   Chapter 6, Problem 28PS

Chapter
Section
Textbook Problem

(a) When n = 4, ℓ = 2, and mℓ = ‒1, to what orbital type does this refer? (Give the orbital label, such as 1s.)(b) How many orbitals occur in the n = 5 electron shell? How many subshells? What are the letter labels of the subshells?(c) How many orbitals occur in an f subshell? What are the values of mℓ?

(a)

Interpretation Introduction

Interpretation: The type of orbital should be identified when n=4,l=2,ml=1

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 principal quantum number and number of subshells are same in a shell.

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

There are n2 number of orbitals in a shell for the principal quantum number, n.

For an orbital ns, the principal quantum number is n

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

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

Explanation

For an orbital ns, the principal quantum number is n. So the principal quantum number is n=4.

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

Each value of l indicates subshell. For l=2, it indicates d subshell.

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

(b)

Interpretation Introduction

Interpretation: Number of orbitals and subshells when n=5 and labels of the subshells 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 principal quantum number and number of subshells are same in a shell.

There are n2 number of orbitals in a shell for the principal quantum number, n.

For an orbital ns, the principal quantum number is n

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

(c)

Interpretation Introduction

Interpretation: Number of orbitals for f subshells and the values of ml 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.

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

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

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

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