# Why the atomic (metallic) radius of gallium is less than that of aluminium?

It is a well known fact that on moving down the group of p-block elements, the atomic radius is expected to increase. However, gallium is an exception. The atomic radius i.e., the metallic radius of gallium ($135~\mathrm{pm}$) is less than that of aluminium ($143~\mathrm{pm}$).

My book provides the following reason:

It is due to the presence of additional 10 d-electrons in gallium which offer poor screening effect for the outer electrons from the increased nuclear charge.

But if that is the case, why the effect is not that same in case of the heavier members?

Moreover, there must be something else which governs this exceptional property of gallium. Maybe the structure, but I am not sure. Can someone elaborate?

• I am not sure of your values, but the book explanation leads me to think that gallium has a fairly low atomic radius because the 4s, 3d and 4p electrons are so close to each other that the 3d are not completely shielding the 4s and p electrons from the nuclear charge. It is more like one big level with 13 electrons. – Joseph Hirsch Jan 8 '17 at 2:56

First, you have to look at the definition of metallic radius, which is the half distance between two atoms in a lattice. It has a significant dependence on crystal structure.

Tanget relevant to the question and other answers:
Gallium has an orthorhombic crystal structure (CN = 6) whereas as aluminum has a face-centered cubic crystal structure (CN = 12). This difference in coordination requires a goldschmidt correction to compare values as if gallium were 12-coordinated which makes the gallium's corrected metallic radius actually even smaller compared to aluminum at about $\mathrm{130pm}$.

Gallium exists as a diatomic solid in the lattice, which causes the atoms to be closer together on the a axis because they are covalently bonded. Gallium's covalent radius is about $\mathrm{122pm}$ which is very much smaller than the metallic radii of either element. This value between the bonded atoms lowers the average distance between atoms giving gallium a lower metallic radius.

If you look at the Van der Waals radii of the elements, (more representative of a monoatomic gaseous atom) you will see that aluminum is actually smaller though not by a lot, giving some credence to the d-electrons explanations, but not a complete explanation in regard to the metallic radius.

As Joseph's comment above alludes to, the 3d electrons in Gallium exhibit poor shielding, which causes a phenomenon known as "d-block contraction" as seen in elements from Ga to Br. Despite being in the same group as Aluminium, the introduction of the d-orbital means Ga has significantly more protons (31 vs 13) so the positively-charged nucleus has a much greater pull in Ga than in Al. Because of d-block contraction the nucleus is able to exert much greater pulling power on the outermost s- and p-level electrons thus reducing the atomic radius. This also cause the ionisation potential of Ga to be higher than that of Al, when the normal trend is for ionisation potential to decrease down a group.

With each additional proton that is added to a nucleus, the attraction between the nucleus and the electrons is increased and thus the wave function is contracted. This trend is most obvious when going horizontally along a group: a lithium atom is much larger than a neon atom even though the valence electrons are in the same shell — and it is even true for the difference between boron and neon, if you want to restrict it to a single subshell.

Each time a new shell is opened, the atomic radius jumps upwards since these always (i.e. quantum mechanics calculations say so) have a greater contribution further away from the nucleus with at least one additional lobe. So far the basics.

What happens when going from aluminium to gallium? We should consider the case when going across the periodic table from the corresponding alkaline metals sodium and potassium. From sodium, it is two steps to aluminium but from potassium to gallium is 12 steps — the entire 3d block is wedged in-between. Thus, from a hypothetical starting point, we experience a much greater contraction by the time we reach gallium compared to aluminium.

Note that it is irrelevant that the 3d electrons are there and ‘shielding’. Shielding doesn’t play that great a role as is often said.

Another ‘step’ can be experienced when going from indium to thallium. Here, we suddenly have 4f elements perched in-between and thus the radii of indium and thallium are again rather similar.