Chapter 7, Problem 7.55P

(a)

Interpretation Introduction

Interpretation:

The sublevel designation, the allowable $m_l$ values and the number of orbitals for the combination of quantum numbers $n=4$, $l=2$, 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 formula to determine the total number of orbitals is,

$\text{Number of orbitals}=2l+1$ (1)

(b)

Interpretation Introduction

Interpretation:

The sublevel designation, the allowable $m_l$ values and the number of orbitals for the combination of quantum numbers $n=5$, $l=1$, 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 formula to determine the total number of orbitals is,

$\text{Number of orbitals}=2l+1$ (1)

(c)

Interpretation Introduction

Interpretation:

The sublevel designation, the allowable $m_l$ values and the number of orbitals for the combination of quantum numbers $n=6$, $l=3$, 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 formula to determine the total number of orbitals is,

$\text{Number of orbitals}=2l+1$ (1)