I have couple of questions about nuclear physics that perhaps someone could help me with. My son (6th grade) is learning about radiometric dating, and told me that the heavier the isotope, the shorter the half-life. I don't recall hearing about that rule, and somehow it seems too simple a rule to be universal. On the other hand it makes sense since the more neutrons in the nucleus, the more binding energy is needed to keep it all together. So my first question is whether that rule is correct. The second is about the nuclear force. IIRC it is the strong force that keeps the nucleus together. I somehow recall that the force varies inversely with the cube of the distance whereas the electromagnetic and gravitational forces vary inversely with the square of the distance. Is this correct? My third question is about why lighter elements are unable to retain as many neutrons as heavier elements. What is the mechanism that keeps neutrons in a heavy nucleus but frees them in a light nucleus?

I googled and found a cute applet that shows isotope half-lifes:
http://lectureonline.cl.msu.edu/~mmp...uclear/nuc.htm

For hydrogen:
H(1) stable
H(2) stable
H(3) 12.33 years
H(4) 100 years
H(5) 80 years
H(6) 320 years
H(7) does not exist

For uranium:
U(235) 703.8 Myrs
U(236) 23.42 Myrs
U(237) 6.75 days
U(238) 4.468 Gyrs

Of those two lists, the heaviest isotope has the far longest half-life. Of course, uranium has heavier, shorter-lived isotopes.

The basic principle to recall here is that a nucleus will decay only because it can release energy. If it can release more energy, it will have a tendency to decay more quickly.

The mechanisms behind beta decay and alpha decay are different, so it's not really fair to compare the two. Also, different nuclei have different structure. So what happens for one element may not hold as you change from one to another.

The link that ATP provided is very instructive, though it does not indicate the type of decay involved. Half-lives tend to become shorter as you move away from the line of stability. These tend to be beta decays. Alphas happen for larger masses, but along an extension of the line of stability. (in very general terms) So the mass dependence is not really correct.

The strong force is short-ranged, but I don't think it follows a strict power law.


The reason light nuclei don't hold on to extra neutrons is that these atoms will then have vacant proton energy levels that are unfilled, so the system will go to lower energy by beta minus decay: having the neutron become a proton, and emit an electron and antineutrino. This is also why, even though the nuclear force is stronger than the electrostatic force, you don't get light nucei that are only protons. In that case there are vacant neutron levels available, and you get beta plus decay (proton -> neutron + positron + neutrino)

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