The stability verdict
The valley of stability
Plot every known nuclide with protons on one axis and neutrons on the other and the
stable ones form a narrow curved band — the valley of stability.
Light elements sit near N = Z. As Z rises, protons repel each other more strongly and
the nucleus needs proportionally more neutrons to stay bound, so the band bends
upward toward N ≈ 1.5 Z.
Stray above the band and the nuclide is neutron-rich: a neutron converts to a proton
and it emits an electron (β⁻ decay). Stray below and it is
proton-rich, so a proton converts to a neutron and it emits a positron
(β⁺ decay). Past bismuth (Z = 83) the valley simply runs out — no
arrangement of neutrons can hold that many protons together indefinitely.