Find n(Ni) in Decay Chain with Single Equation

In summary, to find the amount of particles of Ni, n(Ni), at any point in time t in the decay chain N1 -> N2 -> N3 -> ... -> Ni -> ... -> Nd, you can either use the Bateman equations suggested by Wikipedia, which may not work for the case when i=d due to division by 0, or you can use an equation with an additional decay to Nd+1 and take the limit of an infinite lifetime of Nd. Another option is to subtract all the other elements from the total number of particles.
  • #1
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For the decay chain N1 -> N2 -> N3 -> ... -> Ni -> ... -> Nd, how can I find the amount of particles of Ni, n(Ni), at any point in time t, with a single equation where i can vary from 1 to d? I have already seen WIkipedia's suggestion on the Bateman equations but that method seems to collapse for the case when i=d (as lambda=0 so we'd be dividing by 0).
 
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  • #2
You can use the equation with an additional decay to Nd+1, and take the limit of an infinite lifetime of Nd. Alternatively, subtract all the other elements from the total number of particles.
 

FAQ: Find n(Ni) in Decay Chain with Single Equation

What is a decay chain?

A decay chain is a series of radioactive decays that occur within a specific element or isotope. This occurs as unstable atoms decay and transform into other elements or isotopes until a stable element is reached.

Why is it important to find n(Ni) in a decay chain?

Finding n(Ni) allows us to determine the number of atoms of nickel (Ni) present in the decay chain. This information is important for understanding the rate of decay and predicting the behavior of the radioactive material over time.

How can a single equation be used to find n(Ni) in a decay chain?

A single equation, called the Bateman equation, can be used to calculate the number of atoms of a specific element in a decay chain. This equation takes into account the half-lives of each decay and the initial amount of the element present.

What factors can affect the accuracy of finding n(Ni)?

The accuracy of finding n(Ni) can be affected by the accuracy of the initial measurement of the element, the accuracy of the half-life values used in the equation, and any potential errors in the experimental setup or data collection.

Can the Bateman equation be used for any decay chain?

Yes, the Bateman equation can be used for any decay chain as long as the half-life values for each decay are known. It is a widely accepted and reliable method for calculating the number of atoms in a decay chain.

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