The statement(s) that are correct about the species $\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}$ and $\mathrm{Mg}^{2+}$.

(A) All are isoelectronic

(B) All have the same nuclear charge

(C) $\mathrm{O}^{2-}$ has the largest ionic radii

(D) $\mathrm{Mg}^{2+}$ has the smallest ionic radii

Choose the most appropriate answer from the options given below :

<p>To answer this question, let's address each statement individually.</p> <p><strong>(A) All are isoelectronic</strong></p> <p>An isoelectronic species is a group of ions or atoms which have the same number of electrons. The electron configuration for each species is as follows:</p> <ul> <li>$\mathrm{O}^{2-}$: Oxygen has 8 protons and normally 8 electrons. Gaining 2 electrons gives it a total of 10 electrons.</li> <li>$\mathrm{F}^{-}$: Fluorine has 9 protons and normally 9 electrons. Gaining 1 electron gives it a total of 10 electrons.</li> <li>$\mathrm{Na}^{+}$: Sodium has 11 protons and normally 11 electrons. Losing 1 electron leaves it with 10 electrons.</li> <li>$\mathrm{Mg}^{2+}$: Magnesium has 12 protons and normally 12 electrons. Losing 2 electrons leaves it with 10 electrons.</li> </ul> <p>All of these ions have the same number of electrons (10), making them isoelectronic. Therefore, statement (A) is <strong>correct</strong>.</p> <p><strong>(B) All have the same nuclear charge</strong></p> <p>The nuclear charge refers to the total charge within the nucleus, which is determined by the number of protons. The nuclear charges are:</p> <ul> <li>$\mathrm{O}^{2-}$: 8 protons</li> <li>$\mathrm{F}^{-}$: 9 protons</li> <li>$\mathrm{Na}^{+}$: 11 protons</li> <li>$\mathrm{Mg}^{2+}$: 12 protons</li> </ul> <p>Since the number of protons varies among these species, they do not have the same nuclear charge. Therefore, statement (B) is <strong>incorrect</strong>.</p> <p><strong>(C) $\mathrm{O}^{2-}$ has the largest ionic radii</strong></p> <p>In a series of isoelectronic ions, the ionic radius decreases with increasing nuclear charge because the greater the nuclear charge, the more strongly the electrons are pulled towards the nucleus, reducing the size of the ion. As $\mathrm{O}^{2-}$ has the lowest nuclear charge among the given ions, it will have the largest ionic radius. Therefore, statement (C) is <strong>correct</strong>.</p> <p><strong>(D) $\mathrm{Mg}^{2+}$ has the smallest ionic radii</strong></p> <p>Following the same logic as above, $\mathrm{Mg}^{2+}$, having the highest nuclear charge among the given isoelectronic species, will have the smallest ionic radius because its electrons are held most tightly by the nucleus. Thus, statement (D) is <strong>correct</strong>.</p> <p>Given the evaluations above, the most appropriate answer is:</p> <p>Option B (A), (C) and (D) only.</p>