)
X
n
(N) = e
-ln (2)N
= (e
ln (2)
)
-N
= 2
-N
This expression is used to generate the values in Table 1.
X
r
(R) = e
-ln (2)R
This expression is used to generate the Decay Factor Chart
for values of R from 0.001 to 0.999.
For the above example
X
n
(5) = 0.03125
X
r
(0.410) = 0.75262
A
f
= X A
i
= [X
n
(N) x X
r
(R)] A
i
= [0.03125 x 0.75262] 43 mCi
A
f
= 1.01 mCi
ATOMLAB Dose Calibrator Operation Manual Appendix C
Biodex Medical Systems C-7 Release 2.0
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