when is the nucleus stable?

Question

for small atomic number, it is when the number of neutrons is approximately equal to the number of protons.. (p = n)
but what for large atomic number.???

Answer 1

For large atomic number, like 12, C-14 is unstable relative to electron (beta-minus) emission. Too many neutrons. For carbon-11, it is a positron (beta-plus) emitter. Too few neutrons.

Consider Tc At. No. 43 and Pm, At. No. 61. No stable isotopes. The reason is that the neutrons and protons in the nucleus are too far from filling a "closed" "shell" or energy level.

Beyond At. No. 83, Bi, no atoms, isotopes of elements are stable, because all of the nucleons fill energy levels that are far from stable. There is hope that about atomic number 120-130, there will be discovered an "Island of Stabilty." In this region, humans may be able to bombard lower isotopes with neutron-rich ions (think calcium-48). Could it be that there is an element, At. No. 125, a material, that we could make next that would be nonradioactive ?