Panasonic PT-DZ12000U Operating Instructions Manual page 21

-ët
A = A e
t o
t = ln(A / A ) / -ë
t
Where; A is the activity at the end of time 't'
t
A is the activity at the beginning
o
ë is 0.693 divided by the half-life
t is the decay time
Example: What is the % activity of Co-60 remaining 12 years
after it was produced ?
Co-60 half-life is 5.271 years
-ët
A = A e
t o
-0.693/5.271 x 12
A = 100e
t
Calculating the Activity of Progeny
A = A
d(t) p(o)
A is the activity of the progeny at the beginning
d(0)
A is the activity of the progeny at the end of time 't'
d(t)
A is the activity of the parent at the beginning
p(0)
Example: What is the activity of Tc-99m 14 hours after its
parent Mo-99 was produced ?
Mo-99 half-life is 66.02 hours, initial activity is 100 uCi
Tc-99 half-life is 6.0058 hours
A = A
d(t) p(o)
A = 100 uCi x 0.693/6.0058/(0.693/6.0058 - 0.693/66.02) x
d(t)
-0.693/66.02 x 14
(e
A = 100 uCi x 1.149 x (e
d(t)
A = 100 uCi x 1.149 x (0.8633 - 0.1989) = 76.3 uCi Tc-99m
d(t)
Radioactive Decay Calculation
0
x ë /(ë - ë ) x (e
d d p
x ë /(ë - ë ) x (e
d d p
-0.693/6.0058 x 14
- e
A = A / e
o t
half-life = -t x 0.693 / ln(A /A )
-1.578
= 100e
-ëpt -ëdt
- e
-ëpt -ëdt
- e
) + A
d(0)
-0.1470 -1.615
- e
-ët
= 100 x 0.206 = 20.6%
-ëdt
) + A e
d(0)
-ëdt
) + A e
d(0)
-0.693/6.0058 x 0)
e
) + 0
t 0