The outer electron configuration of Gd (At. no. 64) is
(a) 4f^3, 5d^5, 6s^2
(b) 4f^8, d^0, 6s^2
(c)

Q: Why does the electron shift to 5d and not somewhere else?

The $5d$ and $4f$ orbitals are very close in energy. Shifting an electron to $5d$ requires very little energy, which is more than compensated by the massive stability gained from a half-filled $4f$ subshell.

Q: Does this mean the Aufbau principle is wrong?

Not wrong, but it's a simplified model. The Aufbau principle doesn't account for the complex electron-electron repulsions and exchange energies that become significant in larger atoms.

Q: How do I know which elements will have these exceptions?

Look for elements whose expected configurations end in $d^4$, $d^9$, $f^6$, or $f^{13}$ (one electron short of half/full) or $d^5$, $d^{10}$, $f^8$, $f^{14}$ (one electron over, though the 'over' case like Gd is rarer and specific to the f-block).

Q: Why is a half-filled orbital so stable?

There are two main reasons: symmetrical distribution of electron density (which minimizes repulsion) and maximum exchange energy (electrons with parallel spins can exchange positions, releasing energy).

Q: Is the 6s orbital affected by this shift?

No, the $6s$ orbital is lower in energy and remains fully filled with $2$ electrons. The interplay happens exclusively between the closely spaced $4f$ and $5d$ orbitals.

Question

The outer electron configuration of Gd (At. no. 64) is

Options:

(A) $4f^3, 5d^5, 6s^2$

(B) $4f^8, d^0, 6s^2$

(C) $4f^4, 5d^4, 6s^2$

(D) $4f^7, 5d^1, 6s^2$

Sigma Percentile · Accepted Answer

### The Secret Life of Gadolinium: A Tale of Orbital Stability

The Aufbau principle is like a perfectly organized hotel manager, assigning electrons to rooms strictly based on energy levels. Most of the time, this system works flawlessly. But occasionally, elements like Gadolinium ($Z=64$) decide to break the rules in pursuit of something greater: ultimate stability.

### The Expected Path

Let's start by finding Gadolinium's nearest noble gas, which is Xenon ($Z=54$). This leaves us with exactly $10$ electrons to place. Following the standard Aufbau rules, we first fill the $6s$ orbital with $2$ electrons. The remaining $8$ electrons should naturally flow into the $4f$ orbital.

If we stopped here, we would expect the configuration to be $[	ext{Xe}] 4f^8 6s^2$. However, nature has a different plan.

### The Twist of Stability

The $4f$ orbital has a maximum capacity of $14$ electrons. In quantum mechanics, a perfectly half-filled orbital ($7$ electrons) is incredibly stable. This stability arises from a symmetrical distribution of electron density and a maximization of exchange energy—a phenomenon where electrons with parallel spins swap positions, releasing energy and stabilizing the atom.

With $8$ electrons, the $4f$ orbital is uncomfortably close to this perfect half-filled state, but just one electron over. It's like having a perfectly balanced scale with one tiny extra weight ruining the equilibrium.

### The Resolution

To achieve that sweet stability, the eighth electron from the $4f$ orbital packs its bags and moves next door to the slightly higher energy $5d$ orbital. The energy required to make this jump is minimal and is vastly outweighed by the massive stability gained from leaving behind a perfectly half-filled $4f^7$ core.

This elegant shift gives us the actual, experimentally verified configuration: **$[	ext{Xe}] 4f^7 5d^1 6s^2$**.

This phenomenon isn't unique to Gadolinium. We see similar rule-breaking behavior in $d$-block elements like Chromium ($3d^5 4s^1$) and Copper ($3d^{10} 4s^1$). It is a beautiful reminder that in chemistry, the pursuit of energetic stability often trumps strict rule-following.

Animated Solution for Chemistry - d and f-Block Elements: The outer electron configuration of Gd (At. no. 64) is

Select Answer:

Visualized Solution

\text{Gadolinium (Gd)}

\text{Noble Gas Core}

\text{Filling } 6s \text{ Orbital}

\text{Expected Configuration}

\text{Stability Constraint}

\text{Electron Shift}

\text{Actual Configuration}

\text{Key Takeaway}

The Sigma Insight: Inner Transition Elements

The Secret Life of Gadolinium

The Expected Path

The Twist of Stability

The Resolution

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