The bond order and magnetic property of acetylide ion are same as that of

<p>We want to find which of the given diatomic species (among $\mathrm{O}_2^+$, $\mathrm{O}_2^-$, $\mathrm{N}_2^+$, and $\mathrm{NO}^+$) has <strong>the same bond order and the same magnetic property</strong> (dia- or paramagnetic) as the acetylide ion, $\mathrm{C}_2^{2-}$.</p> <h2>1. Electron Count and MO Considerations</h2><br/> <h3>(a) Acetylide Ion, $\mathbf{C_2^{2-}}$</h3> <p><p>A <strong>neutral</strong> $\mathrm{C}_2$ molecule would have $2 \times 6 = 12$ electrons.</p></p> <p><p>In $\mathrm{C}_2^{2-}$, there are <strong>2 extra electrons</strong>, giving a total of $12 + 2 = 14$ electrons.</p></p> <h3>(b) Matching Total Electrons Among the Options</h3> <p>Let us see how many electrons are in each species:</p> <p>$\mathrm{O}_2$ has $2 \times 8 = 16$ electrons </p> <p><p>$\mathrm{O}_2^+$ has $16 - 1 = 15$ electrons </p></p> <p><p>$\mathrm{O}_2^-$ has $16 + 1 = 17$ electrons</p></p> <p>$\mathrm{N}_2$ has $2 \times 7 = 14$ electrons </p> <p>$\mathrm{N}_2^+$ has $14 - 1 = 13$ electrons</p> <p>$\mathrm{NO}$ has $7 + 8 = 15$ electrons </p> <p>$\mathrm{NO}^+$ has $15 - 1 = 14$ electrons</p> <p>Hence the only diatomic species in the list <strong>that has 14 electrons</strong> (like $\mathrm{C}_2^{2-}$) is $\mathrm{NO}^+$.</p> <h2>2. Bond Order and Magnetic Property</h2> <h3>(a) $\mathrm{C}_2^{2-}$ (14 Electrons)</h3> <p>From molecular orbital (MO) theory for 14-electron diatomics (similar to $\mathrm{N}_2$ with 14e), we generally get:</p> <p><p><strong>Bond order</strong> = 3 </p></p> <p><p>All electrons paired in MOs → <strong>diamagnetic</strong>.</p></p> <h3>(b) $\mathrm{NO}^+$ (also 14 Electrons)</h3> <p>Similarly, $\mathrm{NO}^+$ also has 14 electrons and, by the same reasoning in MO theory, has:</p> <p><p><strong>Bond order</strong> = 3 </p></p> <p><p>Diamagnetic (no unpaired electrons).</p></p> <h2>3. Conclusion</h2> <p>Among the given choices:</p> <p><p>$\mathrm{O}_2^+$ has 15 electrons (not 14) </p></p> <p><p>$\mathrm{O}_2^-$ has 17 electrons </p></p> <p><p>$\mathrm{N}_2^+$ has 13 electrons </p></p> <p><p>$\mathrm{NO}^+$ has 14 electrons</p></p> <p>Therefore, the species with the <strong>same</strong> bond order (3) <strong>and</strong> the <strong>same</strong> magnetic property (diamagnetic) as $\mathrm{C}_2^{2-}$ is:</p> <p>$ \boxed{\mathrm{NO}^{+} \text{ (Option D).}} $</p>