Chapter 6, Problem 67GQ

Answer the following questions as a summary quiz on the chapter.

1. (a) The quantum number n describes the ______ of an atomic orbital.
2. (b) The shape of an atomic orbital is given by the quantum number _______.
3. (c) A photon of green light has _______ (less or more) energy than a photon of orange light.
4. (d) The maximum number of orbitals that may be associated with the set of quantum numbers n = 4 and ℓ = 3 is ________.
5. (e) The maximum number of orbitals that may be associated with the quantum number set n = 3, ℓ = 2, and m_ℓ = −2 is _______.
6. (f) Label each of the following orbital pictures with the appropriate letter:

1. (g) When n = 5, the possible values of ℓ are _________.
2. (h) The number of orbitals in the n = 4 shell is _______.

Interpretation Introduction

Interpretation: For an atomic orbital what does the quantum number n describes should be given.

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.

Answer to Problem 67GQ

n represents energy and the size of an atomic orbital

Explanation of Solution

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

Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.

Therefore, n represents energy and the size of an atomic orbital.

Interpretation Introduction

Interpretation: The quantum number that indicates the shape of an atomic orbital should be given.

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.

Answer to Problem 67GQ

Quantum number l indicates the shape of an atomic orbital

Explanation of Solution

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

Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number describes the shape of the orbitals.

Therefore, the shape of an orbital is given by quantum number l.

Interpretation Introduction

Interpretation: The photon of green light is whether less or more energetic than a photon of orange light should be determined.

Concept introduction:

• Electromagnetic radiations are a type of energy surrounding us. They are of different types like radio waves, IR, UV, X-ray etc.
• Visible light lies in the wavelength of $\text{400}\text{nm}$ to $\text{700}\text{nm}$

• Planck’s equation,

  $\begin{array}{c}\text{E}\text{=}\text{hν}=\frac{\text{hc}}{\text{λ}}\\ \text{where, E}\text{=}\text{energy}\\ \text{h}\text{=}\text{Planck's}\text{constant}\\ \text{ν}=\text{frequency}\end{array}$

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

Answer to Problem 67GQ

The photon of green light has more energy than a photon of orange light 

Explanation of Solution

$\text{E}\text{=}\frac{\text{hc}}{\text{λ}}$ so the energy increases as the wavelength of the light decrease. So the radiation having lower wavelength has higher energy per photon.

Here photon of orange is having higher wavelength than photon of green.

Therefore, photon of green has more energy than photon of orange.

Interpretation Introduction

Interpretation: The maximum number of orbitals that is associated when $\text{n}\text{=}4$ and $l=3$ 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 ${\text{m}}_{\text{l}}$ 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 67GQ

The maximum number of orbitals that is associated when $\text{n}\text{=}4$ and $l=3$ is $7$.

Explanation of Solution

Each value of l indicates subshell and For $l=3$, it indicates f subshell.

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 f subshells.

Therefore, the maximum number of orbitals that is associated when $\text{n}\text{=}4$ and $l=3$ is $7$.

Interpretation Introduction

Interpretation: The maximum number of orbitals that is associated when $\text{n}\text{=}4$ and $l=3$ 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 ${\text{m}}_{\text{l}}$ 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.

The values of l when the principal quantum number is n are from $0$ to $\left(\text{n}-1\right)$. Each l value indicates subshell.

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

Answer to Problem 67GQ

The maximum number of orbitals that is associated when $\text{n}\text{=}3$, $l=2$, and $m_l=-2$ is 1

Explanation of Solution

The values of l when the principal quantum number is n are from $0$ to $\left(\text{n}-1\right)$. The values of $m_l$ when the orbital angular quantum number is l are from $-l$ to $+l$.

Therefore, when $\text{n}\text{=}3$, $l=2$, and $m_l=-2$ indicates that there is only $1$ orbital for given sets of quantum.

Interpretation Introduction

Interpretation: The appropriate letters should be labelled for the given orbital pictures.

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.

The values of l when the principal quantum number is n are from $0$ to $\left(\text{n}-1\right)$. Each l value indicates subshell.

Answer to Problem 67GQ

From the left the picture represents d, s and p orbitals

Explanation of Solution

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom. Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number describes the shape of the orbitals.

For $l=0,1,2$ represents s, p, d subshells.

The s subshell is in spherical shape.

The p subshells are in dumbbell shape whereas three of the d subshells are in double dumbbell shape.

  

Therefore, from the left the picture represents d, s and p orbitals.

Interpretation Introduction

Interpretation: The possible values of l when $\text{n}\text{=}5$ 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 ${\text{m}}_{\text{l}}$ 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.

• The values of l when the principal quantum number is n are from $0$ to $\left(\text{n}-1\right)$. Each l value indicates subshell.

Answer to Problem 67GQ

The possible values of l are, $l=0,1,2,3,4$

Explanation of Solution

The values of l when the principal quantum number is n are from $0$ to $\left(\text{n}-1\right)$.

Therefore, when $\text{n}\text{=}5$, the values of l are, $l=0,1,2,3,4$

Interpretation Introduction

Interpretation: The number of orbitals when $\text{n}\text{=}4$ 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 ${\text{m}}_{\text{l}}$ 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.

There are $n^2$ number of orbitals in a shell for the principal quantum number, n.

Answer to Problem 67GQ

When $\text{n}\text{=}4$, there are $16$ orbitals in the shell

Explanation of Solution

The principal quantum number and number of subshells are same in a shell. There are $n^2$ number of orbitals in a shell.

Hence, when $\text{n}\text{=}4$, there are $4^2=16$ orbitals in the shell.