Question
Assume that you have a large sample of radioactive atoms, arranged in a rectangular lattice. Imagine that this lattice has some number of rows and
Assume that you have a large sample of radioactive atoms, arranged in a rectangular lattice.
Imagine that this lattice has some number of rows and columns, with an atom in each lattice-position.
Now, in this scenario, the atoms do *NOT* decay independently.
Instead, each row and column of atoms decays independently.
More specifically, imagine that each row of atoms decays as a random variable, independently of all other rows and columns.
Say that the probability of any particular row decaying over the course of one hour is 10%.
In addition, each column of atoms decays as a random variable, independently of all other rows and columns.
Say that the probability of any particular column decaying over the course of one hour is 40%.
Can you make a model for how the total number of atoms decays?
Make a graph/plot of your model, illustrating the amount of radioactive material you expect as a function of time (in hours).
Does the total number of atoms decay exponentially?
If so, can you define a decay rate for the total number of atoms?
I have attached some personal notes for reference as well!
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