Hund's Maximum Multiplicity Rule And Pauli's Exclusion Principle , Important Topics For JEE 2025

Hund's Maximum Multiplicity Rule : Welcome, young scientists, to the intriguing world of electronic configuration rules! As we journey through the microscopic realm of atoms, understanding how electrons are arranged within them is crucial. In this article, we'll delve into two fundamental principles governing electron behaviour: Hund's Maximum Multiplicity Rule and Pauli's Exclusion Principle. By unravelling these rules, you'll gain valuable insights into the behaviour of electrons and the structure of atoms.

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Before we delve into the specifics of Hund's Rule and Pauli's Principle, let's grasp the concept of electronic configuration. Electronic configuration refers to the arrangement of electrons within an atom's electron shells and subshells. These configurations follow specific rules that dictate how electrons occupy various orbitals around the nucleus.

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Hund's Maximum Multiplicity Rule

Hund's Maximum Multiplicity Rule : Hund's Rule, named after German physicist Friedrich Hund, states that electrons occupy degenerate orbitals (orbitals with the same energy) singly before pairing up. In simpler terms, electrons prefer to occupy empty orbitals within the same subshell with parallel spins (spin-up) rather than pairing with opposite spins (spin-down) until necessary.

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This rule deals with the filling of electrons into the orbitals belonging to the same subshell (that is, orbitals of equal energy, called degenerate orbitals).

It states, pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each i.e., it is singly occupied.

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Since there are three p, five d and seven f orbitals, therefore, the pairing of electrons will start in the p, d and f orbitals with the entry of 4 ^th , 6 ^th and 8 ^th electron, respectively.

(i) ₂₁ Sc → 1s ² , 2s ² , 2p ⁶ , 3s ² , 3p ⁶ , 4s ² , 3d ¹

Or [Ar] 4s ² 3d ¹

[Ar] 3d ¹ 4s ²

∴ No. of unpaired electrons = 1

∴ Total spin

(ii) ₂₆ Fe → 1s ² , 2s ² , 2p ⁶ , 3s ² , 3p ⁶ , 4s ² 3d ⁶

Or [Ar] 4s ² , 3d ⁶

No. of unpaired electrons = 4

∴ Total spin

(iii) ₁₀ Ne → 1s ² , 2s ² 2p ⁶

No. of unpaired electrons = 0

Total spin = 0

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Pauli's Exclusion Principle

Pauli's Exclusion Principle : Pauli's Exclusion Principle, formulated by Austrian physicist Wolfgang Pauli, states that no two electrons in an atom can have the same set of quantum numbers . Specifically, it prohibits two electrons within the same atom from having identical values for all four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s). This principle ensures that each orbital can hold a maximum of two electrons with opposite spins.

i.e. an orbital can accommodate maximum 2 electrons with opposite spin.

Ex.1. → 1s ² 2s ² 2p ²

n = 1 1 2

l = 0 0 1

m = 0 0 +1, 0, –1

s =

Ex.2. ₁₇ Cl → 1s ² 2s ² 2p ⁶ 3s ² 3p ⁵

n = 1 2 2 3 3

l = 0 0 1 0 1

m = 0 0 +1, –1, 0 0 +1, –1, 0

s =

Pauli's Exclusion Principle dictates that no two electrons in an atom can have identical sets of quantum numbers. This principle ensures that each electron within an atom is uniquely defined by its quantum numbers, preventing electron overlap and ensuring the stability and integrity of the atom's electronic configuration. As a result, each orbital can accommodate a maximum of two electrons with opposite spins, contributing to the overall stability of the atom.

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Configuration of Ion

(a) First we have to write the configuration of atom in its ground state.

(b) Now, based upon the charge present on the atom we have to remove or add electron in its valence shell.

Na ⁺ : (a) Na → 1s ² , 2s ² , 2p ⁶ , 3s ¹

(b) Na ⁺ → 1s ² , 2s ² 2p ⁶

Cr+: (a) Cr → 1s ² , 2s ² 2p ⁶ , 3s ² 3p ⁶ , 4s ¹ , 3d ⁵

(b) Cr ⁺ → 1s ² , 2s ² 2p ⁶ , 3s ² 3p ⁶ 3d ⁵

Cr ⁺² → 1s ² , 2s ² , 2p ⁶ , 3s ² 3p ⁶ 3d ⁴

Cr ⁺³ → 1s ² , 2s ² 2p ⁶ , 3s ² 3p ⁶ 3d ³

Fe ⁺² : Fe → 1s ² , 2s ² 2p ⁶ , 3s ² 3p ⁶ 4s ² 3d ⁶

Fe ⁺² → 1s ² , 2s ² 2p ⁶ , 3s ² 3p ⁶ 4s ⁰ 3d ⁶

Solved Example Hund's Maximum Multiplicity Rule

Q1. Which of the following arrangment of electron is correct?

(1) (2)

(3) (4)

(5)

Ans. (4)

Q2. Which of the following set of quantum numbers is not possible ?

(1) n = 2, l = 0, m = –1, s =

(2) n = 3, l = 2, m = 0, s =

(3) n = 2, l = 3, m = –2, s =

Sol. (1) Not possible (2) Possible (3) Not possible

Q3. Write the electronic configuration and find the no. of unpaired electrons as well as total spin for the following atoms:

(i) ₆ C (ii) ₈ O (iii) ₁₅ P (iv) ₂₁ Sc

(v) ₂₆ Fe (vi) ₁₀ Ne

Sol. (i) ₆ C → 1s ² , 2s ² , 2p ²

No. of unpaired electrons → 2.

Total spin

(ii) ₈ O → 1s ² , 2s ² , 2p ⁴

∴ No. of unpaired electrons = 2

Total spin =

(iii) ₁₅ P → 1s ² , 2s ² , 2p ⁶ , 3s ² , 3p ³

∴ No. of unpaired electrons = 3

Total spin =

Q4. Calculate total spin, magnetic moment for the atoms having Atomic no. 7, 24 and 36.

Sol. The electronic configuration are

₇ N : 1s ² , 2s ² 2p ³ unpaired electron = 3

₂₄ Cr : 1s ² , 2s ² 2p ⁶ , 3s ² 3p ⁶ 3d ⁵ , 4s ¹ unpaired electron = 6

₃₆ Kr : 1s ² , 2s ² , 2p ⁶ , 3s ² 3p ⁶ 3d ¹⁰ , 4s ² 4p ⁶ unpaired electron = 0

∴ Total spin for an atom = ±1/2 × no. of unpaired electron

For ₇ N, it is = ± 3/2; For ₂₄ Cr, it is = ± 3; For ₃₆ Kr, it is = 0

Also magnetic moment =

For ₇ N, it is = ; For ₂₄ Cr, it is = ; For ₃₆ Kr, it is =

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