Chapter 5, Problem 97A

Interpretation Introduction

(a)

Interpretation:

Possible orientation for the orbitals related to $s$ sublevels needs to be determined.

Concept introduction:

The magnetic quantum number specifies the orientation in space of an orbital of a given energy $\left(n\right)$ and shape $\left(l\right).$

Answer to Problem 97A

$s$ = 1

Explanation of Solution

Magnetic Quantum Number $\left(m_l\right): m_l =-l\mathrm{...}\mathrm{0...}+l.$

For this quantum number, the subshell is divided into the individual orbitals in which electrons can be filled. In each subshell, there are $2l+1$ orbitals. Since, for s orbital the value of l is equal to 0 thus the  $s$  subshell has only one oriented orbital.

Interpretation Introduction

(b)

Interpretation:

Possible orientation for the orbitals related to $p$ sublevels needs to be determined.

Concept introduction:

The magnetic quantum number specifies the orientation in space of an orbital of a given energy $\left(n\right)$ and shape $\left(l\right).$

Answer to Problem 97A

$p$ = 3

Explanation of Solution

Magnetic Quantum Number $\left(m_l\right): m_l =-l\mathrm{...}\mathrm{0...}+l.$

For this quantum number, the subshell is divided into the individual orbitals in which electrons can be filled. In each subshell, there are $2l+1$ orbitals. Since, for p orbital the value of l is equal to 1 thus the p subshell has three oriented orbital.

Interpretation Introduction

(c)

Interpretation:

Possible orientation for the orbitals related to $d$ sublevels needs to be determined.

Concept introduction:

The magnetic quantum number specifies the orientation in space of an orbital of a given energy $\left(n\right)$ and shape $\left(l\right).$

Answer to Problem 97A

$d$ = 5

Explanation of Solution

Magnetic Quantum Number $\left(m_l\right): m_l =-l\mathrm{...}\mathrm{0...}+l.$

For this quantum number, the subshell is divided into the individual orbitals in which electrons can be filled. In each subshell, there are $2l+1$ orbitals. Since, for d orbital the value of l is equal to 2 thus the d subshell has 5 oriented orbital.

Interpretation Introduction

(d)

Interpretation:

Possible orientation for the orbitals related to $f$ sublevels needs to be determined.

Concept introduction:

The magnetic quantum number specifies the orientation in space of an orbital of a given energy $\left(n\right)$ and shape

Answer to Problem 97A

$f$ = 7

Explanation of Solution

Magnetic Quantum Number $\left(m_l\right): m_l =-l\mathrm{...}\mathrm{0...}+l.$

For this quantum number, the subshell is divided into the individual orbitals in which electrons can be filled. In each subshell, there are $2l+1$ orbitals. Since, for f orbital the value of l is equal to 3 thus the f subshell has only 7 oriented orbital.