What Is the Bateman Two-Step Decay Kinetics Calculator?
The Bateman equations describe the abundances and activities in a radioactive decay chain as a function of time.
They model isotopes that decay into unstable daughters which subsequently decay into stable or further radioactive products.
How Does the Bateman Two-Step Decay Kinetics Calculator Work?
Daughter activity starts from zero, rises to a maximum at t_max, and then declines.
When T1 >> T2, secular equilibrium is established where daughter activity equals parent activity.
When T1 > T2, transient equilibrium occurs where the daughter activity exceeds parent activity by a constant ratio.
Bateman Two-Step Decay Kinetics Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Bateman analytical solution for sequential radioactive chain decay activity.
How to Use the Bateman Two-Step Decay Kinetics Calculator
- Enter parent and daughter half-lives in hours.
- Specify the initial activity of the pure parent radioisotope.
- Enter the target decay time to determine current activities and peak production time.
Step-by-Step Example Calculation
Bateman Decay Standard Case
Input Values:
Understanding Your Result
Parent activity decays exponentially according to exp(-lambda1 * t).
Daughter activity accounts for both production from parent and decay into granddaughter.
Time of peak daughter activity indicates the optimal elution or harvesting time.
Factors That Affect the Result
- Half-life ratio: Governs whether secular, transient, or no equilibrium develops.
- Branching ratio: Some decays yield multiple daughter states, requiring fractional weighting.
When Should You Use This Calculator?
- Medical radioisotope generator scheduling (e.g., Mo-99/Tc-99m and Ge-68/Ga-68 generators).
- Nuclear waste radiotoxicity decay tracking and environmental radiation dosimetry.
Assumptions & Limitations
- Assumes 100% branching transition from parent to daughter.
- Assumes zero initial daughter concentration at t = 0.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact analytical solution of first-order coupled linear differential decay equations.