   Chapter 6, Problem 36PS

Chapter
Section
Textbook Problem

What is the maximum number of orbitals that can be identified by each of the following sets of quantum numbers? When “none” is the correct answer, explain your reasoning. (a) n = 4, ℓ = 3 (b) n = 5 (c) n = 2, ℓ = 2 (d) n = 3, ℓ = 1, mℓ = ‒1

(a)

Interpretation Introduction

Interpretation: The maximum number of orbitals for the given sets of quantum numbers should be identified.

Concept introduction:

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom.

1. a) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. b) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. c) Magnetic quantum number is represented by ml and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ms and this number indicates the spin of the electron.

In a subshell there are (2l+1) number of orbital.

Explanation

Given,

n=4,l=3

In a subshell there are (2l+1) number of orbital

(b)

Interpretation Introduction

Interpretation: The maximum number of orbitals for the given sets of quantum numbers should be identified.

Concept introduction:

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom.

1. a) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. b) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. c) Magnetic quantum number is represented by ml and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ms and this number indicates the spin of the electron.

In a shell, there are n2 number of orbital

(c)

Interpretation Introduction

Interpretation: The maximum number of orbitals for the given sets of quantum numbers should be identified and the reason should be briefly explained if a set of quantum numbers has no orbitals.

Concept introduction:

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom.

1. a) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. b) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. c) Magnetic quantum number is represented by ml and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ms and this number indicates the spin of the electron.

The values of l when the principal quantum number is n are from 0 to (n1). Each l value indicates subshell.

(d)

Interpretation Introduction

Interpretation: The maximum number of orbitals for the given sets of quantum numbers should be identified.

Concept introduction:

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom.

1. a) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. b) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. c) Magnetic quantum number is represented by ml and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ms and this number indicates the spin of the electron.

The values of l when the principal quantum number is n are from 0 to (n1). Each value indicates subshell.

The values of ml when the orbital angular quantum number is l are from l to +l.

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