# Number of decayed atoms in a simultaneous decay process

• mike_M
In summary, To calculate the number of atoms that have decayed by a specific process at a given time, we can use the equations N'_rad(t)=-lambda1*N(t) and N'_elim(t)=-lambda2*N(t), which can be derived from the original equation N(t) = N_0 e^{-(\lambda_1 + \lambda_2) t}. This allows us to separate the contribution of each process and solve for the number of atoms that have decayed by that specific process.
mike_M
A certain amount $N_0$ of a radioactive isotope with decay constant $\lambda_1$ is injected into a pacient. Besides that isotope's natural decay process, there's also a biological elimination process, with decay constant $\lambda_2$.

Now, at time t, the number of remaining isotope atoms is given by $N(t) = N_0 e^{-(\lambda_1 + \lambda_2) t}$. My question is, how do I calculate the number of atoms that, at time t, have decayed by *one* specific process (e.g. by radioactive decay alone)? I don't think I can use the above equation, with $\lambda_1$ instead of the sum, because such an equation would describe the number atoms assuming that that only one decay process is occurring (the one characterized by the used value of $\lambda$.

How to proceed then?

Try working with your equation such that you can separate the contribution of each process.

Remember that you can freely separately the exponentials.

Your equation comes from solving N'=-lamba1*N-lambda2*N. Once you've found the total number of atoms as a function of time N(t) (as you've done) then the number of atoms going by one process or another is given by N'_rad(t)=-lambda1*N(t) and N'_elim(t)=-lambda2*N(t). Solve those.

## 1. What is a simultaneous decay process?

A simultaneous decay process refers to the phenomenon where multiple atoms undergo radioactive decay at the same time.

## 2. How is the number of decayed atoms in a simultaneous decay process determined?

The number of decayed atoms in a simultaneous decay process is determined by measuring the change in the number of radioactive atoms over a certain period of time, using techniques such as counting or radiation detection.

## 3. What factors can affect the number of decayed atoms in a simultaneous decay process?

Factors that can affect the number of decayed atoms in a simultaneous decay process include the type and amount of radioactive material, environmental conditions, and the half-life of the material.

## 4. Is the number of decayed atoms in a simultaneous decay process predictable?

The number of decayed atoms in a simultaneous decay process is not entirely predictable, as it is a random process governed by the laws of quantum mechanics. However, the overall rate of decay can be predicted and described using mathematical models.

## 5. How is the concept of half-life related to the number of decayed atoms in a simultaneous decay process?

The half-life of a radioactive material is the amount of time it takes for half of the atoms in a sample to decay. Therefore, the number of decayed atoms in a simultaneous decay process will increase as the half-life is reached and more atoms undergo decay.

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