Electronic Configuration of Elements — Revision Notes

⚡ 30-Second Revision

Aufbau Principle: — Fill lowest energy orbitals first ($1s < 2s < 2p < 3s < 3p < 4s < 3d \dots$).
Pauli's Exclusion Principle: — Max 2 electrons per orbital, with opposite spins ($m_s = +1/2, -1/2$).
Hund's Rule: — For degenerate orbitals, fill singly with parallel spins before pairing.
Quantum Numbers:

- $n$: Principal (energy level, size), $1, 2, 3 \dots$ - $l$: Azimuthal (shape, subshell), $0 \dots (n-1)$ (s, p, d, f) - $m_l$: Magnetic (orientation), $-l \dots +l$ - $m_s$: Spin, $\pm 1/2$

Exceptions: — Cr ($[Ar] 3d^5 4s^1$), Cu ($[Ar] 3d^{10} 4s^1$) due to stability of half/fully-filled d-subshells.
Ion Configuration: — Remove electrons from highest 'n' shell first (e.g., $4s$ before $3d$ for transition metals).

2-Minute Revision

Electronic configuration describes electron arrangement in orbitals, governed by three key rules. The Aufbau principle dictates filling orbitals from lowest to highest energy ($1s, 2s, 2p, 3s, 3p, 4s, 3d, \dots$).

Pauli's Exclusion Principle states that each orbital can hold a maximum of two electrons, and these must have opposite spins. Hund's Rule of Maximum Multiplicity applies to degenerate orbitals (like $2p_x, 2p_y, 2p_z$), requiring them to be singly occupied with parallel spins before any pairing occurs.

Remember the exceptions for Chromium ($[Ar] 3d^5 4s^1$) and Copper ($[Ar] 3d^{10} 4s^1$) due to the enhanced stability of half-filled or fully-filled d-subshells. When forming ions, electrons are removed from the outermost shell (highest 'n' value) first, which means $4s$ electrons are removed before $3d$ electrons in transition metals.

This topic is crucial for understanding periodic trends, chemical bonding, and magnetic properties.

5-Minute Revision

Electronic configuration is the systematic arrangement of electrons within an atom's orbitals, which are defined by quantum numbers. The principal quantum number (n) denotes the main energy shell and orbital size.

The azimuthal quantum number (l) defines the subshell shape (s, p, d, f). The magnetic quantum number (m_l) specifies orbital orientation, and the spin quantum number (m_s) describes electron spin.

These numbers are constrained: $l$ ranges from $0$ to $(n-1)$, and $m_l$ from $-l$ to $+l$.

Three fundamental rules govern electron filling:

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Aufbau Principle: — Electrons occupy orbitals in increasing order of energy, typically $1s < 2s < 2p < 3s < 3p < 4s < 3d < \dots$. This order is often remembered using the (n+l) rule.
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Pauli's Exclusion Principle: — Each orbital can accommodate a maximum of two electrons, but only if they possess opposite spins ($+1/2$ and $-1/2$). This ensures each electron has a unique quantum state.
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Hund's Rule of Maximum Multiplicity: — For degenerate orbitals (same energy, e.g., $2p_x, 2p_y, 2p_z$), electrons first fill each orbital singly with parallel spins before any pairing occurs. This maximizes stability by minimizing electron-electron repulsion and maximizing exchange energy.

Key Exceptions: Chromium (Cr, Z=24) and Copper (Cu, Z=29) are prime examples where an electron from the $4s$ orbital promotes to the $3d$ orbital to achieve a more stable half-filled ($3d^5$) or fully-filled ($3d^{10}$) configuration. So, Cr is $[Ar] 3d^5 4s^1$ (not $3d^4 4s^2$) and Cu is $[Ar] 3d^{10} 4s^1$ (not $3d^9 4s^2$).

Ions: When forming cations, electrons are removed from the orbital with the highest principal quantum number (n) first. For transition metals, this means $4s$ electrons are removed before $3d$ electrons. For example, $Fe$ (Z=26) is $[Ar] 3d^6 4s^2$, but $Fe^{2+}$ is $[Ar] 3d^6$ (two $4s$ electrons removed). This is a common trap in NEET. The number of unpaired electrons (determined by Hund's rule) dictates magnetic properties (paramagnetic if unpaired, diamagnetic if all paired).

Prelims Revision Notes

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Electronic Configuration Definition: — Distribution of electrons in atomic orbitals.
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Quantum Numbers:

* n (Principal): Energy level, size. Values: $1, 2, 3, \dots$. * l (Azimuthal/Angular): Subshell, shape. Values: $0$ to $(n-1)$. $l=0 \implies s$, $l=1 \implies p$, $l=2 \implies d$, $l=3 \implies f$. * m_l (Magnetic): Orbital orientation. Values: $-l$ to $+l$ (including $0$). * m_s (Spin): Electron spin. Values: $+1/2$ or $-1/2$.

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Rules for Filling Orbitals:

* Aufbau Principle: Fill orbitals in increasing energy order. General sequence: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p$. * Pauli's Exclusion Principle: Max 2 electrons per orbital, with opposite spins. * Hund's Rule of Maximum Multiplicity: For degenerate orbitals, fill singly with parallel spins first, then pair up.

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Exceptions to Aufbau:

* Chromium (Cr, Z=24): Expected: $[Ar] 3d^4 4s^2$. Actual: $[Ar] 3d^5 4s^1$ (half-filled d-subshell stability). * Copper (Cu, Z=29): Expected: $[Ar] 3d^9 4s^2$. Actual: $[Ar] 3d^{10} 4s^1$ (fully-filled d-subshell stability). * Similar exceptions for Mo, Ag, Au.

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Electronic Configuration of Ions:

* Cations: Remove electrons from the outermost shell (highest 'n' value) first. For transition metals, $ns$ electrons are removed before $(n-1)d$ electrons. Example: $Fe (Z=26) = [Ar] 3d^6 4s^2 \implies Fe^{2+} = [Ar] 3d^6$. * Anions: Add electrons to the lowest energy available orbital.

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Periodic Table Relationship:

* Period: Highest 'n' value in the configuration. * Block (s, p, d, f): Determined by the subshell of the last differentiating electron. * Group: Based on valence electrons (s-block: valence e-, p-block: $10 +$ valence e-, d-block: $ns + (n-1)d$ electrons).

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Magnetic Properties:

* Paramagnetic: Contains unpaired electrons (attracted to magnetic field). * Diamagnetic: All electrons are paired (repelled by magnetic field). * Use Hund's rule to determine unpaired electrons.

Vyyuha Quick Recall

To remember the Aufbau filling order (up to 7p):

Some People Don't Follow Simple Patterns Doing Fine So People Don't Forget.

$1s \ 2s \ 2p \ 3s \ 3p \ 4s \ 3d \ 4p \ 5s \ 4d \ 5p \ 6s \ 4f \ 5d \ 6p \ 7s \ 5f \ 6d \ 7p$

(The numbers for s, p, d, f start from 1, 2, 3, 4 respectively and increment for each subsequent appearance of the letter).