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!

Exponential Decay XXXXX X X R= * of rows (ie, R: 4 ) X C = # of cols A = R. C = 4 x 7 - 28 atoms. (ie, (= 7 ) Decay events are correlated ! X X X X - an entire now may decay at some rate dR X I anentire column may decay at some rate Ac .Key: individual atoms are NOT independent from. one another! Not even close! We can't apply the loan ham radioactive decay to this scenario : Assumptions will be very you from accurate ( unless there is only a single now/ Column ) . Question : does order / sequence matter? Answer: only to the extent that order matters in radioactive decay. Hint: What is independent ? Are there any quantities that can be modeled as collections of objects that do decay randomly & independently from one another ?Hint I 2 : imagine the following chemical reaction: X + Y Z Note for next question : at X ( = - x [ X ] [ ] + $ 1 z ] See the terms on RHS. Y ( ) = - x / X ] 1 4] + 1 12] Some Jawand at Others reverse d at Z ( t ) = + a sx ]ry] - p 1Z ] There are added together Now imagine that d, B = D ( no reactions happen ), but that X x Y both decay radioactively ... How will the interaction Probability [ X] ly ] change as a function of time