[hamza (OP)]

 I was confused about the concept of Half life when we study it in radioactive elements. Theoretically, the element can never actually go out of existence if it obeys  half life. It just keeps reducing to half after a fixed time. I wanted to know if the dilemma arises when we actually introduce the concept of half life to the element, when in "reality" it can end to nothing anyway. What are your thoughts on this!!
                 

[CPT ArkAngel]

The half life of particles is only a probability that you can apply on a large number of particles. It is the averaged time to reduce the original number of particles by half, and its precision tend to 100% with increasing quantity of particles. The environment may change the half life...

[CliffordK]

True.

It never completely goes away, although over time the concentration will become so low that it may be undetectable.  Except that one is truly dealing with discrete atoms, so eventually the last one could possibly decay away.

There is a certain amount of radiation that is considered "background radiation".  I.E. what is normal in the environment.  We consider a radioactive isotope to have decayed to zero when it reaches background.

However, there are also some elements that are only found as synthetic nuclear reactor byproducts.  These then could potentially be considered separate from the background.

Think of Carbon 14.
The Carbon 14 on the surface of the Earth is almost all generated in the sun and stars and arrives here via solar wind and cosmic rays.

It has a halflife of 5700 years. 
It seems like a long time.
But, say we have a coal deposit that is 570 million years old.

That would mean that it has gone through 10,000 half lives.

And the fraction of the original concentration is now 1/(2¹⁰⁰⁰⁰)

Which is about 5.012372749×10^-3011

Needless to say, that is a lot of zeros.  While you may find some carbon 14 in a 500 million year old coal deposit, it would be exceptionally scarce, beyond our ability to read.

Hmmm, odd....
Apparently that was a bad example.
http://www.talkorigins.org/faqs/c14.html

And that one actually often finds more Carbon-14 in coal than might be otherwise expected due to radioactive in nearby rocks.

Likewise, some of the more unstable synthetic elements and decay chain products may have a halflife of less than a second.  If a very small amount is synthesized, perhaps a few atoms, then it can completely decay in a manner of minutes.

[yor_on]

Your question reminds me of the hare and the turtle competing in a race. The turtle starts before the hare and for each step by, the much faster, hare it will still have moved slightly forward relative that hare. So, which one will reach the goalpost first?

Why?

[rosy]

The half-life of a  radioactive element means that, on average, half of the unstable nuclei will decay within one half-life. So if the half-life is 1 year, then after 3 years there will be (roughly) 1/8 of the original number of unstable nuclei in the sample. However, it is only an average, and once you get down to very small numbers the average only provides a very rough guide.

Iodine-131 has a half-life of about 8 days (actually more like 8.14).

1 g of iodine-131 contains about 4.6 x 10 ²¹ unstable nuclei.
After 8.14 days, there are about 2.3 x 10 ²¹ unstable nuclei.
After another 8.14 days, there are about 1.2 x 10 ²¹ unstable nuclei.
And....
So....
On....

After 70 half lives (about 570 days, or a year and a half), however, we might expect to be down to about 4 unstable nuclei, and another 8 days after that, two, and another 8 days after that, just one (note that because this is a random process by the time we get down to small numbers like this it's not really reasonable to assume that it'll all fall out neatly like this, but that's the general ballpark.

Now, we're down to one radioactive atom, and this is where it really becomes clear that to say that "It just keeps reducing to half after a fixed time" no longer applies:

A nucleus either decays or it doesn't... if you have 1 radioactive nucleus, there is a 50/50 chance of its decaying within one half-life, and if it doesn't then there's a 50/50 chance of its decaying in the following half-life, and so on. But we can be pretty confident it will eventually decay.

At this point, all the iodine-131 we started with has gone, we've got 1 g (well, near enough) of xenon-131 instead.

The answer to the original question, then, is "no", the half-life does not mean something can never decay away completely... although it may take a surprisingly long time.

[Geezer]

It doesn't say it can never decay completely. What it says is that it may never decay completely. It asymptotically approaches complete decay, but when it actually gets there is anybody's guess.

That's why we use the half-life measurement. If the "whole-life" was known, we would obviously use that instead.

[foobar_decay]

Think of Carbon 14.
The Carbon 14 on the surface of the Earth is almost all generated in the sun and stars and arrives here via solar wind and cosmic rays.

This is completely wrong. Carbon 14 is all generated in earth's atmosphere. It doesn't came from the space, not even slightest bit of it

[yor_on]

Heh

Depends on definitions that one.  The Cosmic Story of Carbon-14.  so no, CliffordK wasn't that wrong, he just didn't fill in the whole sequence, on the other tentacle, neither were you but together I think you both are (Yoda
=

One can, if one like, put a did in the were. eh so to speak.

[PmbPhy]

I was confused about the concept of Half life when we study it in radioactive elements. Theoretically, the element can never actually go out of existence if it obeys  half life. It just keeps reducing to half after a fixed time. I wanted to know if the dilemma arises when we actually introduce the concept of half life to the element, when in "reality" it can end to nothing anyway. What are your thoughts on this!!

You're referring to a rule which strictly applies only to a continuum of matter. However in real life matter is quantized meaning that any quantity of matter is really made of discrete particles. So in real life you will eventually get to the point where there's only one particle left at which time the particle will either decay at any period of time or it won't. If it does decay then all the matter will be gone. If not then wait a longer time and it will either decay or it won't and this repeats forever. In some samples all of it will be gone after a certain finite period.

See how that works?

[evan_au]

I posted this here, but it probably belongs more in this thread...

- At the level of individual atoms, eventually you will reach the situation where there is just one non-decayed atom left in the sample (after very many half-lives)
- When the averaged equation predicts just 0.01 atoms left, you could say that if you tried this experiment on 100 identical samples, in around 99 of those samples, the last non-decayed atom in the sample would have gone out of existence by now.

[Bill S]

Come back, Zeno, all is forgiven!  []

[geordief]

You're referring to a rule which strictly applies only to a continuum of matter.
 However in real life matter is quantized meaning that any quantity of matter is really made of discrete particles.
So in real life you will eventually get to the point where there's only one particle left at which time the particle will either decay at any period of time or it won't. If it does decay then all the matter will be gone. If not then wait a longer time and it will either decay or it won't and this repeats forever. In some samples all of it will be gone after a certain finite period.

See how that works?

Can we say "one "remaining" particle is the new "nothing"? " ** -and that "nothing" is  observer dependent?

** as in "green is the new black" , "60 is the new 40 " etc etc

[syhprum]

I am reminded of the Xmass pudding that queen Elizabeth the first had a hand in making, each year a spoonful is saved to go into the next years pudding so that when you eat some you are eating a pudding that liz 1 had a hand in preparing