I've read that free neutrons decay into a proton, electron and neutrino with an average lifespan of about 15 minutes. Is there anything physically different about a neutron that has existed for 14 minutes and one that has only existed for one minute? Does a random outside event trigger the decay or is something internally in the neutron slowly falling apart?
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$\begingroup$ If you like this question you may also enjoy reading this post. $\endgroup$– Qmechanic ♦Commented Aug 7, 2012 at 13:12
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$\begingroup$ Related, on the more technical side: Can we find the exponential radioactive decay formula from first principles? $\endgroup$– Emilio PisantyCommented Jul 26, 2017 at 13:56
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4 Answers
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Neutron decays into a proton, electron and electron anti-neutrino. Not only electric charge but also (electronic) lepton number has to be conserved (I'm not very sure in this statement). In short: you start and have to finish with 1 matter particle (anti-matter counts as -1).
Mean time $\neq$ half-life. More on wikipedia.
Physically there is no difference between a 14 minutes old neutron and a fresh neutron. Both will eventually decay. If you would observed a neutron for 14 minutes and then started observing another one, the older one would most probably decayed first. If you would started observing two neutrons after 14 minutes, both would decay with same probability. Why? Because neutrons are indistinguishable. You can't tell which is older. Basically, neutrons don't get older with time. Also decay is purely random and doesn't depend on neutron's past.
The opposite is for humans. Of course an 80 years old person will die first with much greater probability then a child. But what can you say about two human beings, if you wouldn't know anything about them?
There is no trigger for decay. Internal nor external. But there are physical reasons for decay, of course. One of them is, that neutrons are slightly heavier than protons and therefore decays to lower energy state ($E=mc^2$). Why are neutrons heavier, I don't know. But there are reasons for that, too. And this is not because $u$ and $d$ quarks have different weight. Quarks mass is only a small part of neutron and proton mass
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$\begingroup$ Thank you for pointing out that mean lifetime and half-life are not the same. $\endgroup$ Commented Aug 7, 2012 at 13:28
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2$\begingroup$ "If you would observed a neutron for 14 minutes and then started observing another one, the older one would most probably decayed first." Not sure what you mean here. The rest looks good though, including lepton number conservation. $\endgroup$– user10851Commented Aug 8, 2012 at 9:16
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1$\begingroup$ This is a good answer and it perfectly fits the OP's needs. However technically 3. is not correct. A neutron that is prepared at time t=0 will be at time t in the state $|n\rangle(t) = \exp{(-\lambda t)} |n\rangle + (1-\exp{(-\lambda t})) |p+e^-+\bar{\nu}_e\rangle $ $\endgroup$– JannickCommented Dec 3, 2015 at 16:50
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$\begingroup$ @Jannick You should square root those coefficients. $\endgroup$– J.G.Commented Jul 26, 2017 at 14:32
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The quantum mechanical description of the process gives you probabilities for all possible events and the 15 minutes happen to be the mean life time for this process. It's random and you don't have a guarantee for anything, except that the average result will converge against the propability distribution if you let many neutrons decay. There is "no need to talk about something internally happening" in a different way to end up with the two different possibilities of 14 and 15 minutes. And there is nothing really different between the neutron which decays after 14 minutes and the neutron which decays after 15 minutes aprart from the latter decaying 1 minute later.
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$\begingroup$ Downvote because you did not look up the actual half-life of neutrons and because your discussion of probability is not written to the level of understanding demonstrated by the OP. $\endgroup$ Commented Aug 7, 2012 at 12:22
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$\begingroup$ @AdamRedwine: Thanks Adam. As a matter of fact I did both, I took a look at OPs profile and I checked the wiki article where they claim While bound neutrons in stable nuclei are stable, free neutrons are unstable; they undergo beta decay with a mean lifetime of just under 15 minutes (881.5±1.5 s). $\endgroup$ Commented Aug 7, 2012 at 12:27
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$\begingroup$ I'll remove the downvote because of the link. I still think the language and explaination needs clearing up. $\endgroup$ Commented Aug 7, 2012 at 12:51
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$\begingroup$ @AdamRedwine: You're welcome to edit it if it's too complicated. $\endgroup$ Commented Aug 7, 2012 at 13:02
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I think you are misunderstanding what is meant by a half-life. When you start describing quantum mechanics (and nuclear decay is a fundamentally quantum mechanical event) you have to incorporate statistics. A half-life is the amount of time in which, on average, half of a large number of identical specimen will have decayed. When someone says the half-life of a neutron is 10.4 minutes, what they mean is, given any random neutron, if you wait for 10.4 minutes, there is a 50% chance that the neutron will have decayed during that time.
answered Aug 7, 2012 at 12:22
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There is a possibility that a one minute old neutron will beta decay. The probability is very low, but it can decay before the 14 minute old neutron. I think this answers the question does the neutron have a past before it decays, and the answer is no. It is how like a photon is dependent on the observation of the event.
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1$\begingroup$ What does your last sentence mean? $\endgroup$ Commented Dec 3, 2015 at 16:19
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2$\begingroup$ This is incorrect. If I prepare a neutron at time $t=0$, wait for 14 minutes, verify that it hasn't decayed, and prepare a new neutron at that time, then both neutrons are equally likely to decay over the next minute (and indeed over any subsequent time span). $\endgroup$ Commented Jul 26, 2017 at 13:58