Question about exponential decay timing.

[tybomb]

I'm trying to understand the concept of exponential decay. To clarify, the decay of Uranium is not the same as say pulling the plug in a tub full of water. The water will drain out of a tub at a steady rate from start to finish. I assume Uranium doesn't do that. So you COULD say the water has a half life but there's no point right? But with Uranium the process is more complicated and needs to be measured by the half life.
Is Uranium decay like a popcorn maker? Some kernels will pop soon after it's started and the frequency will pick up until it climax's a couple minutes in and then it will gradually stop again as the job completes? Most of the kernels will pop between say 120 seconds and 180 seconds in and the job will be finished at 220 seconds?

 

[phyzguy]

No! Each atom has a constant probability of decaying in a given time interval. With popcorn, the probability of a given kernel popping per second is small at first, then increases as time goes on, then decreases again. If I have a bunch of newly created uranium atoms, each atom is just as likely to decay in the first second as in a second 10 billion years later. The reason the number of atoms decays exponentially is that there are fewer and fewer atoms as time goes on.

 

[tybomb]

ok. The concept sounds so simple but it's difficult to visualize. I suppose it's the same with carbon 14 except on a shorter scale? Obviously the process is very reliable if it can be used to date things but why don't all the atoms decay at the exact same time if it's so reliable? It's confusing that there's some reason why the atoms decay at differen't times yet the process is still reliable.
What actually causes the variation the atoms decay? Are there different arrangements of the nucleus that have varying degree's of strength? I would have thought every atom was the same but they can't be if one decays today and another one decays a billion years from now.

I don't think it could be an environmental factor or the method wouldn't be reliable?

 

[tybomb]

Or does the nucleus decay when something hits it from outer space that is always coming at a constant rate? That would make more sense.

 

[NascentOxygen]

I'm trying to understand the concept of exponential decay. To clarify, the decay of Uranium is not the same as say pulling the plug in a tub full of water. The water will drain out of a tub at a steady rate from start to finish.

Not so. The water drains fastest while the level is deep, but as the tub empties and the level falls, there is less pressure to force more water down the drain and the volumetric flow rate tapers off.

For exponential decay, imagine there is a city over-run by rats. The rats run out of food, and must resort to cannibalism, each surviving rat needing to eat one of the others every day. On day 1 there are 1,000,000 rats. On day two, just 500,000. After day three, 250,000, and so on. Plot the numbers on a graph, it is a decaying exponential — the population exhibiting a half-life of one day.

 

[Borek]

Just don't assume U atoms have to eat each other, this analogy doesn't go so far

phyzguy already gave the best explanation - each atom has a constant probability of decaying in the given period of time. Say it is 0.1 per year. That means during a year 10% of atoms will decay and you are left with 90%. Same happens in the next year - 10% decays, but it is 10% not of the initial population, but of the 90% that were left after the first year - so after two years you are left with 81%. And it continues for ever (or till there are no more atoms left).

 

[phyzguy]

ok. The concept sounds so simple but it's difficult to visualize. I suppose it's the same with carbon 14 except on a shorter scale? Obviously the process is very reliable if it can be used to date things but why don't all the atoms decay at the exact same time if it's so reliable? It's confusing that there's some reason why the atoms decay at differen't times yet the process is still reliable.
What actually causes the variation the atoms decay? Are there different arrangements of the nucleus that have varying degree's of strength? I would have thought every atom was the same but they can't be if one decays today and another one decays a billion years from now.

I don't think it could be an environmental factor or the method wouldn't be reliable?

(1) Yes, the process is the same for C-14, it's just that the probability of decay per unit time is higher for C-14 than for U-238.

(2) As for what causes different atoms to decay at different times, quantum mechanics says that nothing causes it. The universe is inherently probabilistic, and the idea that all effects have causes is simply incorrect. The idea that there is some mechanism within each nucleus that determines when it decays is called a "hidden variable" theory, and most types of hidden variable theories have been explicitly disproven. You might try reading about the Bell inequalities, which say that no "locally realistic" hidden variable model can explain the results of quantum mechanics.

 

[tybomb]

It's kind of tough understanding this stuff when I really think about it. It's simple at first glance but I can't think of anything natural to compare atomic decay to so that it feels farmiliar. The population of man doesn't fit because even though we die young we're more likely to die the older we get. There's not a constant rate and tons of environmental and genetic factors that guide the process.
ATomic decay has no explanation.
Plus you end up with a paradox if it's always a certain percentage of what's left that decays .

I can understand how at any given time any atom has the same probability of decaying throughout the entire period but it's hard to picture without knowing why and what the mechanism is that works with such consistency.

 

[tybomb]

Is there anything that can influence the rate of atomic decay? I think I remember reading something not long ago that mentioned scientists had tested to see if they could find anything with 'limited success" and the rate basically remained the same. That sounds like they may have found something but not enough to brag about.

 

[Borek]

Is there anything that can influence the rate of atomic decay?

Short answer: no.

Long answer is "yes" (you know, 3 letters compared with 2), but I am afraid details won't help your understanding, besides, in a way they confirm the short answer. There is a rare type of decay (called electron capture) in which decay speed may depend on the electron density around the nucleus. However, what it shows is that even in this case, nucleus "readiness" to undergo change is always the same, it is just that this type decay is limited by availability of something external to the nucleus. No electrons (fully ionized atom - nucleus only) most likely means no decay by electron capture.