Chapter 6, Problem 39QAP

Write the orbital diagram for

(a) Li(b) P(c) F(d) Fe

Interpretation Introduction

(a)

Interpretation:

To write the orbital diagram for each of the Li element.

Concept introduction:

The simplest method for describing the arrangement of electrons in an atom is by writing its electronic configuration. Since the set of four quantum numbers is used to describe the atomic orbitals in an atom, therefore by writing the electronic configuration, one can get details of the number of electrons present in each sublevel.To show the distribution of electrons in the various orbitals, orbital diagrams are used.The filling of electrons in the atomic orbitals takes place according to the Aufbau principal which states that when an atom is present in its ground state, electrons are filled in order of increasing energy of the orbitals, which means that firstly lower energy orbitals are filled, and then filling of higher energy orbitals takes place.

Answer to Problem 39QAP

The orbital diagram for Li is:

$\begin{array}{l}1s\text{ 2s}\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \end{array}\end{array}$

Explanation of Solution

When the electronic configuration of an atom is written, it describes the number of electron present in each sublevel by the superscript. Atomic number of an element gives the total number of electrons present in an atom. Since the atomic number of Lithium atom denoted by Li is 3, therefore its ground state electronic configuration is:

1s²2s¹

According to Hund’s Rule, when several orbitals having equal energy are available, then electrons are filled singly with parallel spins.No two electrons can have same spin in a given orbital. The most stable arrangement of electrons is the one in which two electrons present in two different orbitals have parallel spins.The total number of orbitals in a given sublevel are given by 2l+1, where l = 0,1,2,3 for s, p, d and f sublevels respectively. In case of Lithium, since the electrons are present in only s-sublevel,l=0.

This means 2l+1 = 2(0) +1= 1

Hence, one orbital is present for each sublevel. The orbital diagram for its electronic configuration is shown below:

$\begin{array}{l}1s\text{ 2s}\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \end{array}\end{array}$

Interpretation Introduction

(b)

Interpretation:

To write the orbital diagram for each of the P element.

Concept introduction:

The simplest method for describing the arrangement of electrons in an atom is by writing its electronic configuration. Since the set of four quantum numbers is used to describe the atomic orbitals in an atom, therefore by writing the electronic configuration, one can get details of the number of electrons present in each sublevel. To show the distribution of electrons in the various orbitals, orbital diagrams are used. The filling of electrons in the atomic orbitals takes place according to the Aufbau principal which states that when an atom is present in its ground state, electrons are filled in order of increasing energy of the orbitals, which means that firstly lower energy orbitals are filled, and then filling of higher energy orbitals takes place.

Answer to Problem 39QAP

The orbital diagram for P is:

$\begin{array}{l}1s\text{ 2s 2p 3s 3p}\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft & \upharpoonleft & \upharpoonleft \end{array}\end{array}$

Explanation of Solution

When the electronic configuration of an atom is written, it describes the number of electron present in each sublevel by the superscript. Atomic number of an element gives the total number of electrons present in an atom. Since the atomic number of Phosphorus atom denoted by P is 15, therefore its ground state electronic configuration is:

${\text{1s}}^{2}2s^{2}2p^{6}3s^2{\text{ 3p}}^3$

According to Hund’s Rule, when several orbitals having equal energy are available, then electrons are filled singly with parallel spins. No two electrons can have same spin in a given orbital. The most stable arrangement of electrons is the one in which two electrons present in two different orbitals have parallel spins. The total number of orbitals in a given sublevel are given by 2l+1, where l = 0,1,2,3 for s, p, d and f sublevels respectively. In case of Phosphorus, since the electrons are present in both s and p-sublevel ,l=0 for s and l=1 for p-sublevels

This means 2l+1 = 2(0) +1= 1

Hence one orbital is present for each s-sublevel.

For a p-sublevel, the total number of orbitals is

2(1) +1

2+1

3

This means that three orbitals are present in each p-sublevel of Phosphorus atom.

The orbital diagram for its electronic configuration is shown below:

$\begin{array}{l}1s\text{ 2s 2p 3s 3p}\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft & \upharpoonleft & \upharpoonleft \end{array}\end{array}$

Interpretation Introduction

(c)

Interpretation:

To write the orbital diagram for each of the F element.

Concept introduction:

The simplest method for describing the arrangement of electrons in an atom is by writing its electronic configuration. Since the set of four quantum numbers is used to describe the atomic orbitals in an atom, therefore by writing the electronic configuration, one can get details of the number of electrons present in each sublevel. To show the distribution of electrons in the various orbitals, orbital diagrams are used. The filling of electrons in the atomic orbitals takes place according to the Aufbau principal which states that when an atom is present in its ground state, electrons are filled in order of increasing energy of the orbitals, which means that firstly lower energy orbitals are filled, and then filling of higher energy orbitals takes place.

Answer to Problem 39QAP

The orbital diagram for F is:

$\begin{array}{l}1s\text{ 2s 2p }\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \end{array}\end{array}$

Explanation of Solution

When the electronic configuration of an atom is written, it describes the number of electron present in each sublevel by the superscript. Atomic number of an element gives the total number of electrons present in an atom. Since the atomic number of Fluorine atom denoted by F is 9, therefore its ground state electronic configuration is:

${\text{1s}}^{2}2s^{2}2p^5$

According to Hund’s Rule, when several orbitals having equal energy are available, then electrons are filled singly with parallel spins. No two electrons can have same spin in a given orbital. The most stable arrangement of electrons is the one in which two electrons present in two different orbitals have parallel spins. The total number of orbitals in a given sublevel are given by 2l+1, where l = 0,1,2,3 for s, p, d and f sublevels respectively. In case of Fluorine, since the electrons are present in both s and p-sublevel, l=0 for s and l=1 for p-sublevels

This means 2l+1 = 2(0) +1= 1

Hence one orbital is present for each s-sublevel.

For a p-sublevel, the total number of orbitals is

2(1) +1

2+1

3

This means that three orbitals are present in p-sublevel of Fluorine atom.

The orbital diagram for its electronic configuration is shown below:

$\begin{array}{l}1s\text{ 2s 2p }\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \end{array}\end{array}$

Interpretation Introduction

(d)

Interpretation:

To write the orbital diagram for each of the Fe element.

Concept introduction:

The simplest method for describing the arrangement of electrons in an atom is by writing its electronic configuration. Since the set of four quantum numbers is used to describe the atomic orbitals in an atom, therefore by writing the electronic configuration one can get details of the number of electrons present in each sublevel.The filling of electrons in the atomic orbitals takes place according to the Aufbau principal which states that when an atom is present in its ground state, electrons are filled in order of increasing energy of the orbitals, which means that firstly lower energy orbitals are filled, and then filling of higher energy orbitals takes place.

To show the distribution of electrons in the various orbitals, orbital diagrams are used.

Answer to Problem 39QAP

The orbital diagram for Fe is:

$\begin{array}{l}1s\text{ 2s 2p 3s 3p 3d 4s}\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright \end{array}\begin{array}{ccccc}\upharpoonleft \downharpoonright & \upharpoonleft & \upharpoonleft & \upharpoonleft & \upharpoonleft \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\end{array}$

Explanation of Solution

When the electronic configuration of an atom is written, it describes the number of electron present in each sublevel by the superscript. Atomic number of an element gives the total number of electrons present in an atom. Since the atomic number of Iron atom denoted by Fe is 26, therefore its ground state electronic configuration is:

${\text{1s}}^{2}2s^{2}2p^6{\text{ 3s}}^2{\text{ 3p}}^6{\text{ 3d}}^6{\text{ 4s}}^2$

According to Hund’s Rule, when several orbitals having equal energy are available, then electrons are filled singly with parallel spins. No two electrons can have same spin in a given orbital. The most stable arrangement of electrons is the one in which two electrons present in two different orbitals have parallel spins. The total number of orbitals in a given sublevel are given by 2l+1, where l = 0,1,2,3 for s, p, d and f sublevels respectively. In case of Iron, since the electrons are present in s, p and d-sublevel, l=0 for s, l=1 for p and l=2 for d-sublevel.

This means 2l+1 = 2(0) +1= 1

Hence one orbital is present for each s-sublevel.

For a p-sublevel, the total number of orbitals is:

2(1) +1

2+1

3

This means that three orbitals are present in each p-sublevel of Fe atom.

For a d-sublevel, the total number of orbitals is:

2(2) + 1=5

Hence there are five orbitals present in d-sublevel of Fe atom.

The orbital diagram for its electronic configuration is shown below:

$\begin{array}{l}1s\text{ 2s 2p 3s 3p 3d 4s}\\ \begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\begin{array}{ccc}\upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright & \upharpoonleft \downharpoonright \end{array}\begin{array}{ccccc}\upharpoonleft \downharpoonright & \upharpoonleft & \upharpoonleft & \upharpoonleft & \upharpoonleft \end{array}\begin{array}{c}\upharpoonleft \downharpoonright \end{array}\end{array}$