The elements of Group 13 with highest and lowest first ionisation enthalpies are respectively:

The first-ionisation enthalpy (I.E.) of an element depends mainly on its atomic size and on the extent of shielding of the outermost electron.

For the Group 13 elements the experimental first-ionisation enthalpies are approximately:

$$\begin{aligned} \text{B} &:& 800 \text{ kJ mol}^{-1} \\ \text{Al}&:& 577 \text{ kJ mol}^{-1} \\ \text{Ga}&:& 579 \text{ kJ mol}^{-1} \\ \text{In}&:& 558 \text{ kJ mol}^{-1} \\ \text{Tl}&:& 589 \text{ kJ mol}^{-1} \end{aligned}$$

1. Highest first-ionisation enthalpy
    • Boron lies at the top of the group, has the smallest atomic radius, and its outermost electrons experience the strongest effective nuclear charge.
    ⇒ Boron possesses the maximum I.E. in the group.

2. Lowest first-ionisation enthalpy
    • As we move down the group, atomic size increases and I.E. normally falls.
    • However, Ga and Tl contain additional $$3d/4d$$ and $$4f$$ electrons which shield the nuclear charge poorly. This d- and f-block contraction slightly raises their I.E. values above the expected trend.
    • Indium, which has significant size but far fewer inner f-electrons than Tl, shows the minimum measured value in the series.

Therefore, the element with the highest first-ionisation enthalpy is $$\mathbf{B}$$ and the element with the lowest first-ionisation enthalpy is $$\mathbf{In}$$.

Hence, the required pair is $$\mathbf{B \; \& \; In}$$, given in Option D.