Chapter 7, Problem 7.54QE

(a)

Interpretation Introduction

Interpretation:

The notation of subshell if $n$ is 1, $l$ is 1, $m_l$ is 0, and $m_s$ is $-\text{1/2}$ has to be determined. Also, the reason for not allowed combination has to be determined.

Concept Introduction:

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 $-\text{1/2}$.

Answer to Problem 7.54QE

The given combination of quantum numbers is not allowed.

Explanation of Solution

The value of principal quantum number $\left(n\right)$ is 1.

If the value of angular momentum quantum number $\left(l\right)$ is 1 then the subshell is $p$.

The value of magnetic quantum number $\left(m_l\right)$ is 0.

The value of electron spin quantum number $\left(m_s\right)$ is $-\text{1/2}$.

Since value of $l$ must be lesser than $n$ but here both values are equal to 1 thus the given combination of quantum numbers is not allowed.

(b)

Interpretation Introduction

Interpretation:

The notation of subshell if $n$ is 4, $l$ is 2, $m_l$ is 2, and $m_s$ is $+\text{1/2}$ has to be determined. Also, the reason for not allowed combination has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 7.54QE

The given combination of quantum numbers is not allowed.

Explanation of Solution

The value of principal quantum number $\left(n\right)$ is 4.

If the value of angular momentum quantum number $\left(l\right)$ is 2 then the subshell is $d$.

The value of magnetic quantum number $\left(m_l\right)$ is 2.

The value of electron spin quantum number $\left(m_s\right)$ is $+\text{1/2}$.

Since the value of $l$ is lesser than $n$ and $m_l$ is also in the range of $-l$ to $\text{+}l$, thus it is an allowed combination.

Therefore, the notation of subshell is $4d$.

(c)

Interpretation Introduction

Interpretation:

The notation of subshell if $n$ is 2, $l$ is 0, $m_l$ is 0, and $m_s$ is $+\text{1/2}$ has to be determined. Also, the reason for not allowed combination has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 7.54QE

The notation of subshell is $2s$.

Explanation of Solution

The value of principal quantum number $\left(n\right)$ is 2.

If the value of angular momentum quantum number $\left(l\right)$ is 0 then the subshell is $s$.

The value of magnetic quantum number $\left(m_l\right)$ is 0.

The value of electron spin quantum number $\left(m_s\right)$ is $+\text{1/2}$.

Since the value of $l$ is lesser than $n$ and $m_l$ is also in the range of $-l$ to $\text{+}l$, thus it is an allowed combination.

Therefore, the notation of subshell is $2s$.

(d)

Interpretation Introduction

Interpretation:

The notation of subshell if $n$ is 3, $l$ is 0, $m_l$ is 1, and $m_s$ is $-\text{1/2}$ has to be determined. Also, the reason for not allowed combination has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 7.54QE

The given combination of quantum numbers is not allowed.

Explanation of Solution

The value of principal quantum number $\left(n\right)$ is 3.

If the value of angular momentum quantum number $\left(l\right)$ is 0 then the subshell is $s$.

The value of magnetic quantum number $\left(m_l\right)$ is 1.

The value of electron spin quantum number $\left(m_s\right)$ is $-\text{1/2}$.

Since the value of $l$ is lesser than $n$ but the value of $m_l$ greater than the value of $l$ thus the given combination is not allowed.

(e)

Interpretation Introduction

Interpretation:

The notation of subshell if $n$ is 3, $l$ is 2, $m_l$ is 0, and $m_s$ is $+\text{1/2}$ has to be determined. Also, the reason for not allowed combination has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 7.54QE

The notation of subshell is $3d$.

Explanation of Solution

The value of principal quantum number $\left(n\right)$ is 3.

If the value of angular momentum quantum number $\left(l\right)$ is 2 then the subshell is $d$.

The value of magnetic quantum number $\left(m_l\right)$ is 0.

The value of electron spin quantum number $\left(m_s\right)$ is $+\text{1/2}$.

Since the value of $l$ is lesser than $n$ and $m_l$ is also in the range of $-2$ to $\text{+}2$, thus it is an allowed combination.

Therefore, the notation of subshell is $3d$.

(f)

Interpretation Introduction

Interpretation:

The notation of subshell if $n$ is 6, $l$ is 0, $m_l$ is 0, and $m_s$ is $+\text{1/2}$ has to be determined. Also, the reason for not allowed combination has to be determined.

Concept Introduction:

Refer to part (a).

Answer to Problem 7.54QE

The notation of subshell is $6s$.

Explanation of Solution

The value of principal quantum number $\left(n\right)$ is 6.

If the value of angular momentum quantum number $\left(l\right)$ is 0 then the subshell is $s$.

The value of magnetic quantum number $\left(m_l\right)$ is 0.

The value of electron spin quantum number $\left(m_s\right)$ is $+\text{1/2}$.

Since the value of $l$ is lesser than $n$ and $m_l$ is also in the range of $-l$ to $\text{+}l$, thus it is an allowed combination.

Therefore, the notation of subshell is $6s$.