biodex ATOMLAB 500, Operation And Service Manual, Page: 178 / 212

Decay Calculation Methods – An Explanation
Calculator Method
The radioactivity of an isotope can be calculated as it decays using the following expression:
A
f
= A
i
𝑒
!"
Where:
A
f
= final activity at the end of the decay time;
A
i
= initial activity measured at the specified starting time;
t = net decay time in units inverse to 𝜆 , and
𝜆 =
(lamda)
decay constant specific to the radioisotope.
𝜆 = In (2) ÷ T
1/2
= 0.693 ÷ T
1/2
Where: T
1/2
= half life specific to the radioisotope.
Therefore, using a calculator with the e
x
function, decay calculations can be performed as
illustrated in the beginning of this appendix.
Decay Factor Method
Without a calculator with an e
x
function, the above expression can be rewritten as follows:
A
f
= X × A
i
Where:
X = X
n
(N) × X
r
(R)
N = an integer number of half lives in time t;
R = the decimal remainder after dividing t by T
1/2
.
To verify the result, remember three important relations regarding exponentials:
1. 𝑒
! ! !
= 𝑒
!
× 𝑒
!
2.
𝑒
!" !
= 𝐴
3. 𝑒
!"
= 𝑒
! !
𝑡 ÷ 𝑇
! / !
= 𝑁 + 𝑅
Where: N is an integer
R is the remainder less than 1.