Chapter 6, Problem 62GQ

How many orbitals correspond to each of the following designations?

1. (a) 3p
2. (b) 4p
3. (c) 4P_x
4. (d) 6d
5. (e) 5d
6. (f) 5f
7. (g) n = 5
8. (h) 7s

Interpretation Introduction

Interpretation: The maximum number of orbitals for $3p$ 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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Answer to Problem 62GQ

There is $3$ orbital for $3p$ subshell

Explanation of Solution

Each value of l indicates subshell and for p subshells, $l=1$.

So for $3p$ orbital, $\text{n}\text{=}3\text{,}\text{l}\text{=}1$. In a subshell there are $\left(2l+1\right)$ number of orbital.

Hence, there is $\left(\left(2\times 1\right)+1\right)=3$ orbital for $3p$ subshells.

Interpretation Introduction

Interpretation: The maximum number of orbitals for $4p$ 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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d. Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Answer to Problem 62GQ

There is $3$ orbital for $4p$ subshell

Explanation of Solution

Each value of l indicates subshell and for p subshells, $l=1$. Thus $4p$ orbital, $\text{n}\text{=}4\text{,}\text{l}\text{=}1$.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Hence, there is $\left(\left(2\times 1\right)+1\right)=3$ orbital for $4p$ subshells

Interpretation Introduction

Interpretation: The maximum number of orbitals for $4p_x$ should be identified.

Concept introduction:

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

1. e) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. f) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. g) Magnetic quantum number is represented by ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. h) Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a subshell there are $\left(2l+1\right)$ number of orbital.

In a shell, there are $n^2$ number of orbital

Answer to Problem 62GQ

There is $1$ orbital for $4p_x$ subshell

Explanation of Solution

For $4p$ orbital, $\text{n}\text{=}3\text{,}\text{l}\text{=}1$. In a subshell there are $\left(2l+1\right)$ number of orbital. Each value of l indicates subshell and for p subshells, $l=1$.

Hence, there is $\left(\left(2\times 1\right)+1\right)=3$ orbital for p subshells. The three orbitals of p subshells are p_x, p_y and p_z.

Therefore, for $4p_x$ orbital, there is only one orbital.

Interpretation Introduction

Interpretation: The maximum number of orbitals for $6d$ 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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d. Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Answer to Problem 62GQ

There is $5$ orbital for $6d$ subshell

Explanation of Solution

Each value of l indicates subshell and for d subshells, $l=2$. So for $6d$ orbital, $\text{n}\text{=}6\text{,}\text{l}\text{=}2$

In a subshell there are $\left(2l+1\right)$ number of orbital.

Hence, there is $5$ orbital for $6d$ subshells.

Interpretation Introduction

Interpretation: The maximum number of orbitals for $5d$ 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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d. Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Answer to Problem 62GQ

There is $5$ orbital for  $5d$ subshell

Explanation of Solution

Each value of l indicates subshell and for d subshells, $l=2$. For $5d$ orbital, $\text{n}\text{=}3\text{,}\text{l}\text{=}2$.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Hence, there is $\left(\left(2\times 2\right)+1\right)=5$ orbital for $5d$ subshells.

Interpretation Introduction

Interpretation: The maximum number of orbitals for 5f 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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d. Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Answer to Problem 62GQ

There is $3$ orbital for 5f subshell

Explanation of Solution

Each value of l indicates subshell and for f subshells, $l=3$. For $5f$ orbital, $\text{n}\text{=}5\text{,}\text{l}\text{=}3$.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Hence, there is $\left(\left(2\times 3\right)+1\right)=7$ orbital for 5f subshells.

Interpretation Introduction

Interpretation: The maximum number of orbitals for $\text{n}\text{=}5$ 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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d. Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a shell, there are $n^2$ number of orbital

Answer to Problem 62GQ

There is $25$ orbital for $\text{n}\text{=}5$ subshell

Explanation of Solution

There are $n^2$ number of orbitals in a shell.

Hence, when $\text{n}\text{=}5$, there are $5^2=25$ orbitals in the shell.

Interpretation Introduction

Interpretation: The maximum number of orbitals for $7s$ 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 ${\text{m}}_{\text{l}}$ and this number indicates the orientation of the orbital.
4. d. Spin quantum number is represented by ${\text{m}}_{\text{s}}$ and this number indicates the spin of the electron.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Answer to Problem 62GQ

There is $1$ orbital for $7s$ subshell

Explanation of Solution

Each value of l indicates subshell and for s subshells, $l=0$. For $7s$ orbital, $\text{n}\text{=}7\text{,}\text{l}\text{=}0$.

In a subshell there are $\left(2l+1\right)$ number of orbital.

Hence, there is only $\left(\left(2\times 0\right)+1\right)=1$ orbital for $7s$ subshells.