   # What is the maximum number of electrons that can be identified with each of the following sets of quantum numbers? In some cases, the answer may be “none” In such cases, explain why “none” is the correct answer. (a) n = 4, ℓ = 3, m ℓ = 1 (b) n = 6, ℓ = 1, m ℓ = ‒1, m s = ‒1/2 (c) n = 3, ℓ = 3, m ℓ = ‒3 ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 7, Problem 11PS
Textbook Problem
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## What is the maximum number of electrons that can be identified with each of the following sets of quantum numbers? In some cases, the answer may be “none” In such cases, explain why “none” is the correct answer.(a) n = 4, ℓ = 3, mℓ = 1(b) n = 6, ℓ = 1, mℓ = ‒1, ms = ‒1/2(c) n= 3, ℓ = 3, mℓ = ‒3

a)

Interpretation Introduction

Interpretation:

The maximum number of electrons has to be identified with each of the following.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals. We consider the electronic configuration of neon atom is 1s22s22p6, the electronic configurations describes each electrons as moving independently orbitals, an average filed created ay all other orbitals.

The aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Quantum numbers: These terms are explained for the distribution of electron density in an atom. They are derived from the mathematical solution of Schrodinger’s equation for the hydrogen atom.  The types of quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml) and the electron spin quantum number (ms). Each atomic orbital in an atom is categorized by a unique set of the quantum numbers.

### Explanation of Solution

• The principle quantum number: n = 4
• Azimuthal quantum number: l = 3, indicates the f-orbital.
• Magnetic quantum number: ml = 1, indicates orientation of f-orbitals in space of an orbital of an given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell.

For,(2l+1)=2(3)+1=7 The calculation results in the seven sub-shell orbital.

But the given electron present as shown,

f-orbitals:

b)

Interpretation Introduction

Interpretation:

The maximum number of electrons has to be identified with each of the following.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals. We consider the electronic configuration of neon atom is 1s22s22p6, the electronic configurations describes each electrons as moving independently orbitals, an average filed created ay all other orbitals.

The aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Quantum numbers: These terms are explained for the distribution of electron density in an atom. They are derived from the mathematical solution of Schrodinger’s equation for the hydrogen atom.  The types of quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml) and the electron spin quantum number (ms). Each atomic orbital in an atom is categorized by a unique set of the quantum numbers.

c)

Interpretation Introduction

Interpretation:

The maximum number of electrons has to be identified with each of the following.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals. We consider the electronic configuration of neon atom is 1s22s22p6, the electronic configurations describes each electrons as moving independently orbitals, an average filed created ay all other orbitals.

The aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Quantum numbers: These terms are explained for the distribution of electron density in an atom. They are derived from the mathematical solution of Schrodinger’s equation for the hydrogen atom.  The types of quantum numbers are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml) and the electron spin quantum number (ms). Each atomic orbital in an atom is categorized by a unique set of the quantum numbers.

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