ACTIVITY & DOSERATE CALCULATION PROCEDURE

a. Activity calculation (as on date)
It is known that, given the activity at any previous date and by knowing its half-life, we can calculate the present activity by using the following equation.
A = A₀^e-λt
A = A₀e^{-(0.693/T1/2)t}
Where,
A = Present activity
A₀= Activity as on previous date
T_1/2 = Half-life of source
t = Elapsed time
λ = Decay constant
Note : T_1/2 and t should be in the same units (either in years or months)
TYPICAL CALCULATION OF ACTIVITY FOR TWO BETA AND TWO GAMMA SOURCES
Beta Sources :
1. Sr-90/Y-90 :
Half-Life (T/1/2) = 28.5 Years
Activity (A0) as on 31-01-2016 = 3.7 KBq. = 3700 Bq.
Suppose, we want to find out Activity (A) as on 31-01-2021, then,
Elapsed Time (t) = 5 Years
By using the formula, A = A₀ x e^-λt = A0 x e^{-(0.693/ T1/2) t} ,
Activity (A) as on 31-01-2021 = 3700 x e^{-(0.693/28.5) x 5}
= 3700 x e ^-0.12158
= 3700 x 0.8855
= 3276 Bq.
= 3.276 KBq.

2. Tl-204 :
Half-Life (T/_1/2) = 4 Years
Activity (A₀) as on 31-07-2018 = 10 KBq. =10000 Bq.
Suppose, we want to find out Activity (A) as on 31-01-2021, then,
Elapsed Time (t) = 2 Years 6 Months = 2.5 Years
By using the formula, A = A0 x e^-λt = A0 x e^{-(0.693/ T1/2) t} ,
Activity (A) as on 31-01-2021 = A₀ x e^{-(0.693/4) x 2.5}
10000 x e ^-0.43313
= 10000 x 0.6485
= 6485 Bq.
= 6.485 KBq.

Gamma Sources :
1. Cs-137 :
Half-Life (T/_1/2) = 30 Years
Activity (A₀) as on 31-08-2018 = 111 KBq. =111000 Bq.
Suppose, we want to find out Activity (A) as on 31-01-2021, then,
Elapsed Time (t) = 3 Years 5 Months = 3.4167 Years
By using the formula, A = A₀ x e^-λt = A0 x e^{-(0.693/ T1/2) t} ,
Activity (A) as on 31-01-2021 = A₀ x e^{-(0.693/30) x 3.4167}
= 111000 x e ^-0.07893
= 111000 x 0.9241
= 102575 Bq.
= 102.575 KBq.
2. Co60 :
Half-Life (T/_1/2) = 5.3 Years
Activity (A₀) as on 30-04-2019 = 133.2 KBq. = 133200 Bq.
Suppose, we want to find out Activity (A) as on 31-01-2021, then,
Elapsed Time (t) = 1 Year 9 Months = 1.75 Years
By using the formula, A = A₀ x e^-λt = A0 x e^{-(0.693/ T1/2) t} ,
Activity (A) as on 31-01-2021 = A₀ x e^{-(0.693/5.3) x 1.75}
= 133200 x e ^-0.2288
= 133200 x 0.7955
= 105961 Bq.
= 105.961 KBq.