Chapter 7, Problem 7.87QP

 (a)

Interpretation Introduction

Interpretation: The set of orbitals corresponds to each of the given sets of quantum numbers are to be stated. Also, the number of electrons occupied by these orbitals is to be stated.

Concept introduction: There are four quantum numbers that indicates the size, energy and shape of an atomic orbital. The quantum number $n$ is the principal quantum number that indicates the energy level and size of the orbital and $l$ is the azimuthal quantum number that determines the shape and angular momentum of an orbital. The magnetic quantum number is an integer that takes the values from $\left(-l\text{ to }+l\right)$.

To determine: The set of orbitals correspond to the given set of quantum numbers and the number of electrons occupied by these orbitals.

Answer to Problem 7.87QP

Solution

The given set of quantum number, $n=2$ and $l=0$ represents $\text{2s}$ orbital and the number of electrons in $\text{2s}$ orbital is $\underset{\_}{2}$.

Explanation of Solution

Explanation

The given principal quantum number $\left(n\right)$ is $2$ that represents the energy level and angular momentum quantum number $\left(l\right)$ is $0$ that represents the shape of an orbital. Therefore, $n=2$ and $l=0$ represents $2\text{s}$ sub shell.

The number of electrons occupied by $\text{s}$ orbital is two as one orbital contains maximum of two electrons. Hence, the given set of quantum number, $n=2$ and $l=0$ represents $\text{2s}$ orbital with two electrons.

(b)

Interpretation Introduction

Interpretation: The set of orbitals corresponds to each of the given sets of quantum numbers are to be stated. Also, the number of electrons occupied by these orbitals is to be stated.

Concept introduction: There are four quantum numbers that indicates the size, energy and shape of an atomic orbital. The quantum number $n$ is the principal quantum number that indicates the energy level and size of the orbital and $l$ is the azimuthal quantum number that determines the shape and angular momentum of an orbital. The magnetic quantum number is an integer that takes the values from $\left(-l\text{ to }+l\right)$.

To determine: The set of orbitals correspond to the given set of quantum numbers and the number of electrons occupied by these orbitals.

Answer to Problem 7.87QP

Solution

The given set of quantum number, $n=3$ and $l=1$ represents $\text{3p}$ orbital and the number of electrons in $\text{3p}$ orbital is $\underset{\_}{6}$.

Explanation of Solution

Explanation

The given principal quantum number $\left(n\right)$ is $3$ and angular momentum quantum number $\left(l\right)$ is $1$ that represents $\text{p}$ sub shell. Therefore, $n=3$ and $l=1$ represents $\text{3p}$ sub shell.

The sub shell $\text{3p}$ contains three orbitals $\left({\text{3p}}_{\text{x}}{\text{,3p}}_{\text{y}}{\text{,3p}}_{\text{z}}\right)$. Each orbital contains two electrons Therefore; the maximum number of electrons accommodated in $\text{p}$ sub shell is six. Hence, the given set of quantum number, $n=3$ and $l=1$ represents $\text{3p}$ orbital with six electrons.

(c)

Interpretation Introduction

Interpretation: The set of orbitals corresponds to each of the given sets of quantum numbers are to be stated. Also, the number of electrons occupied by these orbitals is to be stated.

Concept introduction: There are four quantum numbers that indicates the size, energy and shape of an atomic orbital. The quantum number $n$ is the principal quantum number that indicates the energy level and size of the orbital and $l$ is the azimuthal quantum number that determines the shape and angular momentum of an orbital. The magnetic quantum number is an integer that takes the values from $\left(-l\text{ to }+l\right)$.

To determine: The set of orbitals correspond to the given set of quantum numbers and the number of electrons occupied by these orbitals.

Answer to Problem 7.87QP

Solution

The given set of quantum number, $n=4$ and $l=2$ represents $4\text{d}$ orbital and the number of electrons in $\text{4d}$ orbital is $\underset{\_}{10}$.

Explanation of Solution

Explanation

The given principal quantum number $\left(n\right)$ is $4$ and angular momentum quantum number $\left(l\right)$ is $2$ that represents $\text{d}$ sub shell. Therefore, $n=4$ and $l=2$ represents $\text{4d}$ sub shell.

The sub shell $\text{4d}$ contains five orbitals $\left({\text{4d}}_{\text{x}}{\text{,4d}}_{\text{y}}{\text{,4d}}_{\text{z}}{\text{,4d}}_{{\text{x}}^{\text{2}}{\text{-y}}^{\text{2}}}{\text{,4d}}_{{\text{z}}^{\text{2}}}\right)$. Each orbital contains two electrons Therefore; the maximum number of electrons accommodated in $\text{d}$ sub shell is ten. Hence, the given set of quantum number, $n=4$ and $l=2$ represents $\text{4d}$ orbital with ten electrons.

(d)

Interpretation Introduction

Interpretation: The set of orbitals corresponds to each of the given sets of quantum numbers are to be stated. Also, the number of electrons occupied by these orbitals is to be stated.

Concept introduction: There are four quantum numbers that indicates the size, energy and shape of an atomic orbital. The quantum number $n$ is the principal quantum number that indicates the energy level and size of the orbital and $l$ is the azimuthal quantum number that determines the shape and angular momentum of an orbital. The magnetic quantum number is an integer that takes the values from $\left(-l\text{ to }+l\right)$.

To determine: The set of orbitals correspond to the given set of quantum numbers and the number of electrons occupied by these orbitals.

Answer to Problem 7.87QP

Solution

The given set of quantum number, $n=1$ and $l=0$ represents $\text{1s}$ orbital and the number of electrons in $\text{1s}$ orbital is $\underset{\_}{2}$.

Explanation of Solution

Explanation

The given principal quantum number $\left(n\right)$ is $1$ and angular momentum quantum number $\left(l\right)$ is $0$ that represents $\text{s}$ orbital. Therefore, $n=1$ and $l=0$ represents $\text{1s}$ sub shell.

The number of electrons occupied by $\text{s}$ orbital is two as one orbital contains maximum of two electrons. Hence, the given set of quantum number, $n=2$ and $l=0$ represents $\text{2s}$ orbital with two electrons. Hence, the given set of quantum number, $n=1$ and $l=0$ represents $\text{1s}$ orbital with two electrons.

Conclusion

1. a. The set of quantum number, $n=2$ and $l=0$ represents $\text{2s}$ orbital and the number of electrons in $\text{2s}$ orbital is $\underset{\_}{2}$.
2. b. The set of quantum number, $n=3$ and $l=1$ represents $\text{3p}$ orbital and the number of electrons in $\text{3p}$ orbital is $\underset{\_}{6}$.
3. c. The set of quantum number, $n=4$ and $l=2$ represents $4\text{d}$ orbital and the number of electrons in $\text{4d}$ orbital is $\underset{\_}{10}$.
4. d. The set of quantum number, $n=1$ and $l=0$ represents $\text{1s}$ orbital and the number of electrons in $\text{1s}$ orbital is $\underset{\_}{2}$.