Half-life (not the game)

[WillJ]

It's probabilistic; if you have 10,000,000,000 particles, after one half life there will be 5,000,000,000 particles, on average. It won't be exact, but with so many particles, a variation of 2 or 3 is nothing. But with only 10 particles, half of that is 5, but with a variation of 2 or 3 particles that could be 8 or 2 remaining. So it doesn't exactly halve it; it is, at the end of the day, a probability.

I did some basic experiments at uni this year with radioactivity, and the probabilistic nature makes it very interesting!

But since, as has been said, we are generally dealing with between ~10^20 and 10^26 particles, a small variation is nothing.

[and @ what col said]

Is it probabilistic specifically in that each atom has a 50% chance of undergoing radioactive decay in one half life?

That wouldn't seem right, because if that's the case I'd think the variation for 10^26 particles would be much more than a dozen or so, enough to be significant. (Or is that not true?) So if it's not the case, then just how does it work exactly, with regards to one particular atom?

 

[Renata]

@ Will -- radiactive decay is understood best by quantum mechanics, and quantum mechanics is in its nature probabilistic. You can't ever apply it to just one atom at a time; it doesn't work. Sorry I can't explain it any better; you'd almost have to take a course.

Gothmog is right, though, that in practice, it doesn't matter. Just the same way that 1000000 flips of a coin is more likely to give you a result arbitrarily close to 50% heads than 10 flips would, when you're dealing with such huge numbers as the number of molecules of potassium in a lump of rock, the decay rate becomes very precisely and accurately defined.

Of course, everything gets more difficult in practice -- how exactly do you *measure* the amount of argon trapped in a bit of rock? -- but most radiometric dating methods are now considered extremely reliable. (By the way, many types and ages of material can be dated by more than one method. When this is possible, it provides a nice empirical check -- independent of crack-brained theory and kludgy technique -- that the result is accurate. If both methods give the same date, you're on pretty solid ground. If a third method can be employed and also gives the same date, well, then you can be all but positive your theory and practice are sound. Radiometric dating methods stand up to this sort of test very well when properly applied.)

@ Col -- you're right that the decay rate hasn't ever been observed to vary under normal conditions. (Except possibly for one oddball type of decay. Can't remember any more which it was, but I don't think it's been mentioned so far here.) C-14 dating, though, *is* affected by things like atmospheric composition -- the article had that much right, although not much else.

That's because the carbon in all living creatures comes ultimately from the atmosphere. Plants draw it in in the form of carbon dioxide; it winds up in all their tissues. Animals acquire their carbon by eating plants or by eating animals which themselves have eaten plants.

Carbon-14 itself is formed by irradiation of the atmosphere by sunlight, and this process *can* be affected by environmental factors. So the amount of C-14 in the atmosphere -- and thus the fraction that winds up in living organisms -- fluctuates over time. The fluctuation isn't large enough to, say, turn a 15,000-year C-14 date into a 400-year or 4-million year date, but for true accuracy, C-14 dates to have to be calibrated against other techniques. This has long since been done, though -- basically all you have to do is take your uncorrected date and look at a chart.

And C-14 dating can't be used on marine organisms at all, if I remember right, although I don't remember exactly why.

Hope that clarifies a little bit, and hope I didn't make any glaring errors -- my memory is a bit fuzzy on the topic.

Renata

 

[WillJ]

@ Will -- radiactive decay is understood best by quantum mechanics, and quantum mechanics is in its nature probabilistic. You can't ever apply it to just one atom at a time; it doesn't work. Sorry I can't explain it any better; you'd almost have to take a course.

Gothmog is right, though, that in practice, it doesn't matter. Just the same way that 1000000 flips of a coin is more likely to give you a result arbitrarily close to 50% heads than 10 flips would, when you're dealing with such huge numbers as the number of molecules of potassium in a lump of rock, the decay rate becomes very precisely and accurately defined.

If you can't apply it to one atom at a time, what happens when there's one atom left? Does the universe implode?

I certainly have no problem taking your word for it when it comes to me not being able to understand the physics behind this until I've taken a course. But can I still not understand the probability behind it?

And rest assured that I don't think my question has much practical signifance. I mostly just asked it as a curiosity.

 

[h4ppy]

I always wondered why it would take the last couple ones so long to break down.

 

[Cheetah]

[and @ what col said]

Is it probabilistic specifically in that each atom has a 50% chance of undergoing radioactive decay in one half life?

I understand it so that the probability of 50% of the mass to decay within a certain time is the half-life.

But there is one thing I don't understand about half-lifes yet:
How do we know that an organism didn't suddenly get a large portion of a "daughter" of an isotope, or an extraordinary amount of an isotope, thus giving wrong dates when measuring the ratios of "mother" isotopes and "daugthers"?

 

[WillJ]

I understand it so that the probability of 50% of the mass to decay within a certain time is the half-life.

I think you meant to say "the time it takes" instead of "the probability of."

But yeah, I know that, but what I don't know is why it works that way. My guess was that during a half life, each atom has a 50% chance of decaying (for reasons I don't care about ), but according to Renata, that's not the case, and to understand it, I'll have to understand quantum mechanics fairly deeply. And that's probably, but hopefully not , true.

 

[Mise]

But there is one thing I don't understand about half-lifes yet:
How do we know that an organism didn't suddenly get a large portion of a "daughter" of an isotope, or an extraordinary amount of an isotope, thus giving wrong dates when measuring the ratios of "mother" isotopes and "daugthers"?

The probability of that happening is very very small, akin to flipping a coin 10^500 times and getting a head every time (to use Renata's analogy). We know that the percentage of C-14 atoms in nature is very small, so it's all down probabilities. (can work out percentage of C-14 based on, e.g. ... something [I forgotten the proper word, but it's where the atoms are ionised by removing 1 electron and subsequently deflected by a EM field - the heavier particles are deflected less, and the mass/charge ratio is measured])

But yeah, I know that, but what I don't know is why it works that way. My guess was that during a half life, each atom has a 50% chance of decaying

I think the probability of any single atom decaying is very very small. But over 10^23 atoms, that probability becomes significant. But when you get down to 10^3 or 10^0 atoms, the probability is still small - so small that the last few atoms probably won't decay for ages and ages.

 

[Renata]

I think you meant to say "the time it takes" instead of "the probability of."

But yeah, I know that, but what I don't know is why it works that way. My guess was that during a half life, each atom has a 50% chance of decaying (for reasons I don't care about ), but according to Renata, that's not the case, and to understand it, I'll have to understand quantum mechanics fairly deeply. And that's probably, but hopefully not , true.

No, you misunderstood me. (Or maybe I just explained it badly.) 50% chance of decaying per half-life is correct. That probability doesn't change just because there's only one atom left, it's just that once you get to small enough numbers, probabilistic predictions (the only ones you can make due to quantum mechanical considerations) become rather useless.

In other words, you'll never be able to predict exactly when that last atom will decay. Say the half-life was one week. You could say there would be a fifty percent chance of the atom not having decayed after one week and a 25% chance after two, but what does that really get you? Not much. Conversely, when you're dealing with large numbers of atoms (and any macroscopic amount of radioactive material is by necessity a *very* large number of atoms), you can make exact predictions. Same material with a one-week half-life, if you have 3.26 pounds of it to begin with, you know exactly that 1.63 pounds will have decayed after the first week.

@ Cheetah -- I'm afraid I can't figure out what you're trying to ask.

Renata

 

[WillJ]

No, you misunderstood me. (Or maybe I just explained it badly.) 50% chance of decaying per half-life is correct. That probability doesn't change just because there's only one atom left, it's just that once you get to small enough numbers, probabilistic predictions (the only ones you can make due to quantum mechanical considerations) become rather useless.

In other words, you'll never be able to predict exactly when that last atom will decay. Say the half-life was one week. You could say there would be a fifty percent chance of the atom not having decayed after one week and a 25% chance after two, but what does that really get you? Not much. Conversely, when you're dealing with large numbers of atoms (and any macroscopic amount of radioactive material is by necessity a *very* large number of atoms), you can make exact predictions. Same material with a one-week half-life, if you have 3.26 pounds of it to begin with, you know exactly that 1.63 pounds will have decayed after the first week.

Ah, OK.

You're right that knowing that a particular atom will have a 50% chance of decaying is rather useless, but I still wanted to know it anyway.

And I now realize I was wrong when I said that if the chance of each atom decaying were 50%, the variation / standard deviation would be signficant even with huge numbers.

 

[Renata]

Cool.

Renata

 

[HighlandWarrior]

Carbon is only used for about 50,000 years in the past. Potassium-Argon dating can be used basically for anything (provided that there was potassium in the substance), as it has a half-life of 1.3 billion years. The half-life is the time that it takes half of the material to decay. In this case, after 1.3 billion years, 5 moles of Potassium would have decayed into 2.5 moles of potassium and 2.5 moles of Argon, along with 2.5 moles of Hydrogen (I guess 1.25 moles of H2, actually).

According to wiki, this would be an example of positron emission.

So how do you know it started with 5 moles of potassium?

 

[YNCS]

I suspect that Meteorpunch's article has a creationist source.

 

[Yom]

So how do you know it started with 5 moles of potassium?

You would know because I defined it as such. Dating works the other way around. If you find 2.5 moles of Potassium and 2.5 moles of Argon, then it would probably be around 1.3 billion years old (having started with 5 moles of Potassium). Since Argon isn't nearly as widespread as Potassium, there's little confusion with having Argon that isn't from decayed Potassium (plus decayed Argon is an isotope of Argon that I believe is different from the type in the atmosphere).

 

[Souron]

So, is it correct that all naturally occuring radioactive isotopes form in the atmosphere?

 

[Yom]

So, is it correct that all naturally occuring radioactive isotopes form in the atmosphere?

Excuse me? Of course radioactive isotopes don't just form in the atmosphere (nor did I imply that). Most atmospheric Argon is 39-Ar, not 40-Ar, which is created from decayed 40-K. Therefore, the source of Argon can be pretty easily determined.

 

[YNCS]

Isotopes of elements with atomic numbers greater than lead (atomic no. 82), all of which are radioactive, are not formed in the atmosphere.

 

[Souron]

Excuse me? Of course radioactive isotopes don't just form in the atmosphere (nor did I imply that). Most atmospheric Argon is 39-Ar, not 40-Ar, which is created from decayed 40-K. Therefore, the source of Argon can be pretty easily determined.

Carbon 14 forms in the atmosphere, as states several times above.

I'm more interested where the original 40-K comes from and why it's consentration was so constant when first exposed to the air; why is it that we are able to say that originally there was only 40-K and no 40-AR? originally being when the thing was alive.

 

[Yom]

Carbon 14 forms in the atmosphere, as states several times above.

I'm more interested where the original 40-K comes from and why it's consentration was so constant when first exposed to the air; why is it that we are able to say that originally there was only 40-K and no 40-AR? originally being when the thing was alive.

Argon doesn't form any compounds naturally, so there's no reason for there to be any Argon in anything organic in the first place. The only way it would be in an organism would be if it were breathing and some 39-Ar was in its lungs when it was covered by lava or something else that would preserve the gases inside of it.

 

[Souron]

Argon doesn't form any compounds naturally, so there's no reason for there to be any Argon in anything organic in the first place. The only way it would be in an organism would be if it were breathing and some 39-Ar was in its lungs when it was covered by lava or something else that would preserve the gases inside of it.

Unless it had decaying potassium in it.

I am not questioning what you are saying. I am simply trying to understand how we can assume that none of the potassium already decayed before the organism was covered with lava.

 

[Souron]

Isotopes of elements with atomic numbers greater than lead (atomic no. 82), all of which are radioactive, are not formed in the atmosphere.

How do they form naturally?