# What happens then

## Main Question or Discussion Point

I know the half life period property of a radioactive element. At present I also studied the half life principle of the second power reactions in chemical kinetics. But I am interested in what happens to the adiation once all atoms have completely radiated. There is nothing such as half radiation. Radiation has to come out in the form of alpha, beta or gamma.

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russ_watters
Mentor
I'm not sure I understand what you mean, but as the atoms decay to more stable atoms, radiation decreases. If a specific atom decays to lead, it will never again undergo radioactive decay and therefore won't release any more radiation from radioactive decay.

lets say that you got 100% radioactive material, this material will radiate and in the process change into another material which is not radioactive (well if the new one isnt stable as well it will continue to decay).
the half-life time is the time it takes for the sample to change from 100% original material to 50% original material.
the reason we use half-life period is that matter decay exponentially and so it'll be zero only after infinity of time...

fargoth said:
the reason we use half-life period is that matter decay exponentially and so it'll be zero only after infinity of time...
That's not quite true. Exponential functions are continuous, but exponential decay, such as in radioactive decay, only takes discrete values. Once you get down to 1 atom of radioactive material, it WILL decay after a finite amount of time - we just won't usually see it.

Yes, I mean how can we find that finite time when one atom remains - just because there is no half radiation.
Moreover may not be that a system contains even numberof atoms or at anycase it need not be a power of two which arises a chance of reaching odd values. What happens then?

The half-life is based on a 50% probability that an atom will decay within the given time period. A half life of one year means that each atom of the substance has a 50% chance of decaying during the first year and a 50% chance of not decaying during this time. If you take a block of substance (a large quantity of atoms) then it will have decayed by approximately 50% after a year since statistically approximately half of its atoms will have decayed and half will have remained radioactive.

But if you take a single atom, say the last remaining radioactive one in an almost-fully decayed block, then it could decay within a year but not necessarily. If it has not decayed at the end of the year then it continues to have a 50% chance of decaying in the following year, or not. Same thing for the year after that. This gives you an increasing probability of decay as you consider longer and longer time periods: 50% for 1 year, 75% for 2 years, 87.5% for 3 years, and so on. There is a calculable possibility that this last atom will not decay for a million years or more. Just don't bet on it.

Do you mean that half life is a macroscopic and not microscopic property in a radioactive decay or second order reaction.

pretty much yes. you'll find that if you have only a few radioactive atoms, then the actual half life may be wildly different from the statistical half life from a macroscopic quantity of the radionuclide.

The term refers to how long it takes for a value to be halved. Of course it assumes that cutting the value in half is possible in the first place. Since it's not possible for a single atom then the term should not apply to it. And if I wanted to nitpick even more I would say that it also does not apply to any odd number of atoms. But for real-world situations this is splitting hair ...or atoms. When I read something about "...the atom's half-life..." I don't try to be a stickler for semantic but just understand the correspondence with the average time of decay for these atoms.

russ_watters
Mentor
vaishakh said:
Do you mean that half life is a macroscopic and not microscopic property in a radioactive decay or second order reaction.
Well, no - half life applies just fine whether you have 1 atom or a billion, it is just looks a little different when dealing with only one atom. But any problem of probability looks different for 1 iteration (or object) than it does for a million. Try applying probability to the repeated flipping of a coin, for example: probability can't tell you anything specific about your next flip of the coin (just that it has the same 50% probability as the last one), but flip the coin a billion times and you will be able to predict with an exceedingly high degree of precision how many came up heads (half a billion).

HallsofIvy