Radioactive Decay chain and Masses of Products

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To calculate the remaining mass of each nuclide in a radioactive decay chain after a specified time, one can use the Bateman equations, which provide a framework for determining the quantities of nuclides based on their half-lives. The formation rate of the final product is influenced primarily by the nuclide with the longest half-life, as it acts as the rate-determining step in the decay process. It is expected that low-half-life nuclides will be nearly depleted before reaching the first long-half-life nuclide, while some quantities of subsequent nuclides will still be present. Additionally, there is a request for assistance with C++ programming related to this topic. Understanding these calculations is crucial for accurately modeling radioactive decay chains.
lapo3399
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Hello,

Based on a starting isotope, isotope mass, and duration of time, what calculations would be used to find the mass remaining of each individual nuclide in the decay chain after the time period? I think that the rate at which the final product is formed depends most on the nuclide with the highest half-life, as chemical systems in chemistry are reliant on the rate determining step. However, what I find difficult to visualise is how much of the other nuclides would be left. I presume that, depending on the time interval, all the low-half-life nuclides before the first long-half-life nuclide would pretty much be gone, with certain quantities of other nuclides after the long-life nuclide being present. Can someone please elaborate on the calculations necessary?

Thanks!
 
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have you tried Bateman equations?
 
Thanks, I researched them and they are exactly what I need.
 
lapo3399 said:
Thanks, I researched them and they are exactly what I need.

great, good luck with your task! =)
 

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