Panasonic PT-DZ12000U

Radioactive Decay Calculation
to ot
A = A e A = A / e
-ët-ët
t0 t0
t = ln(A / A ) / -ë half-life = -t x 0.693 / ln(A /A )
t
Where; A is the activity at the end of time ‘t’
o
A is the activity at the beginning
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
to
A = A e
-ët
t
A = 100e = 100e = 100 x 0.206 = 20.6%
-0.693/5.271 x 12 -1.578
Calculating the Activity of Progeny
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(0)
A is the activity of the progeny at the beginning
d(t)
A is the activity of the progeny at the end of time ‘t’
p(0)
A is the activity of the parent at the beginning
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
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(t)
A = 100 uCi x 0.693/6.0058/(0.693/6.0058 - 0.693/66.02) x
d(0)
(e - e ) + A e
-0.693/66.02 x 14 -0.693/6.0058 x 14 -0.693/6.0058 x 0)
d(t)
A = 100 uCi x 1.149 x (e - e ) + 0
-0.1470 -1.615
d(t)
A = 100 uCi x 1.149 x (0.8633 - 0.1989) = 76.3 uCi Tc-99m
Radioactive Decay Calculation
to ot
A = A e A = A / e
-ët-ët
t0 t0
t = ln(A / A ) / -ë half-life = -t x 0.693 / ln(A /A )
t
Where; A is the activity at the end of time ‘t’
o
A is the activity at the beginning
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
to
A = A e
-ët
t
A = 100e = 100e = 100 x 0.206 = 20.6%
-0.693/5.271 x 12 -1.578
Calculating the Activity of Progeny
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(0)
A is the activity of the progeny at the beginning
d(t)
A is the activity of the progeny at the end of time ‘t’
p(0)
A is the activity of the parent at the beginning
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
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(t)
A = 100 uCi x 0.693/6.0058/(0.693/6.0058 - 0.693/66.02) x
d(0)
(e - e ) + A e
-0.693/66.02 x 14 -0.693/6.0058 x 14 -0.693/6.0058 x 0)
d(t)
A = 100 uCi x 1.149 x (e - e ) + 0
-0.1470 -1.615
d(t)
A = 100 uCi x 1.149 x (0.8633 - 0.1989) = 76.3 uCi Tc-99m
Radioactive Decay Calculation
to ot
A = A e A = A / e
-ët-ët
t0 t0
t = ln(A / A ) / -ë half-life = -t x 0.693 / ln(A /A )
t
Where; A is the activity at the end of time ‘t’
o
A is the activity at the beginning
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
to
A = A e
-ët
t
A = 100e = 100e = 100 x 0.206 = 20.6%
-0.693/5.271 x 12 -1.578
Calculating the Activity of Progeny
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(0)
A is the activity of the progeny at the beginning
d(t)
A is the activity of the progeny at the end of time ‘t’
p(0)
A is the activity of the parent at the beginning
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
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(t)
A = 100 uCi x 0.693/6.0058/(0.693/6.0058 - 0.693/66.02) x
d(0)
(e - e ) + A e
-0.693/66.02 x 14 -0.693/6.0058 x 14 -0.693/6.0058 x 0)
d(t)
A = 100 uCi x 1.149 x (e - e ) + 0
-0.1470 -1.615
d(t)
A = 100 uCi x 1.149 x (0.8633 - 0.1989) = 76.3 uCi Tc-99m
Radioactive Decay Calculation
to ot
A = A e A = A / e
-ët-ët
t0 t0
t = ln(A / A ) / -ë half-life = -t x 0.693 / ln(A /A )
t
Where; A is the activity at the end of time ‘t’
o
A is the activity at the beginning
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
to
A = A e
-ët
t
A = 100e = 100e = 100 x 0.206 = 20.6%
-0.693/5.271 x 12 -1.578
Calculating the Activity of Progeny
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(0)
A is the activity of the progeny at the beginning
d(t)
A is the activity of the progeny at the end of time ‘t’
p(0)
A is the activity of the parent at the beginning
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
d(t) p(o) d d p d(0)
A = A x ë /(ë - ë ) x (e - e ) + A e
-ëpt -ëdt -ëdt
d(t)
A = 100 uCi x 0.693/6.0058/(0.693/6.0058 - 0.693/66.02) x
d(0)
(e - e ) + A e
-0.693/66.02 x 14 -0.693/6.0058 x 14 -0.693/6.0058 x 0)
d(t)
A = 100 uCi x 1.149 x (e - e ) + 0
-0.1470 -1.615
d(t)
A = 100 uCi x 1.149 x (0.8633 - 0.1989) = 76.3 uCi Tc-99m