Covalent Bonding Tendency and Size of Boron Cation

To determine the validity of the statements and their relationship, we analyze them using fundamental concepts of chemical bonding and periodic properties:

1. Analysis of Statement-1:
   Boron has the electronic configuration $1s^2 2s^2 2p^1$. To form an ionic compound involving a trivalent cation ($\text{B}^{3+}$), it would need to lose its three valence electrons. However, due to its extremely small atomic size and high effective nuclear charge, the sum of the first three ionization enthalpies ($\sum_{i=1}^{3} \Delta_i H$) of boron is extraordinarily high:
   $\sum_{i=1}^3 \Delta_i H = \Delta_i H_1 + \Delta_i H_2 + \Delta_i H_3 \approx 6887\text{ kJ mol}^{-1}$
   This enormous energy requirement cannot be compensated by lattice enthalpy in crystal lattices or by hydration enthalpy in solution. Consequently, boron cannot exist as an isolated $\text{B}^{3+}$ ion and always shares electrons, forming covalent bonds in all its compounds. Thus, Statement-1 is True.

2. Analysis of Statement-2:
   According to Fajans' Rules, the covalent character of a chemical bond increases with:

   • Smaller cation size
   • Larger anion size
   • Higher charge on the cation

   The polarising power ($\phi$) of a cation is defined as the ratio of its ionic charge to its ionic radius:
   $\phi = \frac{\text{Charge on cation}}{\text{Radius of cation}}$
   Due to the very high $+3$ charge and the exceptionally small ionic radius of a hypothetical $\text{B}^{3+}$ ion, its polarising power would be extraordinarily high. This extreme polarising power would severely distort the electron cloud of any surrounding anion, causing extensive orbital overlap and electron sharing. Therefore, the small size and high charge density of $\text{B}^{3+}$ strongly favour the formation of covalent bonds over ionic bonds. Thus, Statement-2 is True.

3. Relationship between the statements:
   Because the small size and high charge density (polarising power) of $\text{B}^{3+}$ make ionic bond formation energetically unfeasible and exclusively favour covalent bonding, Statement-2 provides the correct theoretical explanation for Statement-1.

Therefore, Statement-1 is True, Statement-2 is True, and Statement-2 is a correct explanation for Statement-1.

Correct Option: (A)