Why Is a Neutron Stable in a Nucleus but Unstable When Free?

[da_willem]

A (free) neutron has a lifetime of some 10 minutes or so, how come it is stable in a nucleus?

 

[Hootenanny]

Recall that the Pauli exclusion principle states that no two identical fermions (neutrons and protons are fermions) can occupy the same quantum state at the same time. If the neutron were to decay (beta^- decay) into a proton (with the electron and anti-neutrino ejected from the nucleus), then this 'new' proton will try to occupy the quantum state with the lowest possible energy. However, since there are already [possibly many] proton(s) in the nucleus it must occupy a higher quantum state with a higher corresponding energy. However, in order to occupy this higher state the proton would have to absorb some energy. Therefore, normally a neutron does not decay in a nucleus. However, if the nucleus is neutron rich (N>>Z) then it is possible for a neutron to decay inside the nucleus.

I hope that answered your question.

 

[da_willem]

It did, stupid of me to not have thought of that!

BTW: I'm wondering, will the remaining electron occupy an orbital of the atom to form an ion? I suppose if there's enough energy it could also get away from the nucleus?!

 

[jtbell]

The electron emitted in beta decay has an energy of a few MeV (million electron volts) so it flies right out. So you get a positive ion which picks up an electron from its environment in due course. It all balances out in the end, because the emitted electron gets stopped somewhere, and any mobile electrons move around to restore overall neutrality.

 

[Astronuc]

A (free) neutron has a lifetime of some 10 minutes or so, how come it is stable in a nucleus?

Well neutrons are stable up to a point. While there are many isotopes (nuclides) which are stable, there are many more which are not! Not only that, each nuclide has a unique half-life, and there are some elements (for Z<83) like Tc (Z=42) or Pm (Z=61) for which there are no stable isotopes. Bi (Z=83) is the heaviest element with a stable isotope (Bi-209, which is the heaviest stable isotope). Neutron rich nuclides tend to decay by beta emission, and at some point, alpha emission is a preferred decay mode.

Th-232 (T1/2 = 1.40E10 y), U-235 (T1/2 = 7.04E8 y) and U-238 (T1/2 = 4.468E9 y) might be considered quasi-stable due to their extremely long half-lives, but they do decay by alpha emission and with very low probability by spontaneous fission, SF.

And interestingly, there are isotopes which can decay either by beta or alpha emission.

See - http://www.nndc.bnl.gov/chart/ or alternatively -
http://wwwndc.tokai-sc.jaea.go.jp/CN04/index.html

Looking at the simplest element, hydrogen, the isotope deuterium, and paired p,n in the nucleus, is quite stable, but tritium, p,2n is not. Clearly there is an interaction between the p,n which stabilizes the n, while an extra n is not necessarily stable.

 

[mathman]

Bi (Z=83) is the heaviest element with a stable isotope (Bi-209, which is the heaviest stable isotope).

It has been discovered recently that Bi is radioactive with an extremely long halflife (3*10¹⁹ years).