Animated Solution for Chemistry - d and f-Block Elements: The number of $4f$ electrons in the ground state electronic configuration of ${\text{Gd}}^{2+}$ is ...... . [Atomic number of Gd is 64.]

The electronic configuration of f-block elements often feels like a maze of exceptions, but beneath the surface lies a beautiful logic driven by stability and symmetry. Let's dive into the fascinating case of Gadolinium (Gd) and uncover the secret behind its electron arrangement.

A Quest for Stability

Gadolinium, with an atomic number of 64, sits proudly in the lanthanide series. When we start filling its electrons, the first 54 are neatly tucked away in the Xenon core, $[\text{Xe}]$. This leaves us with 10 electrons to distribute among the $6s$, $4f$, and $5d$ orbitals.

Following the standard Aufbau principle, we fill the $6s$ orbital first, giving us $6s^2$. Now, we have 8 electrons left. You might expect them all to crowd into the $4f$ subshell, creating a $4f^8$ configuration. However, nature loves symmetry. A half-filled $4f$ subshell ($4f^7$) is exceptionally stable due to maximized exchange energy and a perfectly symmetrical charge distribution.

To achieve this state of zen, Gadolinium places 7 electrons in the $4f$ subshell and kicks the remaining 1 electron into the slightly higher energy $5d$ orbital. Thus, the ground state electronic configuration of neutral Gadolinium is:

The Outermost First Rule

Now, the question asks for the configuration of the ${\text{Gd}}^{2+}$ ion. To form a $+2$ cation, we must strip away two electrons. But which ones go first?

A common trap is to remove the last electrons that were added (the $5d$ or $4f$ electrons). However, ionization is a physical process of pulling electrons away from the nucleus. Therefore, electrons are always removed from the outermost principal quantum shell first.

In Gadolinium, the outermost shell is $n=6$. So, the two $6s$ electrons are the first to be evicted. The inner $4f$ and $5d$ electrons remain safely shielded.

After removing the $6s$ electrons, the electronic configuration of the ${\text{Gd}}^{2+}$ ion becomes:

The question specifically asks for the number of $4f$ electrons in this state. Looking at our final configuration, the $4f$ subshell is completely untouched and still holds its perfectly stable half-filled arrangement.

Understanding these subtle shifts in electron placement not only helps you solve tricky JEE questions but also gives you a deeper appreciation for the elegant rules that govern the quantum world!