# Is Nuclear Decay random?

#### Paul Dirac

For example tritium has a half life of of 12.3 years. So if you had 2 atoms of tritium then after 12.3 year you would expect to have 1 atom of tritium and 1 atom of h-3. My question is, is it possible that tritium could decay in 1 second? Or how about 1 eon? I know its not probable but is it possible? <Edited to remove personal speculation>

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#### Nugatory

Mentor
you are right about the random nature of radioactive decay. If I take a large number of tritium atoms and watch them... They'll be randomly decaying at a rate such that after 12.3 years half will have decayed.

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#### Paul Dirac

Thanks for your answer. My question is, is it possible that tritium could decay in 1 second? Or how about 1 eon?

#### Matterwave

Gold Member
For one single tritium atom, the decay could theoretically happen from any time to any time. But the most likely times for decay are around the half life times. Other times like 1 second or 1 eon are extremely unlikely.

#### Paul Dirac

thank you! <Edited to remove personal theory>

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#### Renormalized

Early experimenters with radioactive elements measured a Poisson decay curve for all elements tested. That decay curve only occurs if the probability of a decay is random. i.e. it does not depend on previous decays or on any other measurable parameter. Thus, the randomness is established by experimental results.

#### Orodruin

Staff Emeritus
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Matterwave: The most likely time of decay is at t=0 since the decay time for a single nucleus follows an exponential distribution. This is reflected in the fact that if you take a lot of tritium the decay rate will be largest in the beginning (simply due to each tritium atom having a fixed probability of decay per time unit). Of course, this still does not change the fact that the mean life time is non-zero, or that you will have very close to half of the nuclei left after a time equal to the half-life has passed - which follows directly from the central limit theorem.

OP: The probability of N given nuclei decaying within a time t is given by P = (1-exp(-t/T))^N, which for small t/T approximates to (t/T)^N. Taking a mol of tritium for 1s would therefore give t/T = 1.8e-9 and N equal to the Avogadro number. (1.8e-9)^NA is really really really small.

#### Matterwave

Gold Member
Matterwave: The most likely time of decay is at t=0 since the decay time for a single nucleus follows an exponential distribution. This is reflected in the fact that if you take a lot of tritium the decay rate will be largest in the beginning (simply due to each tritium atom having a fixed probability of decay per time unit). Of course, this still does not change the fact that the mean life time is non-zero, or that you will have very close to half of the nuclei left after a time equal to the half-life has passed - which follows directly from the central limit theorem.
Yes, this was my fault for using not the correct language. I was talking about the mean life-time of the particle $\tau\equiv\frac{1}{\Gamma}$ being roughly in the half-life range (rigorously the half life is $\lambda=\tau\ln(2)$).

But you are right, this is not the "most likely time time for decay". It is the mean time for decays averaged over a large sample.

There is no relationship that more electrons = longer lifespan of particles.

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#### bhobba

Mentor
I think, Mr Dirac, you should live up to the eminence of your namesake and study quantum field theory where the answer to such things is found.

Beware however, although well within the capabilities of the great man, to mere mortals like I am, and I suspect you are, it is HARD, very very HARD.

You might like to build up to it so here is my recommended reading list in order of difficulty:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20
https://www.amazon.com/dp/046502811X/?tag=pfamazon01-20
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20
https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20
https://www.amazon.com/dp/0071543821/?tag=pfamazon01-20
https://www.amazon.com/dp/0691140340/?tag=pfamazon01-20
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

All that is simply a build up to what many consider THE book on QET by Peskin and Schroeder:
https://www.amazon.com/dp/0201503972/?tag=pfamazon01-20

It will be a long hard slog but at the end of it you will understand things a lot better than you do now, because to be blunt what you wrote is utter nonsense.

BTW I have those books except QFT for the Gifted Amateur and Peskin and Schroeder and am still worried I may find Peskin and Schroder still too tough. It is really hard. I want to get for the Gifted Amateur text first.

Thanks
Bill

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Mentor

#### Dale

Mentor
The thread is re-opened and has been edited to remove personal speculation. I remind the participants to review and abide by the forum rules.

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#### .Scott

Homework Helper
If a weak nonrandom variation in half-life existed, it should certainly already have been discovered. I think that only on that basis physicists would try to figure out how to accelerate or "freeze" half-life.
Actually they have been discovered. Which means the answer to the OP is that nuclear half lives have a random component of nearly 100%.
The specific cases where decay rates can change are:
7Be: I'm sure there are better citations, but the only one I can find right now is this:

http://connection.ebscohost.com/c/articles/21680118/change-7be-electron-capture-half-life-metallic-environments

163Dy: Stable, but can be made to decay.
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.2164

Staff Emeritus
On of the less attractive features of PF is that people often give an esoteric to answer someone who is struggling with basic concepts. Yes, there are atomic perturbations on the half-lives of nucleii. Usually they are small. They are certainly not relevant for the answer to the very basic question the OP asked.

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