Option A: Nuclear charge $(\mathrm{z})$ is the correct answer.

Isoelectronic species are atoms and ions that have the same number of electrons. When comparing the sizes of isoelectronic species, the major factor that affects their size is the nuclear charge $(\mathrm{z})$, which is the charge of the nucleus or the number of protons in the nucleus. Here’s why:

The more protons there are in the nucleus (higher nuclear charge), the more positively charged the nucleus is, and thus the stronger it can attract the electrons towards it. This results in a smaller radius for the species. Conversely, if there are fewer protons in the nucleus, the attraction to the electrons is weaker, leading to a larger radius. Let's compare the species given:

• $\mathrm{F}^{-}$ (fluoride ion) has 9 protons in the nucleus and 10 electrons.
• $\mathrm{Ne}$ (neon atom) has 10 protons in the nucleus and 10 electrons.
• $\mathrm{Na}^{+}$ (sodium ion) has 11 protons in the nucleus and 10 electrons.

Despite having the same number of electrons, the $\mathrm{Na}^{+}$ ion will be the smallest among the three due to the higher nuclear charge of 11 protons, which attracts the same number of electrons more strongly than $\mathrm{Ne}$ with 10 protons and $\mathrm{F}^{-}$ with 9 protons. Hence, $\mathrm{Na}^{+}$ has a lower atomic radius compared to $\mathrm{Ne}$, which in turn is smaller than $\mathrm{F}^{-}$.

Considering Option B (size being the same), Option C (electron-electron interaction), and Option D (principal quantum number), none of these factors are as significant as the difference in nuclear charge for isoelectronic species.

The principal quantum number (n) is the same for all these isoelectronic species since they all have their outer electrons in the second energy level (n=2) in the ground state. Electron-electron interactions do contribute to energy levels and could affect the size slightly, but the primary and determining factor for isoelectronic species remains the nuclear charge, as it directly influences the effective nuclear charge felt by the electrons. Therefore, Option A is the best answer.