Ionisation Enthalpy Comparison of Representative Elements and Alkaline Earth Metals

To determine the correct option, let us evaluate the two statements independently:

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Evaluation of Statement (I)

Statement (I) asserts that the first ionisation enthalpy ($\text{IE}_1$) follows the order: $\text{Na} > \text{Mg} > \text{Cl} > \text{Ar}$

The elements $\text{Na}$ ($Z=11$), $\text{Mg}$ ($Z=12$), $\text{Cl}$ ($Z=17$), and $\text{Ar}$ ($Z=18$) belong to the third period of the periodic table.

Across a period, as the effective nuclear charge ($Z_{\text{eff}}$) increases and atomic size decreases, the first ionisation enthalpy generally increases from left to right. Therefore, the actual order of first ionisation enthalpy for these elements is: $\text{Na} < \text{Mg} < \text{Cl} < \text{Ar}$

The statement gives the reverse order ($\text{Na} > \text{Mg} > \text{Cl} > \text{Ar}$), which is incorrect.

Hence, Statement (I) is false.

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Evaluation of Statement (II)

Statement (II) asserts that among $\text{Ca}, \text{Al}, \text{Fe}$, and $\text{B}$, the third ionisation enthalpy ($\text{IE}_3$) is very high for $\text{Ca}$.

Let us analyze the electronic configurations of the given elements and their divalent cations:

1. Calcium ($\text{Ca}$):

   • Ground state configuration: $[\text{Ar}]\,4s^2$
   • Divalent state ($\text{Ca}^{2+}$): $[\text{Ar}]$ (noble gas core with a completely filled octet, $3s^2 3p^6$)
   • Removing the third electron from $\text{Ca}^{2+}$ requires breaking into a highly stable, closed shell octet configuration: $\text{Ca}^{2+} ([\text{Ar}]) \longrightarrow \text{Ca}^{3+} ([\text{Ne}]\,3s^2 3p^5) + e^-$
   • Thus, the third ionisation enthalpy ($\text{IE}_3$) for $\text{Ca}$ is extraordinarily high.

2. Aluminium ($\text{Al}$):

   • Configuration: $[\text{Ne}]\,3s^2 3p^1$
   • $\text{IE}_3$ corresponds to losing the third valence electron to achieve a noble gas configuration ($\text{Al}^{3+}: [\text{Ne}]$), which is relatively low compared to $\text{Ca}$.

3. Boron ($\text{B}$):

   • Configuration: $1s^2 2s^2 2p^1$
   • $\text{IE}_3$ removes the last valence electron to form $\text{B}^{3+}$ ($1s^2$), which is also favorable.

4. Iron ($\text{Fe}$):

   • Configuration: $[\text{Ar}]\,3d^6 4s^2$
   • $\text{IE}_3$ converts $\text{Fe}^{2+}$ ($[\text{Ar}]\,3d^6$) into the extra stable half-filled $d$-subshell configuration of $\text{Fe}^{3+}$ ($[\text{Ar}]\,3d^5$).

Therefore, $\text{Ca}$ has an exceptionally high third ionisation enthalpy compared to $\text{Al}, \text{Fe}$, and $\text{B}$.

Hence, Statement (II) is true.

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Conclusion

• Statement (I) is false.
• Statement (II) is true.

This corresponds to Option D.