What is Bateman Equation Method for Half Life Determination?
Half life determination: Part 4
Determination of t1/2 by Bateman Equation Method
Using decay chain (Using Bateman equation)
A. Distant parent daughter relationship
.PNG)
N9 (from A9) to be estimated by gamma spectrometry. t is known. λ2-λ9 should be known. N1(from A1) should be estimated. λ1 only unknown parameter.
B. Immediate parent daughter relationship (e.g. Secular, transient, no equilibrium)
90Sr (β-, 28.1y) → 90Y (β-, 64h) → 90Zr (Stable)
144Ce (β-, 285d) → 144Pr (β-, 17min)→144Nd (Stable)
244Cm(α, 18.10y) → 240Pu (α, 6563 y) → 236U (α, 2.858 y)
N2 (from A2) to be estimated by radiometry. t is known. N1(from A1) should be estimated. λ1 only unknown parameter.
Advantage
Less tedious experiment
Disadvantage
More tedious calculation
Very selective radioisotopes have their decay chains
Reference
H. Bateman Solution of a system of differential equations occurring in the theory of radioactive transformations Proc. Cambridge Philos. Soc., 15 (1910), pp. 423-427
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