Animated Solution for Chemistry - d and f-Block Elements: Which of the following factors may be regarded as the main cause of lanthanide contraction?

Imagine you are diving deep into the microscopic world of a Lanthanide atom. At the very center lies the positively charged nucleus, a dense core of protons and neutrons. Surrounding this nucleus is a bustling cloud of electrons arranged in various shells. The outermost boundary of this atom is defined by the $6s$ electrons. However, the real magic happens deep inside, in the $4f$ subshell. As we move across the Lanthanide series from Cerium to Lutetium, the atomic number increases, and the incoming electrons don't go to the outer edge; instead, they dive deep into this buried $4f$ subshell.

Nuclear Pull vs. Shielding

In every atom, there is a constant tug of war. The positively charged nucleus pulls the outermost electrons inward. This attractive force is governed by what we call the Effective Nuclear Charge ($Z_{eff}$). But the outer electrons aren't facing the full brunt of the nucleus. The inner electrons act like a protective wall, repelling the outer electrons and shielding them from the nuclear pull. Mathematically, this is expressed as $Z_{eff}=Z-\sigma$, where $Z$ is the actual nuclear charge and $\sigma$ is the shielding constant.

Diffused $4f$ Orbitals

Here is where the plot thickens. Not all electron orbitals are created equal. While $s$ and $p$ orbitals are relatively compact and offer great shielding, the $4f$ orbital is highly diffused. Its electron density is spread out over a very large, complex volume. Because of this spread-out geometry, a $4f$ electron is terrible at blocking the nuclear pull. More importantly, one $4f$ electron is very bad at shielding another $4f$ electron in the same subshell. We call this phenomenon poor mutual shielding.

So, what happens as we march across the Lanthanide series? At each step, we add exactly one proton to the nucleus, increasing $Z$ by $1$. We also add one electron to the $4f$ subshell. Because of the poor mutual shielding of these diffused $4f$ electrons, the shielding constant $\sigma$ increases by less than $1$.

As a result, the net Effective Nuclear Charge ($Z_{eff}$) steadily increases. The nucleus wins the tug of war, pulling the outermost $6s$ shell closer and closer. This steady, relentless shrinking of the atomic radius across the series is the famous Lanthanide Contraction. It is a beautiful example of how the abstract shapes of quantum orbitals dictate the physical reality of the elements. Consequently, the correct answer is that the contraction is caused by the poor shielding of one $4f$ electron by another in the subshell.