# Half Lives

1. Mar 14, 2009

### 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?

2. Mar 14, 2009

### signerror

No, they are acting independently without communicating.

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.

3. Mar 14, 2009

### Mentallic

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.

4. Mar 14, 2009

### signerror

Random chance.

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?

5. Mar 14, 2009

### Mentallic

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.

6. Mar 14, 2009

### tiny-tim

"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!

7. Mar 14, 2009

### Mentallic

I guess I expressed the analogy in a poor way :tongue2:
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?

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?)

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?

8. Mar 14, 2009

### 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

9. Mar 14, 2009

### Staff: Mentor

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 was stated earlier, decay for a single atom is an event, not a process. It happens all at once.
Yes.
Yes, yes.
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.

Last edited by a moderator: May 4, 2017
10. Mar 14, 2009

### Staff: Mentor

11. Mar 14, 2009

### 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?

AM

12. Mar 14, 2009

### Mentallic

Oh and the flicking of the switch was intending to describe the instant the radionuclide becomes stable.

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...

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.

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.

13. Mar 14, 2009

### Staff: Mentor

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...

14. Mar 14, 2009

### 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.

15. Mar 14, 2009

### 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.
Rough quote from my physics teacher:
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)

From the small amount of media coverage I heard about this issue, this was never mentioned. Thanks, this is a great eye-opener

16. Mar 14, 2009

### Mentallic

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:
I just hope I can get more information on this weak interaction.

17. Mar 15, 2009

### DaleSwanson

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 http://www.random.org/files/" [Broken] 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.

Last edited by a moderator: May 4, 2017
18. Mar 15, 2009

### Mentallic

Very true. And it's evident that these media ploys have manipulated the understanding of many people.

I hardly know much about radioactive effects on biological cells, but I have heard that it only takes one altered cell to reproduce and begin a cancer. Even with a small amount of this radioactive material, isn't there a good chance that the alpha/beta emissions would interact with the dna of a cell and cause problems?

While I sit there flipping this coin, each event will turn up a head or tail, depending upon a number of factors, including: power of flick, height above table, the way the coin hits the table etc.
But what is happening in the nucleus to cause the decay process to suddenly land face up? After many years, this unstable atom has managed to maintain its nucleus intact, but all of a sudden something happens and causes it to errupt.

19. Mar 15, 2009

### Staff: Mentor

This has been discussed above: it is an energy issue that causes instability.
Strictly speaking, they are not the same. Each has it's own separate random motion. Tiny random differences, like in Mentallic's coin flips.
Age has nothing to do with it. A flipped coin doesn't know what the result of the last flip was.
It does! http://www.sea.co.th/seaweb/p5205.htm [Broken]

Last edited by a moderator: May 4, 2017
20. Mar 15, 2009

### Staff: Mentor

If there were no random motion, there'd be no half life. If an atom's internal energy were greater than it's binding energy and the motion always exactly the same, all radioactive elements would decay instantly. But the motion is random, so whether the energy actually is above the binding energy and the motion of the atoms is a matter of probability.

Consider this: you have a warm pot of water on the stove. Do you understand the mechanism behind evaporation or boiling? The water evaporates at a certain rate. When it boils, it boils at a certain rate. Why? Why doesn't the water explode, every atom breaking free into a gas at the same time? Temperature is a gaussian distirbution of average energies. The water molecules are all bouncing around together like billards balls and every now and then, a particular molecule right on the surface gains an energy level above the bond energy of liquid water and pops off into the air. Can you predict which molecule is going to evaporate at what time? No - it is random. Random for each particle, yet it still happens at a very specific rate. It is determined by that gaussian distribution of temperatures.

21. Mar 15, 2009

### Andrew Mason

The http://www.infoplease.com/ipa/A0762181.html" now is more than double the population in 1960. It isn't exactly the same concept as decay of radionuclides, since there is 0 probability that a person will live more than 200 years. But, like radionuclides, the rate of death depends on the population.

Take one gram of a radionuclide with a half life of 1 year. Now divide it into two parts. How does the number of nuclide decays per unit time in the one half gram compare to the rate of decay in the whole gram (at the present time)? How does the number of undecayed nuclei in that one half gram now compare to the number of undecayed nuclei in the whole gram one year from now?

AM

Last edited by a moderator: Apr 24, 2017
22. Mar 16, 2009

### vanesch

Staff Emeritus
Although the picture with the random motion analogy presented here can help to understand how you can get random phenomena such as half life, I have to object to taking this too literally without a caveat.

In fact, nuclear decay is a quantum-mechanical phenomenon, and in most standard interpretations of quantum theory, there is strictly no difference between the nucleus that will decay in 5 minutes, and the one that will decay in 2 days. That is, the physical state of both, today, is identical. It is only in the Bohmian mechanics interpretation (which tries to give a classical, deterministic view on quantum theory) that there are "different initial conditions". In *that* interpretation, the explanation given here about the random motions is close to how things are pictured.
But in most other interpretations, there is no "random motion" and "different state" explanation, but one accepts that there are random phenomena of which quantum theory gives you a certain probability for them to happen.

23. Mar 16, 2009

### Mentallic

Very good analogy! Thanks a lot, this has cleared up my problems

24. Mar 16, 2009

### daveb

It's a misconception that longer half-life means less (or even more) dangerous. The danger that comes from a given sample is how much of it there is (it's decay rate, also known as activity), the energy of the emission, and the type of emission (photon, beta or alpha). If you have 2 different nuclides of material, and one has a very short half-life and the other a longer, then yes, the longer half life material is (generally) less dangerous due to external radiation. But it's possible shorter half-life material is less dangerous than long half-life material.

Take Tc-99m (6.02 hour half life) used in diagnostic medical procedures, with photon energy emission of 140 keV, and compare it to I-131 (8 day half-life), a mixed beta/gamma emitter with a multitude of decay schemes, also used for both diagnostic and therapeutic procedures. An injection of 1 microcurie of I-131 is less dangerous than 20 millicuries of Tc-99m. But 20 millicuries of each means the iodine is more dangerous.

This has to do with the fact that a beta emitter is generally a little more damaging because it deposits all of its energy in a smaller area than a photon which only deposits some of its energy locally. Alpha emitters are even worse than beta emitters because of the +2 charge and the alpha particle's large mass

If a nuclide is an alpha emitter, then (in general) that means danger due to external radiation (being exposed to it when it's outside the body) is less since alpha emissions can't penetrate dead layers of the skin. But as an internal hazard, alpha emissions are 20 times more dangerous.

This is one of the reasons (along with the large activities and criticality issues) the waste that is to be stored at Yucca has people a little leary. There are kilocurie activities of cesium-137 and strontium-90 (mixed beta/gamma and pure beta emitter), but also large activities of alpha emitters in each waste cask. The cesium and strontium are short half-life compared to the unusued uranium in the waste, but people are concerned that the alpha emitters will leach into the water tables where it will be ingested from water and agricultural/meat products.

Now, don't get me wrong, I'm all for Yucca until reprocessing of the waste (a much better alternative) can be implemented. But you have to understand the issue isn't as simple as a bunch of whacko environmentalists who don't understand the issue. Many don't, but there are respectable scientists who do understand, but view the chance of something happening (as low as it is) as too much of a risk.

25. Mar 16, 2009

### QuantumPion

The thing to understand about probabilities is that the fact that an outcome of a random event has no bearing on the probability of a future outcome. For example, the probability of a fair coin toss being heads is 50%. If you toss a coin 10 times and get 7 heads and 3 tails, that does not increase the chance for the next toin coss to be tails. In other words, there is no such thing as a winning streak, and the same is so with atoms decaying.

As for the danger of long vs. short half life radioactive substances, it depends on your definition of "dangerous"!

A sample of U-238 will be "some level of dangerous" a lot longer then a sample of Co-60 will be. Co-60 is far more dangerous in equal amounts, but it is gone after a couple decades. The Uranium will be around longer then earth will be. If you integrate the "danger factor" over the lifespan of the sample, the Uranium may be considered more "dangerous". This is basically the reasoning anti-nukes use to bash Yucca mountain. Of course this definition of integrating danger over time is silly, since what we are really concerned with is the exposure to people of radiation. And short-lived isotopes are much more damaging to living beings then long-lived ones over the time spans of humans.