Decay chain of radioactive isotopes

In summary, the conversation discusses the efficient calculation of decayed material in a two-step decay chain. The example given is 56Ni -> 56Co -> 56Fe with half-lives of 6.1 days and 77.7 days, respectively. The question is how to accurately calculate the amount of 56Fe created after a specific time from a given quantity of 56Ni. The solution is suggested to be found in the Bateman equations, specifically in the works of Batman and Jerzy Cetnar, for both simple and general problems.
  • #1
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How can I efficiently calculate the amount of material decayed after a specific time in a two-step decay chain?

In my specific example, I have 56Ni -> 56Co -> 56Fe. The half life of the first process is 6.1 days, the second - 77.7 days. How can I accurately calculate the amount of 56Fe that was created after a certain time from a given quantity of 56Ni? Is there a formula for "effective half life" of such a decay, in particular when the objective is to calculate the amount of final substance created after time t, as opposed to the amount of initial substance remaining?
 
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  • #2
This problem can be solved using analytical approach since it's a simple linear decay chain(without branching, the coefficients are distinct), I recommand you the paper published by Batman(Solution of a system of differential equations occurring in the theory of radioactive transformations) 100 years ago(the equation that govern this problem is also known as Batman equation).
For a more general problem(no distinction is needed for coefficients), you can find solution from Jerzy Cetnar's work("General solution of Bateman equations for nuclear transmutations").
Hope that will help^_^
 
  • #3
Thank you, Bateman equations are exactly what I was looking for!
 

FAQ: Decay chain of radioactive isotopes

1. What is a decay chain of radioactive isotopes?

A decay chain of radioactive isotopes is a series of decays that occur in a specific order, starting with a radioactive parent isotope and ending with a stable daughter isotope. This process continues until a stable isotope is reached.

2. How does a decay chain occur?

A decay chain occurs when an unstable radioactive isotope undergoes radioactive decay, releasing energy and particles in the form of alpha, beta, or gamma radiation. This decay process changes the atomic number and mass of the isotope, creating a new isotope that can also undergo further decays.

3. What causes a decay chain to stop?

A decay chain stops when a stable isotope is reached. This can happen after multiple decays, as each decay results in a more stable isotope. Additionally, some isotopes have a half-life that is so long that their decay chain effectively stops within a human timescale.

4. How does a decay chain affect the stability of an element?

A decay chain can significantly affect the stability of an element. The radioactive decay of isotopes can cause changes in the chemical properties of an element, leading to the formation of new elements. Additionally, the release of energy during decay can cause further changes in the atomic structure of an element.

5. Can decay chains be predicted?

Decay chains can be predicted to a certain extent based on the properties of the parent isotope and known decay modes. However, the exact timing and sequence of decays cannot be predicted as they are probabilistic processes. Additionally, new isotopes and decay modes are still being discovered, making it difficult to predict all possible decay chains.

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