Animated Solution for Chemistry - Periodicity in Properties: The increasing order of atomic radii of the following group 13 elements is

Reality

When we first learn about the periodic table, we are taught a very comforting, logical rule: as you move down a group, the atomic radius increases. This makes perfect sense because with each step down, a brand new principal quantum shell is added to the atom. It is like adding layers to an onion; the more layers, the bigger the onion.

Following this logic for Group 13 elements, we would naturally expect the size to increase smoothly from Boron to Thallium. The expected order would be $\text{B}<\text{Al}<\text{Ga}<\text{In}<\text{Tl}$. However, chemistry is a science of beautiful exceptions, and nature has a surprise waiting for us right between Aluminum and Gallium.

If we take actual measurements, we find that the atomic radius of Gallium is $135\text{pm}$, which is surprisingly smaller than that of Aluminum at $143\text{pm}$. To understand why the atom shrank instead of growing, we must look under the hood at their electronic configurations.

Aluminum ($Z=13$) has a straightforward configuration: $[\text{Ne}]3s^{2}3p^1$. Its valence electrons reside comfortably in the third shell.

Now, let's look at Gallium ($Z=31$). Its configuration is $[\text{Ar}]3d^{10}4s^{2}4p^1$. Notice the intruder? Before the outermost $4s$ and $4p$ orbitals are filled, a completely full $3d$ subshell containing 10 electrons is introduced. This is the first time in Group 13 that $d$-electrons make an appearance, and they change the rules of the game.

Poor Shielding

In a multi-electron atom, the inner electrons act as a shield, protecting the outermost valence electrons from the full attractive force of the positively charged nucleus. This is known as the shielding or screening effect. However, not all orbitals are created equal when it comes to shielding.

The $s$ and $p$ orbitals are relatively compact and provide excellent shielding. But $d$-orbitals have a highly diffused, double-dumbbell shape. Their electron density is spread out thinly over a large volume of space. Because of this diffused shape, the ten $3d$ electrons in Gallium are terrible at shielding the outer $4s$ and $4p$ electrons from the nucleus.

Because the shielding is so poor, the outermost electrons feel a much stronger pull from the nucleus than they normally would. We say that the Effective Nuclear Charge ($Z_{\text{eff}}$) acting on the valence shell has increased significantly.

This increased effective nuclear charge pulls the outermost electron shell inward, causing the entire atom to contract. This phenomenon is often referred to as Transition Contraction (or $d$-block contraction).

The inward pull is so strong that it overcomes the size increase we expected from adding the 4th shell. As a result, Gallium ends up being smaller than Aluminum.

Correcting our initial assumption, the true increasing order of atomic radii for Group 13 is $\text{Ga}<\text{Al}<\text{In}<\text{Tl}$. This perfectly matches option (B). Always remember, whenever $d$ or $f$ orbitals are newly introduced, be on the lookout for poor shielding and its dramatic effects on atomic properties!