MHT-CET Chemistry · Structure of Atom

Electronic Configuration and Pauli/Hund Rules

Three rules govern how electrons fill orbitals — Aufbau (lowest energy first), Pauli (no two electrons share all four quantum numbers), and Hund (singly fill degenerate orbitals before pairing) — and from a ground-state configuration you can read off the number of unpaired electrons.

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Why this matters

Six PYQs, and they split cleanly two ways. Half are pure name-the-rule recall — quote the Pauli exclusion principle or Hund's rule verbatim from its statement, worth an easy mark every year. The other half ask you to write a ground-state configuration and count unpaired electrons (nitrogen, copper, zinc), which is where the Cr/Cu half-filled/fully-filled anomaly and Hund's rule earn their keep. Learn the three rules by name and by statement, learn to build configurations, and this whole subtopic is reliable marks.

Concept 1 of 3

The three orbital-filling rules

Intuition

Filling an atom's orbitals is like seating people in a theatre: you take the cheapest seats first (Aufbau), no seat holds more than two people and they must face opposite ways (Pauli), and you spread out across empty seats in a row before doubling up (Hund). The bank tests these mostly as name-the-rule recall, so learn each rule's exact statement.

Definition

Three rules decide the ground-state configuration of every atom:

Aufbau principle — orbitals fill in order of increasing energy, lowest first. The order follows the (n + l) rule: lower $(n+l)$ fills first, and for a tie the lower $n$ fills first. This gives $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, \dots$
Pauli's exclusion principle — no two electrons in an atom can have the same set of all four quantum numbers. Consequence: an orbital holds at most 2 electrons, and they must have opposite spins.
Hund's rule of maximum multiplicity — electrons occupy degenerate orbitals (same subshell) singly first, all with parallel spin, and pairing begins only after every such orbital has one electron.

Rule	Statement	Consequence
Aufbau principle	Orbitals are filled in order of increasing energy (the $(n+l)$ rule).	Filling order $1s, 2s, 2p, 3s, 3p, 4s, 3d, \dots$
Pauli's exclusion principle	No two electrons in an atom can have the same set of all four quantum numbers.	Max 2 electrons per orbital, with opposite spins.Q The bank quotes this one almost verbatim — 'no two electrons ... identical set of four quantum numbers' is always Pauli, never Heisenberg's uncertainty principle.
Hund's rule	Degenerate orbitals are singly occupied before any pairing begins.	Maximum number of parallel-spin unpaired electrons in a subshell.Q Watch the phrasing: 'pairing does not occur unless each orbital of the subshell has one electron' is Hund's rule.

Aufbau sets the order, Pauli caps each orbital at two, Hund spreads before it pairs.

Practice this conceptself-check · 4 quick reps

Try it yourself

State which rule each describes: (i) an orbital can hold at most two electrons of opposite spin; (ii) the 2p orbitals each take one electron before any takes a second.

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Which rule says orbitals fill from lowest energy first?
2.
Which rule limits an orbital to two electrons of opposite spin?
3.
Which rule fills degenerate orbitals singly before pairing?
4.
By the (n + l) rule, which fills first — 4s or 3d?

From the bank · past-year question

Example 1Structure of AtomEASY

"No two electrons in an atom can have the identical set of four quantum numbers." The statement is known as

[Q95 · 20 April Shift II · 2025]

Pauli is about four quantum numbers, not position

The Pauli exclusion principle is stated in terms of the four quantum numbers

(n, l, m_l, m_s)

— two electrons in the same orbital already share

n, l, m_l

, so they must differ in spin

m_s

. Do not confuse it with the Heisenberg uncertainty principle, which is about position and momentum, a common distractor.

Hund means all singly first, then pair

For

2p^3

(nitrogen) Hund's rule gives

\uparrow\ \uparrow\ \uparrow

— three unpaired electrons — not

\uparrow\downarrow\ \uparrow\ \_\,

. Pairing in a subshell begins only after every degenerate orbital already holds one electron.

Drill 2 more on the three orbital-filling rules

Concept 2 of 3

Ground-state configurations and the half-filled/fully-filled anomaly

Intuition

Apply Aufbau, Pauli and Hund in turn and you get the ground-state configuration for most atoms. But two nearby subshells like 4s and 3d are so close in energy that an atom will 'borrow' one electron from 4s to make 3d exactly half-filled (

3d^5

) or exactly full (

3d^{10}

) — because those symmetric arrangements are unusually stable.

Definition

Writing a ground-state configuration, and the two anomalies:

Fill in Aufbau order, obeying Pauli (2 per orbital) and Hund (singly first): e.g. nitrogen $(Z=7)$ is $1s^2\,2s^2\,2p^3$ .
Extra-stability rule: exactly half-filled $(p^3, d^5, f^7)$ and fully-filled $(p^6, d^{10}, f^{14})$ subshells are especially stable (symmetric distribution + favourable exchange energy).
Chromium $(Z=24)$ is $[\text{Ar}]\,4s^1\,3d^5$ , not $4s^2\,3d^4$ — one 4s electron shifts to give a half-filled $3d^5$ .
Copper $(Z=29)$ is $[\text{Ar}]\,4s^1\,3d^{10}$ , not $4s^2\,3d^9$ — the shift gives a fully-filled $3d^{10}$ .

The stable-subshell anomaly (Cr, Cu)

\text{Cr}: [\text{Ar}]\,4s^1 3d^5 \qquad \text{Cu}: [\text{Ar}]\,4s^1 3d^{10}

Worked example

Write the ground-state configuration of chromium (Z = 24) and state how many unpaired electrons it has.

Naive Aufbau order would give $[\text{Ar}]\,4s^2\,3d^4$ .
But a half-filled $3d^5$ is more stable, so one 4s electron moves to 3d: the true configuration is $[\text{Ar}]\,4s^1\,3d^5$ .
Count unpaired: $4s^1$ has 1, and $3d^5$ has 5 (each of the five d orbitals singly filled by Hund).
Total unpaired $= 1 + 5 = 6$ .

Answer:

[\text{Ar}]\,4s^1\,3d^5

; 6 unpaired electrons.

Practice this conceptself-check · 3 quick reps

Try it yourself

Write the ground-state configuration of copper (Z = 29) and find its number of unpaired electrons.

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Ground-state configuration of chromium (Z = 24)?
2.
Ground-state configuration of copper (Z = 29)?
3.
Which two d-subshell fillings are extra-stable?

From the bank · past-year question

Example 2Structure of AtomMODERATE

Find the number of unpaired electrons for copper in ground state configuration.

[Q73 · 14th May Shift 2 · 2024]

Chromium is 3d⁵4s¹, not 3d⁴4s²

The single most-tested anomaly: chromium's ground state is

[\text{Ar}]\,4s^1\,3d^5

, giving a stable half-filled d-subshell. Writing

4s^2\,3d^4

(naive Aufbau) is the classic error — and it changes the unpaired count from the correct 6 to a wrong 4.

Copper's 4s is singly occupied

Copper is

[\text{Ar}]\,4s^1\,3d^{10}

, not

4s^2\,3d^9

. Because

3d^{10}

is completely paired, copper has only 1 unpaired electron (the lone 4s), not 2 or more.

Concept 3 of 3

Counting unpaired electrons

Intuition

To count unpaired electrons, write the configuration, then draw the last, partly-filled subshell as boxes and fill it by Hund's rule — singly first, then pair. Whatever electrons stay alone are the unpaired ones; a completely filled or completely empty subshell contributes none.

Definition

The counting procedure:

Write the ground-state configuration; only the incompletely filled subshell(s) can carry unpaired electrons.
Fill that subshell's degenerate orbitals by Hund's rule (singly, parallel spin, before pairing) and count the singly-occupied boxes.
For a subshell holding $k$ electrons in $N$ orbitals: if $k \le N$ , all $k$ are unpaired; if $k > N$ , the number unpaired is $2N - k$ .
A fully-filled subshell $(p^6, d^{10}, s^2)$ has zero unpaired electrons — e.g. zinc's $3d^{10}4s^2$ is entirely paired.

Unpaired electrons in a subshell

\text{unpaired} = \begin{cases} k, & k \le N \\ 2N - k, & k > N \end{cases}

kelectrons in the subshell
Nnumber of orbitals in the subshell (p:3, d:5, f:7)

Worked example

Which of these has the most unpaired electrons: fluorine (Z = 9), sodium (Z = 11), nitrogen (Z = 7), oxygen (Z = 8)?

Nitrogen: $1s^2\,2s^2\,2p^3$ . The $2p^3$ is singly filled by Hund $(\uparrow\ \uparrow\ \uparrow)$ → 3 unpaired.
Oxygen: $2p^4 = (\uparrow\downarrow\ \uparrow\ \uparrow)$ → 2 unpaired.
Fluorine: $2p^5 = (\uparrow\downarrow\ \uparrow\downarrow\ \uparrow)$ → 1 unpaired.
Sodium: $3s^1$ → 1 unpaired.

Answer:Nitrogen, with 3 unpaired electrons.

Practice this conceptself-check · 4 quick reps

Try it yourself

How many unpaired electrons does the element in period 4, group 12 have (in ground or excited state)?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Number of unpaired electrons in nitrogen (2p³)?
2.
Number of unpaired electrons in oxygen (2p⁴)?
3.
Number of unpaired electrons in zinc ([Ar]3d¹⁰4s²)?
4.
Number of unpaired electrons in fluorine (2p⁵)?

From the bank · past-year question

Example 3Structure of AtomEASY

Which of the following elements contains maximum number of unpaired electrons?

[Q98 · 25 April Shift II · 2025]

Half-filled subshells hold the most unpaired electrons

Among second-period atoms, nitrogen

(2p^3)

beats oxygen

(2p^4)

and fluorine

(2p^5)

— a half-filled

p^3

is where every orbital is singly occupied, giving the maximum 3 unpaired. More total electrons does not mean more unpaired.

Fully-filled means zero unpaired

Zinc's

3d^{10}4s^2

has all subshells complete, so it has zero unpaired electrons — and no accessible excited state changes that. A filled

d^{10}

s^2

contributes nothing to the unpaired count.

Drill 1 more on counting unpaired electrons

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Ground-state configurations and the half-filled/fully-filled anomaly
The stable-subshell anomaly (Cr, Cu)
$\text{Cr}: [\text{Ar}]\,4s^1 3d^5 \qquad \text{Cu}: [\text{Ar}]\,4s^1 3d^{10}$
Counting unpaired electrons
Unpaired electrons in a subshell
$\text{unpaired} = \begin{cases} k, & k \le N \\ 2N - k, & k > N \end{cases}$

Reference tables (1)

The three orbital-filling rules3 rows

Rule	Statement	Consequence
Aufbau principle	Orbitals are filled in order of increasing energy (the $(n+l)$ rule).	Filling order $1s, 2s, 2p, 3s, 3p, 4s, 3d, \dots$
Pauli's exclusion principle	No two electrons in an atom can have the same set of all four quantum numbers.	Max 2 electrons per orbital, with opposite spins.Q The bank quotes this one almost verbatim — 'no two electrons ... identical set of four quantum numbers' is always Pauli, never Heisenberg's uncertainty principle.
Hund's rule	Degenerate orbitals are singly occupied before any pairing begins.	Maximum number of parallel-spin unpaired electrons in a subshell.Q Watch the phrasing: 'pairing does not occur unless each orbital of the subshell has one electron' is Hund's rule.

Aufbau sets the order, Pauli caps each orbital at two, Hund spreads before it pairs.

Watch out for (6)

Pauli is about four quantum numbers, not position
→ The three orbital-filling rules
Hund means all singly first, then pair
→ The three orbital-filling rules
Chromium is 3d⁵4s¹, not 3d⁴4s²
→ Ground-state configurations and the half-filled/fully-filled anomaly
Copper's 4s is singly occupied
→ Ground-state configurations and the half-filled/fully-filled anomaly
Half-filled subshells hold the most unpaired electrons
→ Counting unpaired electrons
Fully-filled means zero unpaired
→ Counting unpaired electrons

Mastery check — 3 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Structure of AtomEASY

"Pairing of electrons in the orbitals belonging to the same subshell does not occur unless each orbital belonging to that subshell has got one electron each." This statement is known as

[Q85 · 26 April Shift II · 2025]

Example 2Structure of AtomMODERATE

What is the total number of unpaired electrons in an element placed at period-4 and group-12 either in excited or at ground state?

[Q79 · 2nd May Shift 1 · 2023]

Example 3Structure of AtomEASY

Which from following rule/principle states that \"No two electrons in an atom can have the same set of four quantum numbers\".

[Q79 · 9th May Shift 1 · 2024]

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Related notes

Electron Configuration and Valence Shells (NDA Chemistry) →