The correct order of the first ionization enthalpy is

The correct option is Tl > Ga > Al.

Generally, as we move down a group in the periodic table, the first ionization enthalpy decreases because of the increase in atomic size and the shielding effect of inner shell electrons. However, Group 13 elements (Boron family) exhibit an anomalous trend in their ionization enthalpies due to the intervention of d and f-orbitals, which offer poor shielding.

Let's understand the factors causing these anomalies:

1. Gallium (Ga) vs. Aluminum (Al):
Gallium is placed below aluminum in the periodic table. However, gallium contains ten d-electrons in its inner shell:
$3d^{10}$
The d-orbitals have a diffuse shape and offer poor shielding of the outer electrons from the nuclear charge. Consequently, the valence electrons in gallium experience a greater effective nuclear charge, holding them more tightly. This makes the atomic radius of Gallium slightly smaller than Aluminum, resulting in a higher first ionization enthalpy for Gallium than Aluminum:
$\mathrm{Ga}>\mathrm{Al}$

2. Thallium (Tl) vs. Gallium (Ga) and Aluminum (Al):
Moving further down to Thallium, it contains fourteen f-electrons:
$4f^{14}$
in addition to d-electrons. The shielding effect of f-orbitals is even poorer than that of d-orbitals (shielding effect order: s > p > d > f). This poor shielding leads to a massive increase in the effective nuclear charge acting on the outermost 6s electrons. Thus, the outer electrons of Thallium are bound very strongly to the nucleus, giving Thallium a higher ionization enthalpy than both Gallium and Aluminum:
$\mathrm{Tl}>\mathrm{Ga}$

Thus, comparing these three elements, the correct order of their first ionization enthalpy is:
$\mathrm{Tl}>\mathrm{Ga}>\mathrm{Al}$