The first ionization energy of magnesium is smaller as compared to that of elements X and Y, but higher than that of Z. The elements X, Y and Z, respectively, are :

<p>We are told:</p> <p><p>$\mathrm{IE}(\mathrm{Mg})$ is <strong>smaller</strong> than $\mathrm{IE}(X)$ and $\mathrm{IE}(Y)$.</p></p> <p><p>$\mathrm{IE}(\mathrm{Mg})$ is <strong>greater</strong> than $\mathrm{IE}(Z)$.</p></p> <p>Hence we want:</p> <p>$ \mathrm{IE}(\mathrm{Mg}) < \mathrm{IE}(X), \quad \mathrm{IE}(\mathrm{Mg}) < \mathrm{IE}(Y), \quad \mathrm{IE}(\mathrm{Mg}) > \mathrm{IE}(Z). $</p> <p>Approximate first ionization energies (in $\mathrm{kJ\,mol^{-1}}$) of the relevant elements:</p> <p><p>$\mathrm{IE}(\mathrm{Ne}) \approx 2080$</p></p> <p><p>$\mathrm{IE}(\mathrm{Na}) \approx 496$</p></p> <p><p>$\mathrm{IE}(\mathrm{Mg}) \approx 738$</p></p> <p><p>$\mathrm{IE}(\mathrm{Al}) \approx 578$ (not listed but for reference)</p></p> <p><p>$\mathrm{IE}(\mathrm{Si}) \approx 787$ (not listed but for reference)</p></p> <p><p>$\mathrm{IE}(\mathrm{P}) \approx 1012$ (not listed but for reference)</p></p> <p><p>$\mathrm{IE}(\mathrm{S}) \approx 1000$ (not listed but for reference)</p></p> <p><p>$\mathrm{IE}(\mathrm{Cl}) \approx 1251$</p></p> <p><p>$\mathrm{IE}(\mathrm{Ar}) \approx 1521$</p></p> <p><p>$\mathrm{IE}(\mathrm{Li}) \approx 520$</p></p> <p>We test each option:</p> <p><strong>(A) neon, sodium, chlorine</strong> </p> <p><p>$X=\mathrm{Ne}$: $\mathrm{IE}(\mathrm{Ne})=2080 > 738$ ✓ </p></p> <p><p>$Y=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$ ✗ (contradicts “$\mathrm{Mg}$ &lt; $Y$”) </p></p> <p><p>$Z=\mathrm{Cl}$: $\mathrm{IE}(\mathrm{Cl})=1251 > 738$ ✗ (contradicts “$\mathrm{Mg}$ &gt; $Z$”) </p></p> <p>So (A) does not fit the requirement.</p> <p><strong>(B) argon, chlorine, sodium</strong> </p> <p><p>$X=\mathrm{Ar}$: $\mathrm{IE}(\mathrm{Ar})=1521 > 738$ ✓ </p></p> <p><p>$Y=\mathrm{Cl}$: $\mathrm{IE}(\mathrm{Cl})=1251 > 738$ ✓ </p></p> <p><p>$Z=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$ ✓ </p></p> <p>Thus $\mathrm{IE}(\mathrm{Mg}) < \mathrm{IE}(\mathrm{Ar}), \,\mathrm{IE}(\mathrm{Cl})$ and $\mathrm{IE}(\mathrm{Mg}) > \mathrm{IE}(\mathrm{Na})$. </p> <p>This <strong>matches perfectly</strong>.</p> <p><strong>(C) chlorine, lithium, sodium</strong> </p> <p><p>$X=\mathrm{Cl}$: $\mathrm{IE}(\mathrm{Cl})=1251 > 738$ ✓ </p></p> <p><p>$Y=\mathrm{Li}$: $\mathrm{IE}(\mathrm{Li})=520 < 738$ ✗ (contradicts “$\mathrm{Mg}$ &lt; $Y$”) </p></p> <p><p>$Z=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$, but the mismatch in $Y$ is enough to discard it.</p></p> <p><strong>(D) argon, lithium, sodium</strong> </p> <p><p>$X=\mathrm{Ar}$: $\mathrm{IE}(\mathrm{Ar})=1521 > 738$ ✓ </p></p> <p><p>$Y=\mathrm{Li}$: $\mathrm{IE}(\mathrm{Li})=520 < 738$ ✗ (contradicts “$\mathrm{Mg}$ &lt; $Y$”) </p></p> <p><p>$Z=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$ is fine for $Z$, but $Y$ fails.</p></p> <p>Hence only <strong>(B)</strong> satisfies all conditions:</p> <p>$ \boxed{\text{(B) argon, chlorine, and sodium.}} $</p>