# Why free neutrons are unstable?

1. May 27, 2014

### majid313mirzae

Outside the nucleus, free neutrons are unstable and have a mean lifetime of 885.7±0.8 s (about 14 minutes, 46 seconds). why??

2. May 27, 2014

### Staff: Mentor

Why not?
There is a possible decay, as a proton (plus an electron and a neutrino) is lighter and all conservation laws are satisfied in the decay.

3. May 27, 2014

### Staff: Mentor

Are you asking why the free neutron is unstable, or why the mean lifetime has that particular value?

4. May 27, 2014

### Staff: Mentor

Free neutrons decay because they're not forbidden to decay by any conservation laws.

The mass of a neutron is greater than the sum of the masses of the proton, electron, and antineutrino that are produced in the decay. The energy associated with the extra mass becomes the kinetic energy of the decay products. So energy conservation doesn't forbid it.

The proton and neutron each have baryon number +1. So baryon number conservation doesn't forbid it.

The electron has lepton number +1 and the antineutrino has lepton number -1. So lepton number conservation doesn't forbid it.

5. May 29, 2014

### Staff: Mentor

Perhaps I am missing something, but I find this statement slightly strange (or misleading/confusing).

Just because something is not forbidden doesn't mean it has to occur. Reaction (I am thinking in terms of chemistry, but they are not much different on a general level) has to be thermodynamically favorable.

So if the reaction is not forbidden and thermodynamically favorable (if I understand correctly this part was covered by mfb - mass of products is lower that the mass of neutron), the real question is - why it doesn't happen in nuclei, but only for isolated neutrons?

6. May 29, 2014

I think the OP is asking why neutrons behave differently outside the nucleus as distinct from inside the nucleus. All neutrons have the same half life for beta decay when they are free and outside the nucleus but not so when they are inside the nucleus,the half lives being different for different nuclei.

7. May 29, 2014

### Staff: Mentor

With nuclear decay, what matters is not the difference in mass between neutron and proton, but instead the difference in mass between the initial and final nuclei.

Another way to put it: in stable nuclei, the energy released by $n \rightarrow p + e^- + \bar \nu$ is not enough to make up the difference in binding energy between the initial and final nuclei.

Similarly, for a free proton, $p \rightarrow n + e^+ + \nu$ is not allowed because of energy conservation, but some nuclei do decay via that process.

Last edited: May 29, 2014
8. May 29, 2014

### Staff: Mentor

Every reaction that is not forbidden happens at finite temperatures - sometimes it happens extremely rare (up to "probably not within the lifetime of the universe"), or the opposite reaction happens more often, but it happens.

It is forbidden inside some nuclei, because there the neutrons and protons have a different energy.

9. May 30, 2014

### Creator

Yeah, Murphy's Law for neutron decay: "If it can happen it will happen." ;))

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