Evaluation of Ionization Enthalpy Trends in Boron and Carbon Group Elements

To determine the correctness of the two statements, let us analyze each statement individually:

Analysis of Statement I:

The second ionization enthalpy ($\Delta_i H_2$) corresponds to the removal of a second electron from the unipositive ion ($M^+$):

1. $\text{B}^+$: Electronic configuration is $[\text{He}] 2s^2$.
2. $\text{Al}^+$: Electronic configuration is $[\text{Ne}] 3s^2$.
3. $\text{Ga}^+$: Electronic configuration is $[\text{Ar}] 3d^{10} 4s^2$.

Due to the poor shielding provided by the filled $3d$-orbitals in $\text{Ga}^+$, the effective nuclear charge ($Z_{\text{eff}}$) acting on the outer $4s$-electrons increases significantly (d-block contraction). As a result, it requires more energy to remove an electron from $\text{Ga}^+$ than from $\text{Al}^+$.

The experimental values for the second ionization enthalpies ($\Delta_i H_2$) are:

• $\text{B} \approx 2427 \text{ kJ mol}^{-1}$
• $\text{Al} \approx 1816 \text{ kJ mol}^{-1}$
• $\text{Ga} \approx 1979 \text{ kJ mol}^{-1}$

Thus, the correct order of second ionization enthalpy is: $\text{B} > \text{Ga} > \text{Al}$

Therefore, Statement I is false.

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Analysis of Statement II:

For Group 14 elements ($\text{C}, \text{Si}, \text{Ge}, \text{Sn}, \text{Pb}$), the experimental values for the first ionization enthalpy ($\Delta_i H_1$) are:

• $\text{Si} \approx 786 \text{ kJ mol}^{-1}$
• $\text{Ge} \approx 761 \text{ kJ mol}^{-1}$
• $\text{Sn} \approx 708 \text{ kJ mol}^{-1}$
• $\text{Pb} \approx 715 \text{ kJ mol}^{-1}$

The general trend decreases down the group from $\text{C}$ to $\text{Sn}$, with a small increase at $\text{Pb}$ due to poor shielding by $4f$ electrons (lanthanoid contraction).

Thus, the correct increasing order of first ionization enthalpy is: $\text{Sn} < \text{Pb} < \text{Ge} < \text{Si}$

Statement II states the order as $\text{Si} < \text{Ge} < \text{Pb} < \text{Sn}$, which is completely opposite to the actual trend.

Therefore, Statement II is false.

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Conclusion:

Since both Statement I and Statement II are false, the correct option is B.