Chapter 7, Problem 7.56QE

(a)

Interpretation Introduction

Interpretation:

The number of subshells present in a shell that has $n$ equal to 3 has to be determined.

Concept Introduction:

The acceptable wave function is characterized by a set of four quantum numbers. These The acceptable wave function is characterized by a set of four quantum numbers. These quantum numbers are related to the shape, size of the electron wave and the location of the electron in space.

1. These quantum numbers are represented by $n$, $l$, $m_l$, and $m_s$. The quantum number $n$ is known as principal quantum number and it allowed values are all positive whole numbers. The quantum number $l$ is known as angular momentum quantum number and its allowed values are all positive integer from 0 to $n-1$.

2. The notation of subshell is used to determine by a combination of both principal quantum number and angular quantum number. In notation, numerical values of $n$ is used while value of $l$ denotes the respective subshell. The table for the $l$ values is as follows:

$\begin{array}{cccccccc}l& 0& 1& 2& 3& 4& 5& 6\\ \text{Subshell}& s& p& d& f& g& h& i\end{array}$

3. The quantum number $m_l$ is known as the magnetic quantum number. It tells about the orbitals present in the subshell and its allowed values lie between $-l$ to $+l$ include 0.

4. The quantum number $m_s$ is known as the electron spin quantum number. It represents the spin of the electron and its allowed values are $+\text{1/2}$ and $-\text{1/2}$.

(b)

Interpretation Introduction

Interpretation:

The number of orbitals present in a $4p$ subshell has to be determined.

Concept Introduction:

Refer to part (a).

(c)

Interpretation Introduction

Interpretation:

The maximum value of $l$ that is allowed in the shell with $n$ equals to 4 has to be determined.

Concept Introduction:

Refer to part (a).

(d)

Interpretation Introduction

Interpretation:

The allowed values of $n$, $l$ and all values of $m_l$ quantum number for $3d$ subshell has to be determined.

Concept Introduction:

Refer to part (a).