##### HEALTH PHYSICS INSTUMENTATION FOR

###### 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 = A_{0}^{e-λt}

A = A_{0}e^{-(0.693/T1/2)t}

Where,

A = Present activity

A_{0}= 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 = A_{0} 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 (A_{0}) 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 = A_{0} 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 (A_{0}) 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 = A_{0} x e^{-λt} = A0 x e^{-(0.693/ T1/2) t} ,

Activity (A) as on 31-01-2021 = A_{0} 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 (A_{0}) 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 = A_{0} x e^{-λt} = A0 x e^{-(0.693/ T1/2) t} ,

Activity (A) as on 31-01-2021 = A_{0} x e^{-(0.693/5.3) x 1.75}

= 133200 x e ^{-0.2288}

= 133200 x 0.7955

= 105961 Bq.

= 105.961 KBq.