Aufbau Principle, Pauli's Exclusion Principle and Hund's Rule — Revision Notes

⚡ 30-Second Revision

Aufbau Principle: — Fill lowest energy orbitals first. Order: $1s, 2s, 2p, 3s, 3p, 4s, 3d, \dots$
$(n+l)$ Rule: — Lower $(n+l)$ sum fills first. If sums are equal, lower $n$ fills first.
Pauli's Exclusion Principle: — No two electrons in an atom can have identical four quantum numbers. Max 2 electrons per orbital, with opposite spins ($\uparrow\downarrow$).
Hund's Rule: — For degenerate orbitals, fill singly with parallel spins ($\uparrow\quad\uparrow\quad\uparrow$) before pairing ($\uparrow\downarrow\quad\uparrow\quad\uparrow$).
Exceptions: — Cr ($[Ar] 3d^5 4s^1$), Cu ($[Ar] 3d^{10} 4s^1$) due to half-filled/fully-filled subshell stability.

2-Minute Revision

Mastering electron configuration is crucial for NEET, and it hinges on three core principles. The Aufbau Principle dictates that electrons occupy orbitals in increasing order of energy. Remember the $(n+l)$ rule: lower $(n+l)$ sum means lower energy; if sums are equal, the orbital with lower $n$ fills first (e.

g., $4s$ before $3d$). Pauli's Exclusion Principle is about electron individuality, stating that no two electrons in an atom can have the same set of all four quantum numbers. Practically, this means an orbital can hold a maximum of two electrons, and they must have opposite spins ($\uparrow\downarrow$).

Finally, Hund's Rule of Maximum Multiplicity applies to degenerate orbitals (like the three $p$ orbitals or five $d$ orbitals). It states that electrons will first occupy each degenerate orbital singly with parallel spins (e.

g., $\uparrow\quad\uparrow\quad\uparrow$ for $p^3$) before any orbital is doubly occupied. This maximizes stability by minimizing electron-electron repulsion. Don't forget the key exceptions to Aufbau for Chromium ($[Ar] 3d^5 4s^1$) and Copper ($[Ar] 3d^{10} 4s^1$), driven by the enhanced stability of half-filled and fully-filled subshells.

These rules collectively explain atomic structure, periodic trends, and magnetic properties.

5-Minute Revision

To ace electron configuration questions in NEET, a deep understanding of the Aufbau Principle, Pauli's Exclusion Principle, and Hund's Rule is essential. Start with the Aufbau Principle, which is the 'building up' rule.

Electrons fill orbitals from lowest to highest energy. The order is best remembered by the $(n+l)$ rule: calculate $(n+l)$ for each orbital; the one with the smaller sum fills first. If $(n+l)$ sums are equal, the orbital with the smaller principal quantum number ($n$) fills first.

For example, for $3d$ ($n=3, l=2 \implies n+l=5$) and $4s$ ($n=4, l=0 \implies n+l=4$), $4s$ fills before $3d$. This is a common point of confusion. Next, Pauli's Exclusion Principle is about the quantum state of individual electrons.

It states that no two electrons in the same atom can have identical values for all four quantum numbers ($n, l, m_l, m_s$). The practical implication is that any single orbital can hold a maximum of two electrons, and these two electrons must have opposite spins (one $+1/2$, one $-1/2$).

This is why we draw them as $\uparrow\downarrow$. Finally, Hund's Rule of Maximum Multiplicity comes into play when you have degenerate orbitals (orbitals of the same energy, like the three $p$ orbitals or five $d$ orbitals).

It states that electrons will first occupy each degenerate orbital singly with parallel spins (e.g., all 'up' spins) before any orbital is doubly occupied. This maximizes the total spin and reduces electron-electron repulsion, leading to a more stable configuration.

For instance, for $p^3$, it's $\uparrow\quad\uparrow\quad\uparrow$, not $\uparrow\downarrow\quad\uparrow\quad$. Remember the crucial exceptions for Chromium (Cr, Z=24) and Copper (Cu, Z=29). Cr's configuration is $[Ar] 3d^5 4s^1$ (not $3d^4 4s^2$) and Cu's is $[Ar] 3d^{10} 4s^1$ (not $3d^9 4s^2$).

These exceptions arise from the extra stability associated with half-filled ($d^5$) and completely filled ($d^{10}$) subshells. Practice writing configurations for various elements and identifying violations of these rules to solidify your understanding.

Prelims Revision Notes

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Aufbau Principle: — Electrons fill orbitals in increasing order of energy. This 'building up' process ensures the atom is in its most stable ground state.

* **$(n+l)$ Rule:** The primary determinant of orbital energy. Orbitals with a lower $(n+l)$ sum are filled first. If two orbitals have the same $(n+l)$ sum, the one with the lower principal quantum number ($n$) is filled first.

* Filling Order: $1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p$. * Exceptions: Chromium (Cr, Z=24): $[Ar] 3d^5 4s^1$ (not $3d^4 4s^2$). Copper (Cu, Z=29): $[Ar] 3d^{10} 4s^1$ (not $3d^9 4s^2$).

These occur due to the extra stability of half-filled ($d^5$) and completely filled ($d^{10}$) subshells.

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Pauli's Exclusion Principle: — No two electrons in the same atom can have the exact same set of all four quantum numbers ($n, l, m_l, m_s$).

* Consequence: An atomic orbital can hold a maximum of two electrons. These two electrons must have opposite spins ($m_s = +1/2$ and $m_s = -1/2$). Represented as $\uparrow\downarrow$. * Maximum electrons in a subshell: For a given $l$, there are $(2l+1)$ orbitals.

Each orbital holds 2 electrons. So, max electrons = $2(2l+1)$. * $s (l=0)$: 1 orbital, max 2 electrons. * $p (l=1)$: 3 orbitals, max 6 electrons. * $d (l=2)$: 5 orbitals, max 10 electrons. * $f (l=3)$: 7 orbitals, max 14 electrons.

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Hund's Rule of Maximum Multiplicity: — For degenerate orbitals (orbitals within the same subshell that have the same energy, e.g., $p_x, p_y, p_z$), electrons will first occupy each orbital singly with parallel spins before any orbital is doubly occupied.

* Reason: This arrangement maximizes the total spin multiplicity and minimizes electron-electron repulsion, leading to a more stable configuration. * **Example for $p^3$:** Correct: $\uparrow\quad\uparrow\quad\uparrow$. Incorrect: $\uparrow\downarrow\quad\uparrow\quad$.

Key Takeaways for NEET:

Be able to write electron configurations for elements up to Z=36 (Krypton) and common ions.
Identify the number of unpaired electrons to determine magnetic properties (paramagnetic if unpaired, diamagnetic if all paired).
Recognize and explain the exceptions for Cr and Cu.
Identify violations of any of the three rules in given configurations or orbital diagrams.
Relate quantum numbers to orbital filling and electron states.

Vyyuha Quick Recall

APple Has: Aufbau (Energy Order), Pauli (Paired Spins), Hund's (Half-fill First).