The concept of half-lives has been burned into my mind by many, many years and classes. I just realized, however, that I was never taught the reasons behind why it works as it does


I think it would have to do with the tendency for things to move from more to less order, and that whatever is breaking down is doing so. But if that's true then why is it so uniform? Half of the remaining substance left at a time? It seems to me that the only way THAT would work would be if the atoms at the outer part of whatever mass it is are in a less uniform environment which makes them break down faster or something. I must know!

For that matter does a half-life occur instantaneously or does it occur gradually over time?

I'm not sure what you mean here? Can you clarify, then I can answer your question properly.

It's basically exponential decay. Just as a capacitor has a discharge curve with R*C as a time constant, the equlivalent of a time constant is the half life.

One thing to remember is that it takes at least 5 time constants (half lifes) for the material to essentially be gone and 1 time constant for 1/2 of the material to be gone.

What I mean is that when the specified time of something's half life has elapsed half of the material is no longer what it originally was. Does this change happen gradually over that elapsed time (so that a substances half-life is the measured time for something to "lose" half of itself) or does this decay occur all at once at the half-life mark?

Still waiting for why something should decay at all

Things decay because they are unstable. How unstable they are determines their halflife.

Half-life is just a nice way of measuring the rate of decay, the decay is continuous. You could just as easily measure the time for 1% or 10% of the substance to decay.

For example: Imagine taking a jar of dice (let's say 100). Each die is an atom in your radioactive substance. You roll them all out onto the floor. Now, you remove the dice that have landed on 6. These are you decayed particles. You take the remaining particles and roll them again, removing the sixes again.

This is how decay works, simplistically. Every x amount of time, a particle has a certain chance to decay. In our example, every roll of the dice, each particle has 1/6th chance to decay. Our "half-life" would be the amount of time it takes for half of our particles to decay. (theoretically, this should be about 3.8 rolls). Note that the half life is the same regardless of how many dice we have, because roughly 1/6th of the dice should be removed each time, 1/2 of the dice should be removed after the same amount of time.

If you now take this example to a sample of radioactive material. You have many billions of atoms, so the half life should be very accurate. (every time you repeat the experiment, you should get very close to the half life). You also have continuous time, instead of there being one roll of the dice followed by another, the particles will decay according to a certain probability over a certain time.

Does this help you understand how the half-life works? I'm sure you have further questions, feel free to ask away!

Mhm, so things decay because everything is moving towards disorder. Thanks for all your help guys!