Question

Why the size of aluminium is greater than the size of gallium?

Answer 1

Poor Shielding effect.

Aluminum and Gallium belongs to group 13.

Generally as we move down to group, the atomic radii increases as the one higher level electronic orbital is required to accommodate the electrons.

Even though Gallium lies below Aluminum, the atomic size of Gallium is smaller than Aluminum because of Shielding Effect.

In case of Gallium the outermost electrons are poorly shielded by d electrons, increasing nuclear attraction of the outer electrons, which results the smaller radius of Gallium.
D orbitals are large, so they don't shield the outer electrons very well like s or p orbitals. So, presence of d orbitals just below outermost orbit reduces increases nuclear pull, due to poor shielding.