Stability of Half-filled and Completely Filled Orbitals — Revision Notes

⚡ 30-Second Revision

Key Concept: — Half-filled ($p^3, d^5, f^7$) and completely filled ($p^6, d^{10}, f^{14}$) subshells exhibit enhanced stability.
Reasons:

1. Symmetry: Symmetrical electron distribution minimizes electron-electron repulsion. 2. Exchange Energy: Maximized number of exchange pairs for electrons with parallel spins, releasing stabilizing energy. Formula: $N = \frac{n(n-1)}{2}$.

Examples (NEET Critical):

- Chromium (Cr, Z=24): Actual: $[Ar] 3d^5 4s^1$ (vs. Aufbau: $[Ar] 3d^4 4s^2$). Half-filled $3d^5$. - Copper (Cu, Z=29): Actual: $[Ar] 3d^{10} 4s^1$ (vs. Aufbau: $[Ar] 3d^9 4s^2$). Completely filled $3d^{10}$.

Consequence: — These factors can override the Aufbau principle, leading to anomalous configurations.

2-Minute Revision

The enhanced stability of half-filled and completely filled orbitals is a crucial concept explaining deviations from the standard Aufbau principle. This phenomenon occurs when a subshell (p, d, or f) is exactly half-filled (e.

g., $p^3, d^5, f^7$) or completely filled (e.g., $p^6, d^{10}, f^{14}$). The two primary reasons for this stability are the symmetrical distribution of electrons and the maximization of exchange energy.

Symmetrical electron arrangements minimize electron-electron repulsions, leading to a lower, more stable energy state. Exchange energy is a stabilizing energy released when electrons with parallel spins in degenerate orbitals can exchange positions.

Half-filled and completely filled subshells provide the maximum number of such exchange possibilities, thus maximizing the released exchange energy. This combined effect is significant enough to cause an electron from a lower energy orbital (like $4s$) to promote to a higher energy orbital (like $3d$) to achieve these stable configurations.

The most important examples for NEET are Chromium (Cr, Z=24), which adopts $[Ar] 3d^5 4s^1$ instead of $[Ar] 3d^4 4s^2$, and Copper (Cu, Z=29), which adopts $[Ar] 3d^{10} 4s^1$ instead of $[Ar] 3d^9 4s^2$.

Understanding these exceptions and their underlying reasons is vital for NEET.

5-Minute Revision

The stability of half-filled and completely filled orbitals is a fundamental principle in atomic structure that explains why certain elements deviate from the simple Aufbau rule when determining their electronic configurations. This enhanced stability is attributed to two main factors:

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Symmetrical Distribution of Electrons: — When a subshell is exactly half-filled (e.g., $p^3, d^5, f^7$) or completely filled (e.g., $p^6, d^{10}, f^{14}$), the electrons are distributed uniformly among all the degenerate orbitals within that subshell. This symmetrical arrangement minimizes electron-electron repulsions, leading to a more stable, lower energy state for the atom. Think of it as a perfectly balanced system.

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Maximization of Exchange Energy: — Exchange energy is a quantum mechanical stabilization energy that arises when electrons with parallel spins occupy degenerate orbitals. These electrons can 'exchange' their positions without any change in the system's energy. Each such exchange contributes to the overall stability. The number of possible exchange pairs (N) for 'n' electrons with parallel spins is given by $N = \frac{n(n-1)}{2}$. Half-filled subshells (e.g., $d^5$ with 5 parallel spins) and completely filled subshells (e.g., $d^{10}$ with 5 spin-up and 5 spin-down electrons, each set contributing) maximize the number of these exchange possibilities, thereby releasing a greater amount of stabilizing exchange energy.

This combined effect is so potent that it can outweigh the energy cost of promoting an electron from a slightly lower energy orbital to achieve such a stable configuration. The classic NEET examples are:

Chromium (Cr, Z=24): — Instead of the Aufbau-predicted $[Ar] 3d^4 4s^2$, it adopts $[Ar] 3d^5 4s^1$. An electron from $4s$ promotes to $3d$ to achieve a half-filled $3d^5$ configuration, which is significantly more stable.
Copper (Cu, Z=29): — Instead of the Aufbau-predicted $[Ar] 3d^9 4s^2$, it adopts $[Ar] 3d^{10} 4s^1$. An electron from $4s$ promotes to $3d$ to achieve a completely filled $3d^{10}$ configuration, which is exceptionally stable.

Understanding these specific configurations and the underlying reasons (symmetry and exchange energy) is critical for NEET, as questions frequently test this concept directly or indirectly through related topics like ionization energy or magnetic properties.

Prelims Revision Notes

Stability of Half-filled and Completely Filled Orbitals (NEET Quick Facts)

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Core Principle: — Atomic electronic configurations are more stable when their subshells are either exactly half-filled or completely filled.

* Half-filled examples: $p^3$, $d^5$, $f^7$ * Completely filled examples: $p^6$, $d^{10}$, $f^{14}$

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Reasons for Enhanced Stability:

* Symmetrical Distribution: Electrons are distributed uniformly in degenerate orbitals, minimizing electron-electron repulsion. This leads to a lower energy state. * Exchange Energy: Electrons with parallel spins in degenerate orbitals can exchange positions, releasing stabilizing energy. The more exchange pairs, the greater the stability. The number of exchange pairs (N) for 'n' parallel-spin electrons is $N = \frac{n(n-1)}{2}$.

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Key Examples (Crucial for NEET):

* Chromium (Cr, Z=24): * Aufbau-predicted: $[Ar] 3d^4 4s^2$ * Actual (Stable): $[Ar] 3d^5 4s^1$ * Reason: One $4s$ electron promotes to $3d$ to achieve a stable half-filled $3d^5$ configuration. * Copper (Cu, Z=29): * Aufbau-predicted: $[Ar] 3d^9 4s^2$ * Actual (Stable): $[Ar] 3d^{10} 4s^1$ * Reason: One $4s$ electron promotes to $3d$ to achieve a highly stable completely filled $3d^{10}$ configuration.

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Consequences/Implications:

* These stability factors can override the Aufbau principle. * Elements with these configurations often exhibit higher ionization energies (more energy needed to remove an electron). * Influences magnetic properties (e.g., $d^5$ has maximum unpaired electrons for a d-subshell).

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Common Traps:

* Confusing half-filled with completely filled. * Picking the Aufbau-predicted configuration instead of the actual stable one for Cr/Cu. * Misunderstanding the role of electron repulsion (stability comes from *reduced* repulsion).

Formula Recall:

Exchange pairs: $N = \frac{n(n-1)}{2}$ (where 'n' is the number of electrons with parallel spins in degenerate orbitals).

Practice Tip: Always write out the Aufbau configuration first, then check if promoting an electron would lead to a half-filled or completely filled d/f subshell. If so, apply the stability rule.

Vyyuha Quick Recall

Cr Cu Stay Extra Stable: Chromium and Copper configurations are Stable due to Exchange energy and Symmetry.