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## Half Lives

This problem has always bugged me, and the only answers I've been given were on the lines of "meh". What I don't understand is that if we are given 1 gram of a radioactive substance with a half life of n years, why is it that after n years, the substance is reduced to 0.5 grams of radioactive material; but after another n years, the substance has now reduced 0.25g.
Does the substance know how much radioactive material is in its vicinity? What is actually happening at the atomic level in terms of the amount of radioactive atoms that become inactive? I doubt it has anything to do with probabilities of whether a certain atom will decay or not.

So what is actually going on here?
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 Quote by Mentallic Does the substance know how much radioactive material is in its vicinity?
No, they are acting independently without communicating.

 What is actually happening at the atomic level in terms of the amount of radioactive atoms that become inactive? I doubt it has anything to do with probabilities of whether a certain atom will decay or not.
Oh, it has everything to do with probabilities of individual atoms. Every atom has an equal probability of decaying at any time, up until it decays. When there are more atoms around, statistically more of them are decaying; as some decay away, there are fewer left, and fewer decays per second. If there fewer atoms, there are fewer possible decays, so less total activity.

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 Quote by signerror Oh, it has everything to do with probabilities of individual atoms. Every atom has an equal probability of decaying at any time, up until it decays. When there are more atoms around, statistically more of them are decaying; as some decay away, there are fewer left, and fewer decays per second. If there fewer atoms, there are fewer possible decays, so less total activity.
So for each and every atom, there is a 50% probability of decaying after 1 half life? ok so what actually causes some atoms to decay in fractions of a half life, but others lasting many half lives? Why don't all the atoms decay at the same rate. i.e. They discharge radiation altogether and thus have a very short half life.

## Half Lives

 Quote by Mentallic so what actually causes some atoms to decay in fractions of a half life, but others lasting many half lives?
Random chance.

 Why don't all the atoms decay at the same rate.
They do.

Start with 16 atoms, with 1s half life. In one second, each atom has a 50% chance of decaying, so about half of them do. Say half decay: you have 8 decays over the 1 second, and 8 atoms remaining.

Of the 8 remaining, each has a 50% chance of decaying during the next second. So about half do: you get 4 more decays, and 4 atoms remaining (after 2s).

See the theme?

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Quote by signerror
Random chance.

 Quote by mentallic Why don't all the atoms decay at the same rate.
They do.

Start with 16 atoms, with 1s half life. In one second, each atom has a 50% chance of decaying...
I don't understand the link between "decaying at the same rate" and "each have 50% chance of decaying".
Using an analogy: Quadruplets are born the same day, live out equal lives and age at the same rate. However, through chance, these kids will die at vastly different ages.

Sorry, I still can't understand what causes this chance for complete decay; especially when each and every atom decays at the same rate.

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 Quote by Mentallic Using an analogy: Quadruplets are born the same day, live out equal lives and age at the same rate. However, through chance, these kids will die at vastly different ages.
 Sorry, I still can't understand what causes this chance for complete decay; especially when each and every atom decays at the same rate.
"complete" decay?

and an individual atom doesn't decay at a "rate" … it doesn't "gradually decay", it decays all at once … just when you're least expecting it!

it's like being dead … you can't be slightly dead … and an atom can't be slightly decayed

one moment you're/it's there, the next moment you're/it's gone!

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 Quote by tiny-tim Same with four radioactive atoms
I guess I expressed the analogy in a poor way
What I was meant to say is: without any external factors, how could it be that these quadruplets die at completely different ages in their life? What is causing them to die, just like what is causing these atoms to decay one after the other?

 Quote by tiny-tim "complete" decay?
Sorry, I was thinking of lanthanides and their multiple emissions before becoming stable. (a side question: As a Uranium atom decays by emitting alpha radiation, does it expel all protons at once, or one every now and then?)

 Quote by tiny-tim and an individual atom doesn't decay at a "rate" … it doesn't "gradually decay", it decays all at once … just when you're least expecting it! it's like being dead … you can't be slightly dead … and an atom can't be slightly decayed one moment you're/it's there, the next moment you're/it's gone!
This might be the answer to my little side question

Yeah this whole idea is what I'm not understanding. Is it just some unusual way that mother nature works?

Lets isolate this scenario down to just one radioactive atom which has a half life of 1 year. Without interacting with the outside world, this atom can decay at any moment? And has a 50% chance of living to be 1 year old? And no matter how 'old' it gets, it still has the same chance of surviving a further year?
I'm sorry, this must be nerve-racking, but I just can't see how this works the way it does. What flicks the switch to turn on the decay process?

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 Quote by Mentallic Lets isolate this scenario down to just one radioactive atom which has a half life of 1 year. Without interacting with the outside world, this atom can decay at any moment? And has a 50% chance of living to be 1 year old? And no matter how 'old' it gets, it still has the same chance of surviving a further year?
Yes, at any moment it can decay, and no matter how 'old' it gets, it still has the same chance of surviving a further second
 I'm sorry, this must be nerve-racking, but I just can't see how this works the way it does. What flicks the switch to turn on the decay process?
There's no switch … it's on all the time

why is it like that? something to do with the weak interaction, i think

Mentor
 Quote by Mentallic ....what is causing these atoms to decay one after the other?
What causes an atom to decay is that it is unstable. What determines how long the half life will be is based on how unstable it is. Basically, particles in an atom are moving randomly and at any time have a certain chance of popping out of the atom.

There are many, many unstable situations in the real world that work the same way.
 As a Uranium atom decays by emitting alpha radiation, does it expel all protons at once, or one every now and then?)
As was stated earlier, decay for a single atom is an event, not a process. It happens all at once.
 Lets isolate this scenario down to just one radioactive atom which has a half life of 1 year. Without interacting with the outside world, this atom can decay at any moment?
Yes.
 And has a 50% chance of living to be 1 year old? And no matter how 'old' it gets, it still has the same chance of surviving a further year?
Yes, yes.
 I'm sorry, this must be nerve-racking, but I just can't see how this works the way it does. What flicks the switch to turn on the decay process?
Instability and the nature of the concept of "probability". Imagine you're playing with one of these:

The object of the game is to hit the ball with the paddle repeatedly. You have some skill and you find after hundreds of tests that on average you can do it 50 times. You try it and do it 43 times. Then you try it again and you do it 87 times. Then you try it again and you mess up after the first try. Such is the nature of probability. Every time you try to hit the ball, you have an identical probability of messing up: 1/50. When you actually mess up is random, but goverened by the math of the probability.

Mentor
 An atom is stable if the forces among the particles that make up the nucleus are balanced. An atom is unstable (radioactive) if these forces are unbalanced--if the nucleus has an excess of internal energy. Unstable atoms are called radionuclides. The instability of a radionuclide's nucleus may result from an excess of either neutrons or protons. An unstable nucleus will continually vibrate and contort and, sooner or later, attempt to reach stability by some combination of means: ejecting neutrons, and protons converting one to the other with the ejection of a beta particle or positron the release of additional energy by photon (i.e., gamma ray) emission.

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 Quote by Mentallic This problem has always bugged me, and the only answers I've been given were on the lines of "meh". What I don't understand is that if we are given 1 gram of a radioactive substance with a half life of n years, why is it that after n years, the substance is reduced to 0.5 grams of radioactive material; but after another n years, the substance has now reduced 0.25g. Does the substance know how much radioactive material is in its vicinity? What is actually happening at the atomic level in terms of the amount of radioactive atoms that become inactive? I doubt it has anything to do with probabilities of whether a certain atom will decay or not. So what is actually going on here?
Think of the poplulation of world in the past decade and in the 1960s (and ignore changes in life expectancy). Is the number of people who died each year in the 1960s less than the number who die each year now? Why?

AM

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 Quote by tiny-tim Yes, at any moment it can decay, and no matter how 'old' it gets, it still has the same chance of surviving a further second There's no switch … it's on all the time … why is it like that? something to do with the weak interaction, i think
Oh and the flicking of the switch was intending to describe the instant the radionuclide becomes stable.

 Quote by russ_watters What causes an atom to decay is that it is unstable. What determines how long the half life will be is based on how unstable it is.
So, by my logic, I would assume that atoms with longer half lives are more stable than those with very short half lives. Yet, Uranium is still very dangerous...

 Basically, particles in an atom are moving randomly and at any time have a certain chance of popping out of the atom. There are many, many unstable situations in the real world that work the same way. As was stated earlier, decay for a single atom is an event, not a process. It happens all at once... Instability and the nature of the concept of "probability".
Thanks for elaborating on this. And yes, I understand the concept of probabilitiy, but found it hard to believe that it could be applied to the processes of an atom.

 Quote by Andrew Mason Think of the poplulation of world in the past decade and in the 1960s (and ignore changes in life expectancy). Is the number of people who died each year in the 1960s less than the number who die each year now? Why?
Um I wouldn't have any reason to believe more die now than back then as there wouldn't be a great difference in the size of the world's population then to the size now. This isn't really the same concept as the decay of radionuclides though.

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 Quote by Mentallic So, by my logic, I would assume that atoms with longer half lives are more stable than those with very short half lives. Yet, Uranium is still very dangerous...
You are letting popular misconceptions block your understanding. It is the popular perception that a longer half life = more radioactive. But as you have just figured out, that isn't the case. Isotopes with shorter half lives are more radioactive and thus more dangerous. So when someone tells you something (like radioactive waste) is dangerous for a long time, they are not necessarily right. If it has a long half life, it isn't very dangerous. In fact, with a half life sufficiently long, some waste is safe enough that it is essentially just dumped in regular landfills. Much of what we were planning on storing in the Yucca Mountain facility is actually safer than when it was dug out of the ground. Think about it: there is a certain amount of radioactivity in a lump of uranium when it was dug out of the ground. It is processed to separate out the more radioactive parts, which are then used in a reactor. What's left is still radioactive, but it is less radioactive than when first dug out of the ground.

Not sure where Andrew was going with that thing about death rates...
 Blog Entries: 2 Good thread, but an obvious question is what really causes "chance occurences" to occur? That is what causes "random probability" in sub-atomic physics? Consider a sample of C14: Half life 5730 years. One C14 atom decays in 5 seconds, while another waits for 57,300 years (10 half lives) until it decays. Difficult to imagine how these 2 atoms could really be the same initially. Are the C14 atoms differant ages? It might make more sense if radioactive decay were to follow a gaussian distribution.

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 Quote by russ_watters You are letting popular misconceptions block your understanding. It is the popular perception that a longer half life = more radioactive. But as you have just figured out, that isn't the case. Isotopes with shorter half lives are more radioactive and thus more dangerous. So when someone tells you something (like radioactive waste) is dangerous for a long time, they are not necessarily right. If it has a long half life, it isn't very dangerous. In fact, with a half life sufficiently long, some waste is safe enough that it is essentially just dumped in regular landfills.
Yes I've pondered over this as well. But the media always implies that the long half lives are always correspondent with being more dangerous.
Rough quote from my physics teacher:
 "Radioactive isotopes are used in medicine such as (I think caesium). It is injected into the body. And has a very short half-life and thus after a week there is barely any sign of traces; this is why it's fairly safe".
I never quite understood how a radioactive substance with a short half-life can be safer than a substance with a long half-life. Of course either it's just this popular misconception as you said, or they take into consideration the types of radiation released and number of stages in the radioactive decay process. (Uranium must eject many more p+n than caesium)

 Much of what we were planning on storing in the Yucca Mountain facility is actually safer than when it was dug out of the ground. Think about it: there is a certain amount of radioactivity in a lump of uranium when it was dug out of the ground. It is processed to separate out the more radioactive parts, which are then used in a reactor. What's left is still radioactive, but it is less radioactive than when first dug out of the ground.
From the small amount of media coverage I heard about this issue, this was never mentioned. Thanks, this is a great eye-opener

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 Quote by Xnn Good thread, but an obvious question is what really causes "chance occurences" to occur? That is what causes "random probability" in sub-atomic physics? Consider a sample of C14: Half life 5730 years. One C14 atom decays in 5 seconds, while another waits for 57,300 years (10 half lives) until it decays. Difficult to imagine how these 2 atoms could really be the same initially. Are the C14 atoms differant ages? It might make more sense if radioactive decay were to follow a gaussian distribution.
Yes this is exactly what I've been trying to understand We are talking about nature, and no external factors are affecting the times these equal atoms decay, yet they do so at vastly different ages. I'm not ready to accept that the 'probability' of decay is the same as flicking a coin or any other analogy to explain these effects.

Tiny-tim may be on to something though:
 Quote by tiny-tim why is it like that? something to do with the weak interaction, i think
I just hope I can get more information on this weak interaction.

 Quote by Mentallic Yes I've pondered over this as well. But the media always implies that the long half lives are always correspondent with being more dangerous.
The media is generally a very bad place to get info about nuclear related issues. To many people nuclear = bombs. People are more likely to watch something if they think there is something to fear then if they think everything is fine.

It is true that longer half life = safer. In the case of a radioactive element being put into the body they can use the exact amount they see fit. So even if they are using a shorter half life and thus more radioactive element they can just compensate by using less of it.

As for the reason for the huge variance in decay times, it is simply due to probability. In any given second there is a small chance of an atom decaying. Given a large enough sample of atoms some will decay very soon, while others will take a very long time. In any given half life time period there is a 50/50 chance of decay. It doesn't matter how many previous half life periods it made it through, each period is a new 50/50 chance. All that needs to happen is for a very long string of "heads" which given a large sample is expected to happen.

I know this has already been said, but it is the reason why. If you are having a hard time believing there can be unusually long or short runs in random events then sit down with a die or coin and try it out. Most people are surprised at how many strings of heads or tails there are when you actually flip a coin 100 times.

If this doesn't sound like fun to you head on over to random.org and get a random file. Go through and let a 0 represent not decaying and a 1 represent decaying. Notice how some atoms go very quickly while other last a long time.

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