Request for corrections and critiques.

[RR Edwards]

I want to accurately model and represent radioactive decay in the most abstract way possible.

 

Imagine first a completely innocuous ability to index each atom of a rock of uranium ore. We place it into a conceptual black box which functions as a perfectly benign mobile automatic lab. As an atom decays the box detects the decay the local of its origin, and displays that information.

From outside the box, the decay appears random to us, but using the Law of Large Numbers we can guarantee the decay rate will follow the continuous variable as defined by an exponential decay curve described in the Universal Law of Radioactive Decay.

 

Using this information we are guaranteed each sample treated in this way will conform exactly to its appropriate exponential decay curve.

[BearOfNH]

Why do you care about the location of the atom that decayed?

 

OTOH, you should care about what decayed. Depending on the isotope, U-->Th-->Ra-->Rn-->Po etc. (where --> means "decays to"). Each of these has different half-lives so your box needs to display which isotope of which element just decayed.

[RR Edwards]

well, i am trying to establish an abstraction that correctly conveys the randomness of the decay - such that it is unknown which atom will decay.

[BearOfNH]

Let's say you start off with a sample of a billion atoms of pure ²²²Rn, which has a half-life of 3.8 days. I can see you building a radioactive decay model based on just the Radon. Trouble is, it decays to ²¹⁸Polonum, with a half-life of 3.1 minutes. So in addition to Radon decaying to Polonium (by emitting an α-particle), you've got Polonium decaying to ²¹⁴Lead, also via α-decay. Furthermore, the Lead decays to radioactive Bismuth, which can then decay to either Polonium or Thallium. C'mon, I don't see how you can model all this with a single variable. I think you need to look at each element in the decay chain, at least until you hit an element that decays in microseconds or megacenturies, and sum up the individual components.

 

I think it would be interesting to write a program to simulate all this and plot the combined half-lives of all the atoms as time progresses.

[hoola]

isn't what is intended to be studied is the decay of a particular atom in relation to a proximate neighbor atom's decay? In a lattice of evenly spaced atoms, does a close neighboring atom's decay - increase/decrease/have no relation to - a particular atom (the control) decay probability? In this study each atom's position must be known. Could a lattice of buckyballs, each holding one atom be a proper structure for a test? If it were a square sheet of buckyballs, the ability to locate a particular atom's decay would be simpler than if were a cubical form with equal sides. Wouldn't the simpler 2D sheet be a good enough for a test of control decay probability being altered by proximate decays?

Edited December 15, 2013 by hoola