= Solution
A useful convention for the <semi-empirical mass formula> is
$$
B(A,Z)=a_vA-a_sA^{2/3}-a_c\frac{Z(Z-1)}{A^{1/3}}
-a_a\frac{(A-2Z)^2}{A}+\delta(A,Z),
$$
where $B>0$ is the binding <energy>. The nuclear <mass> is $Zm_p+(A-Z)m_n-B/c^2$. Atomic-mass comparisons instead use hydrogen-atom <masses> and account for <electron> binding at the desired accuracy. No numerical fit coefficients are specified here.
The volume term represents short-range nuclear attraction with saturation: each <nucleon> has a limited number of close neighbours. The surface term subtracts the binding lost by <nucleons> at the boundary. Coulomb repulsion penalizes a large <proton> fraction. The asymmetry term penalizes unequal <neutron> and <proton> populations, reflecting the cost of filling different <Fermi seas> and nuclear interactions. Pairing favours even-even nuclei and penalizes odd-odd nuclei; odd-$A$ nuclei have zero pairing term in this approximation. For example, one may choose $\delta=\pm a_pA^{-1/2}$; an alternative fitted power requires a correspondingly different coefficient.
At fixed $A$, the smooth <mass> dependence on $Z$ is approximately parabolic. Neglecting the neutron-proton <mass> difference, pairing and small linear-in-$Z$ Coulomb corrections, minimization gives
$$
Z_{\rm stable}\simeq\frac{A}{2+(a_c/2a_a)A^{2/3}}.
$$
Thus the preferred <neutron excess> grows with <mass number>. The surface penalty disfavors very light systems, while the growing Coulomb penalty reduces the binding per <nucleon> of very heavy systems; this explains broad fusion and fission <energy> trends. The formula is a bulk approximation: shell closures, deformation and small separation-energy differences can give important exceptions. A fitted average binding trend is not a reliable substitute for a measured decay threshold near a boundary of stability.
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