   Chapter 6, Problem 37PS

Chapter
Section
Textbook Problem

Explain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom. In each case, change the incorrect value (or values) to make the set valid. (a) n = 4, ℓ= 2, mℓ = 0, ms = 0 (b) n = 3, ℓ = 1, mℓ = −3, ms = −1/2 (c) n = 3, ℓ = 3, mℓ = −1, ms = +1/2

(a)

Interpretation Introduction

Interpretation: The reason for invalid sets of quantum numbers should be briefly explained and the valid set of quantum numbers should be determined.

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 value of ms indicates the spin of the electron and is always either 1/2 or +1/2.

Explanation

n=4,l=2,ml=0,ms=0

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

(b)

Interpretation Introduction

Interpretation: The reason for invalid sets of quantum numbers should be briefly explained and the valid set of quantum numbers should be determined.

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

(c)

Interpretation Introduction

Interpretation: The reason for invalid sets of quantum numbers should be briefly explained and the valid set of quantum numbers should be determined.

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).

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