Chapter 7, Problem 7.51P

(a)

Interpretation Introduction

Interpretation:

All possible $m_l$ values for orbital with $l=2$ are 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:

All possible $m_l$ values for orbitals with $n=1$ are 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:

All possible $m_l$ values for orbital with $n=4$ and $l=3$ are 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 $m_l$.