Chapter 7, Problem 7.75P

(a)

Interpretation Introduction

Interpretation:

The orbital that has the highest value of the principal quantum number $\left(n\right)$ is to be determined.

Concept introduction:

Quantum numbers are a set of four numbers that describe the movement of an electron within an atom. Out of the four, the three quantum numbers that define the shape, size, and orientation of an orbital are the principal quantum number, the orbital angular momentum quantum number, and the magnetic quantum number.

The principal quantum number – The principal quantum number indicates the distance of an electron from the nucleus. As the value of the principal quantum number increases, the distance of the electron from the nucleus increases. The farther the electron is from the nucleus, the higher is the energy of the electron. The principal quantum number is denoted by $n$.

The angular momentum quantum number – The orbital angular momentum quantum number defines the shape of the orbital. The value of orbital angular momentum quantum number depends on the value of the principal quantum number. It is denoted by $l$.

The magnetic quantum number – The magnetic quantum number determines the total number of orbitals and their orientation within a sub-shell. The magnetic quantum number is represented by the symbol $m_l$.

(b)

Interpretation Introduction

Interpretation:

The orbital that has 1 and 2 value for $l$ is to be determined.

Concept introduction:

Quantum numbers are a set of four numbers that describe the movement of an electron within an atom. Out of the four, the three quantum numbers that define the shape, size, and orientation of an orbital are the principal quantum number, the orbital angular momentum quantum number, and the magnetic quantum number.

The principal quantum number – The principal quantum number indicates the distance of an electron from the nucleus. As the value of the principal quantum number increases, the distance of the electron from the nucleus increases. The farther the electron is from the nucleus, the higher is the energy of the electron. The principal quantum number is denoted by $n$.

The angular momentum quantum number – The orbital angular momentum quantum number defines the shape of the orbital. The value of orbital angular momentum quantum number depends on the value of the principal quantum number. It is denoted by $l$.

The magnetic quantum number – The magnetic quantum number determines the total number of orbitals and their orientation within a sub-shell. The magnetic quantum number is represented by the symbol $m_l$.

(c)

Interpretation Introduction

Interpretation:

The number of orbitals that have the same value of $n$ and have the same shape as orbital B and orbital C is to be determined.

Concept introduction:

Quantum numbers are a set of four numbers that describe the movement of an electron within an atom. Out of the four, the three quantum numbers that define the shape, size, and orientation of an orbital are the principal quantum number, the orbital angular momentum quantum number, and the magnetic quantum number.

The principal quantum number – The principal quantum number indicates the distance of an electron from the nucleus. As the value of the principal quantum number increases, the distance of the electron from the nucleus increases. The farther the electron is from the nucleus, the higher is the energy of the electron. The principal quantum number is denoted by $n$.

The angular momentum quantum number – The orbital angular momentum quantum number defines the shape of the orbital. The value of orbital angular momentum quantum number depends on the value of the principal quantum number. It is denoted by $l$.

The magnetic quantum number – The magnetic quantum number determines the total number of orbitals and their orientation within a sub-shell. The magnetic quantum number is represented by the symbol $m_l$.

(d)

Interpretation Introduction

Interpretation:

The orbital that has the highest energy and lowest energy is to be determined.

Concept introduction:

The orbital energy is dependent upon the principle of the quantum number as well as the azimuthal quantum number.

The orbitals energy are ordered on the basis of $\left(n+l\right)$ rule. The higher the value of $\left(n+l\right)$, higher will be the energy of the orbital.