something has a half life of say... 15 minutes. Every 15 minutes, half of it decays.

 

So, what happenes when there's only one molecule left, and 15 minutes passes? does it decay too?

 

Or is this not how half-life works...

That's not really how half-life works. The half-life is a measurement of the 'average' decay rate of a sample. It's really just a probability. It says that in 15 minutes, the probability of half the sample decaying is close to 100%. As you get down to smaller and smaller numbers of atoms, you don't have a large enough sample size for this 'probability calculation' to really mean anything.

consider schrodinger's cat

That's not really how half-life works. The half-life is a measurement of the 'average' decay rate of a sample. It's really just a probability. It says that in 15 minutes, the probability of half the sample decaying is close to 100%. As you get down to smaller and smaller numbers of atoms, you don't have a large enough sample size for this 'probability calculation' to really mean anything.

 

would the sample eventually completely decay? or would there always be at least 1 particle...

Eventually it would completely decay. It's just that when you get to such small numbers of atoms, you can't be really too sure when it will decay since radioactive decay is a spontaneous event. That means that it will happen whenever and wherever. With large, measureable quantities of atoms, you can use the half-life to determine how much is left due to the incredibly large sample size. When you start getting down to the level where you can physically count the atoms, you really can't go by the half-life since the sample size is so completely small.

 

Thinks of it this way; if you flip a coin 80-trillion times, the probability that heads is flipped will be about 50%. If you only flip a coin 4 times, however, there's a good chance that the probability of heads will work out to be 3/4 or possibly even 4/4. So if you have 80-trillion-trillion-trillion Uranium atoms, the chances of half of them decaying over the next 4.5 billion years is near 100%. If you have 80 Uranium atoms, the chances of only half of them decaying over the next 4.5 billion years isn't exactly 100%. You may only get five atoms decaying, or you may get 78 atoms decaying, or you may have all of the atoms decaying by that point.

It would eventually completely decay, I think. A half life of 15 minutes means, roughly speaking, that in any given 15 minutes there's a 50/50 chance that any given atom will decay, so that last atom is going to decay sometime.

Eventually it would completely decay. It's just that when you get to such small numbers of atoms' date=' you can't be really too sure when it will decay since radioactive decay is a spontaneous event. That means that it will happen whenever and wherever. With large, measureable quantities of atoms, you can use the half-life to determine how much is left due to the incredibly large sample size. When you start getting down to the level where you can physically count the atoms, you really can't go by the half-life since the sample size is so completely small.

 

Thinks of it this way; if you flip a coin 80-trillion times, the probability that heads is flipped will be about 50%. If you only flip a coin 4 times, however, there's a good chance that the probability of heads will work out to be 3/4 or possibly even 4/4. So if you have 80-trillion-trillion-trillion Uranium atoms, the chances of half of them decaying over the next 4.5 billion years is near 100%. If you have 80 Uranium atoms, the chances of only half of them decaying over the next 4.5 billion years isn't exactly 100%. You may only get five atoms decaying, or you may get 78 atoms decaying, or you may have all of the atoms decaying by that point.[/quote']

 

Ah.. so it's a 50% chance that each molecule in the chunk of whatever will decay every half life... and with 80 trillion, the chance that half of them will decay is VERY high, becauase it's like flipping a coin 80 trillion times...

 

If that's right, thanks for the help!

Ah.. so it's a 50% chance that each molecule in the chunk of whatever will decay every half life... and with 80 trillion' date=' the chance that half of them will decay is VERY high, becauase it's like flipping a coin 80 trillion times...

 

If that's right, thanks for the help![/quote']

 

 

Yes. The statistics break down when you have a small sample.