Chapter 7, Problem 7.89QP

(a)

Interpretation Introduction

Interpretation:

The ground-state electron configurations for the given elements should be identified.

Concept Introduction:

An orbital is an area of space in which electrons are orderly filled.  The maximum capacity in any type of orbital is two electrons.  An atomic orbital is defined as the region of space in which the probability of finding the electrons is highest.  It is subdivided into four orbitals such as $s,p,dandf$ orbitals which depend upon the number of electrons present in the nucleus of a particular atom.

There are three basic principles in which orbitals are filled by the electrons.

1. 1. Aufbau principle: In German, the word 'aufbau' means 'building up'.  The electrons are arranged in various orbitals in the order of increasing energies.
2. 2. Pauli exclusion principle: An electron does not have all the four quantum numbers.
3. 3. Hund’s rule: Each orbital is singly engaged with one electron having the maximum same spin capacity after that only pairing occurs.

The electron configuration is the allocation of electrons of an atom in atomic orbitals.  Electronic configuration of a particular atom is written by following the three basic principles.

To find: Identify the ground-state electron configuration for $\text{B}$

Answer to Problem 7.89QP

The ground-state electron configuration for $\text{B}$ is $1s^{2}2s^{2}2p^1$

Explanation of Solution

Boron ($\text{B}$) is placed in IIIA group of the periodic table. Its atomic number is 5.  Therefore, boron has five electrons in its shells.  Boron ($\text{B}$) is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell. 

Put all the 5 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

All the 5 electrons of boron ($\text{B}$) occupy the atomic orbitals from lowest energy to highest energy orbitals.  The maximum capacity of each orbital has two electrons which have opposite spins.  $s$-atomic orbitals have a single shell whereas $p$-atomic orbitals have three sub-shells.  The 5 electrons are going into the $1s$-atomic orbitals first, followed by $2s$-atomic orbitals which are again followed by $2p$-atomic orbitals.  Blue colored orbital corresponds to $1s$-atomic orbital.  Black colored orbital corresponds to $2s$-atomic orbital.  Red colored orbital corresponds to $2p$-atomic orbitals.

There are 2 electrons present in $1s$-atomic orbital, two electrons in $2s$-atomic orbital and one electron in $2p$-atomic orbital.  Therefore, the ground-state electron configuration for $\text{B}$ is $1s^{2}2s^{2}2p^1$.

(b)

Interpretation Introduction

Interpretation:

The ground-state electron configurations for the given elements should be identified.

Concept Introduction:

An orbital is an area of space in which electrons are orderly filled.  The maximum capacity in any type of orbital is two electrons.  An atomic orbital is defined as the region of space in which the probability of finding the electrons is highest.  It is subdivided into four orbitals such as $s,p,dandf$ orbitals which depend upon the number of electrons present in the nucleus of a particular atom.

There are three basic principles in which orbitals are filled by the electrons.

1. 1. Aufbau principle: In German, the word 'aufbau' means 'building up'.  The electrons are arranged in various orbitals in the order of increasing energies.
2. 2. Pauli exclusion principle: An electron does not have all the four quantum numbers.
3. 3. Hund’s rule: Each orbital is singly engaged with one electron having the maximum same spin capacity after that only pairing occurs.

The electron configuration is the allocation of electrons of an atom in atomic orbitals.  Electronic configuration of a particular atom is written by following the three basic principles.

To find: Identify the ground-state electron configuration for $\text{V}$

Answer to Problem 7.89QP

The ground-state electron configuration for $\text{V}$ is $\left[\text{Ar}\right]3d^{3}4s^2$

Explanation of Solution

Vanadium ($\text{V}$) is placed in VB group of the periodic table. Its atomic number is 23.  Therefore, vanadium has 23 electrons in its shells.  Vanadium ($\text{V}$) is a $d$-block element.  So, its outermost electrons are located in a $d$-subshell. 

The noble gas core for $\text{V}$ is $\left[\text{Ar}\right]$, where atomic number of $\text{Ar}$ is 18.  So, the order of filling beyond the noble gas core is $4s\text{ and }3d$. The electrons in $\text{V}$ beyond its noble gas core are $\left(\text{23 – 18}\right)=\text{ 5}$ electrons.  These 5 electrons enter into the $4s\text{ and }3d$ subshells.

Put all the 5 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 5 electrons of vanadium ($\text{V}$) occupy the atomic orbitals from lowest energy to highest energy orbitals.  The maximum capacity of each orbital has two electrons which have opposite spins.  $s$-atomic orbitals have a single shell whereas $d$-atomic orbitals have five sub-shells.  The 5 electrons are going into the $4s$-atomic orbitals first, followed by $3d$-atomic orbitals.  Blue colored orbital corresponds to $4s$-atomic orbital.  Black colored orbital corresponds to $3d$-atomic orbital. 

There are 2 electrons present in $4s$-atomic orbital, three electrons in $3d$-atomic orbital.  Therefore, the ground-state electron configuration for $\text{V}$ is $\left[\text{Ar}\right]3d^{3}4s^2$.

(c)

Interpretation Introduction

Interpretation:

The ground-state electron configurations for the given elements should be identified.

Concept Introduction:

An orbital is an area of space in which electrons are orderly filled.  The maximum capacity in any type of orbital is two electrons.  An atomic orbital is defined as the region of space in which the probability of finding the electrons is highest.  It is subdivided into four orbitals such as $s,p,dandf$ orbitals which depend upon the number of electrons present in the nucleus of a particular atom.

There are three basic principles in which orbitals are filled by the electrons.

1. 1. Aufbau principle: In German, the word 'aufbau' means 'building up'.  The electrons are arranged in various orbitals in the order of increasing energies.
2. 2. Pauli exclusion principle: An electron does not have all the four quantum numbers.
3. 3. Hund’s rule: Each orbital is singly engaged with one electron having the maximum same spin capacity after that only pairing occurs.

The electron configuration is the allocation of electrons of an atom in atomic orbitals.  Electronic configuration of a particular atom is written by following the three basic principles.

To find: Identify the ground-state electron configuration for $\text{C}$

Answer to Problem 7.89QP

The ground-state electron configuration for $\text{C}$ is $1s^{2}2s^{2}2p^2$

Explanation of Solution

Carbon ($\text{C}$) is placed in IVA group of the periodic table. Its atomic number is 6.  Therefore, carbon has six electrons in its shells.  Carbon ($\text{C}$) is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell. 

Put all the 6 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 6 electrons of carbon ($\text{C}$) occupy the atomic orbitals from lowest energy to highest energy orbitals.  The maximum capacity of each orbital has two electrons which have opposite spins.  $s$-atomic orbitals have a single shell whereas $p$-atomic orbitals have three sub-shells.  The 6 electrons are going into the $1s$-atomic orbitals first, followed by $2s$-atomic orbitals which are again followed by $2p$-atomic orbitals.  Blue colored orbital corresponds to $1s$-atomic orbital.  Black colored orbital corresponds to $2s$-atomic orbital.  Red colored orbital corresponds to $2p$-atomic orbitals.

There are 2 electrons present in $1s$-atomic orbital, two electrons in $2s$-atomic orbital and two electrons in $2p$-atomic orbital.  Therefore, the ground-state electron configuration for $\text{C}$ is $1s^{2}2s^{2}2p^2$.

(d)

Interpretation Introduction

Interpretation:

The ground-state electron configurations for the given elements should be identified.

Concept Introduction:

An orbital is an area of space in which electrons are orderly filled.  The maximum capacity in any type of orbital is two electrons.  An atomic orbital is defined as the region of space in which the probability of finding the electrons is highest.  It is subdivided into four orbitals such as $s,p,dandf$ orbitals which depend upon the number of electrons present in the nucleus of a particular atom.

There are three basic principles in which orbitals are filled by the electrons.

1. 1. Aufbau principle: In German, the word 'aufbau' means 'building up'.  The electrons are arranged in various orbitals in the order of increasing energies.
2. 2. Pauli exclusion principle: An electron does not have all the four quantum numbers.
3. 3. Hund’s rule: Each orbital is singly engaged with one electron having the maximum same spin capacity after that only pairing occurs.

The electron configuration is the allocation of electrons of an atom in atomic orbitals.  Electronic configuration of a particular atom is written by following the three basic principles.

To find: Identify the ground-state electron configuration for $\text{As}$

Answer to Problem 7.89QP

The ground-state electron configuration for $\text{As}$ is $\left[\text{Ar}\right]3d^{10}4s^{2}4p^3$

Explanation of Solution

Arsenic ($\text{As}$) is placed in VA group of the periodic table. Its atomic number is 33.  Therefore, arsenic has 33 electrons in its shells.  Arsenic ($\text{As}$) is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell. 

The noble gas core for $\text{As}$ is $\left[\text{Ar}\right]$, where atomic number of $\text{Ar}$ is 18.  So, the order of filling beyond the noble gas core is $4s,3d\text{ and }4p$. The electrons in $\text{As}$ beyond its noble gas core are $\left(\text{33 – 18}\right)=\text{ 15}$ electrons.  These 15 electrons enter into the $4s,3d\text{ and }4p$ subshells.

Put all the 15 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 15 electrons of arsenic ($\text{As}$) occupy the atomic orbitals from lowest energy to highest energy orbitals.  The maximum capacity of each orbital has two electrons which have opposite spins.  $s$-atomic orbitals have a single shell whereas $p$-atomic orbitals have three sub-shells.  $d$-atomic orbitals have five sub-shells.  The 15 electrons are going into the $4s$-atomic orbitals first, followed by $3d$-atomic orbitals which is again followed by $4p$- atomic orbitals.  Blue colored orbital corresponds to $4s$-atomic orbital.  Black colored orbital corresponds to $3d$-atomic orbital.  Red colored orbital corresponds to $4p$-atomic orbitals.

There are 2 electrons present in $4s$-atomic orbital, ten electrons in $3d$-atomic orbitals and three electrons in $4p$-atomic orbitals.  Therefore, the ground-state electron configuration for $\text{As}$ is $\left[\text{Ar}\right]3d^{10}4s^{2}4p^3$.

(e)

Interpretation Introduction

Interpretation:

The ground-state electron configurations for the given elements should be identified.

Concept Introduction:

An orbital is an area of space in which electrons are orderly filled.  The maximum capacity in any type of orbital is two electrons.  An atomic orbital is defined as the region of space in which the probability of finding the electrons is highest.  It is subdivided into four orbitals such as $s,p,dandf$ orbitals which depend upon the number of electrons present in the nucleus of a particular atom.

There are three basic principles in which orbitals are filled by the electrons.

1. 1. Aufbau principle: In German, the word 'aufbau' means 'building up'.  The electrons are arranged in various orbitals in the order of increasing energies.
2. 2. Pauli exclusion principle: An electron does not have all the four quantum numbers.
3. 3. Hund’s rule: Each orbital is singly engaged with one electron having the maximum same spin capacity after that only pairing occurs.

The electron configuration is the allocation of electrons of an atom in atomic orbitals.  Electronic configuration of a particular atom is written by following the three basic principles.

To find: Identify the ground-state electron configuration for $\text{I}$

Answer to Problem 7.89QP

The ground-state electron configuration for $\text{I}$ is $\left[\text{Kr}\right]4d^{10}5s^{2}5p^5$

Explanation of Solution

Iodine ($\text{I}$) is placed in VIIA group of the periodic table. Its atomic number is 53.  Therefore, iodine has 53 electrons in its shells.  Iodine ($\text{I}$) is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell. 

The noble gas core for $\text{I}$ is $\left[\text{Kr}\right]$, where atomic number of $\text{Kr}$ is 36.  So, the order of filling beyond the noble gas core is $5s,4d\text{ and }5p$. The electrons in $\text{I}$ beyond its noble gas core is $\left(\text{53 – 36}\right)=\text{ 17}$ electrons.  These 17 electrons enter into the $5s,4d\text{ and }5p$ subshells.

Put all the 17 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 17 electrons of iodine ($\text{I}$) occupy the atomic orbitals from lowest energy to highest energy orbitals.  The maximum capacity of each orbital has two electrons which have opposite spins.  $s$-atomic orbitals have a single shell whereas $p$-atomic orbitals have three sub-shells.  $d$-atomic orbitals have five sub-shells.  The 17 electrons are going into the $5s$-atomic orbitals first, followed by $4d$-atomic orbitals which is again followed by $5p$- atomic orbitals.  Blue colored orbital corresponds to $5s$-atomic orbital.  Black colored orbital corresponds to $4d$-atomic orbital.  Red colored orbital corresponds to $5p$-atomic orbitals.

There are 2 electrons present in $5s$-atomic orbital, ten electrons in $4d$-atomic orbitals and five electrons in $5p$-atomic orbitals.  Therefore, the ground-state electron configuration for $\text{I}$ is $\left[\text{Kr}\right]4d^{10}5s^{2}5p^5$.

(f)

Interpretation Introduction

Interpretation:

The ground-state electron configurations for the given elements should be identified.

Concept Introduction:

An orbital is an area of space in which electrons are orderly filled.  The maximum capacity in any type of orbital is two electrons.  An atomic orbital is defined as the region of space in which the probability of finding the electrons is highest.  It is subdivided into four orbitals such as $s,p,dandf$ orbitals which depend upon the number of electrons present in the nucleus of a particular atom.

There are three basic principles in which orbitals are filled by the electrons.

1. 1. Aufbau principle: In German, the word 'aufbau' means 'building up'.  The electrons are arranged in various orbitals in the order of increasing energies.
2. 2. Pauli exclusion principle: An electron does not have all the four quantum numbers.
3. 3. Hund’s rule: Each orbital is singly engaged with one electron having the maximum same spin capacity after that only pairing occurs.

The electron configuration is the allocation of electrons of an atom in atomic orbitals.  Electronic configuration of a particular atom is written by following the three basic principles.

To find: Identify the ground-state electron configuration for $\text{Au}$

Answer to Problem 7.89QP

The ground-state electron configuration for $\text{Au}$ is $\left[\text{Xe}\right]4f^{14}5d^{10}6s^1$

Explanation of Solution

Gold ($\text{Au}$) is placed in IB group of the periodic table.  Its atomic number is 79.  Therefore, gold has 79 electrons in its shells.  Gold ($\text{Au}$) is a $d$-block element.  So, its outermost electrons are located in a $d$-subshell. 

The noble gas core for $\text{Au}$ is $\left[\text{Xe}\right]$, where atomic number of $\text{Xe}$ is 54.  So, the order of filling beyond the noble gas core is $4f,5d\text{ and }6s$. The electrons in $\text{Au}$ beyond its noble gas core is $\left(\text{79 – 54}\right)=\text{ 25}$ electrons.  These 25 electrons enter into the $4f,5d\text{ and }6s$ subshells.

Put all the 25 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the electrons of gold ($\text{Au}$) occupy the atomic orbitals from lowest energy to highest energy orbitals.  The maximum capacity of each orbital has two electrons which have opposite spins.  $s$-atomic orbitals have a single shell whereas $d$-atomic orbitals have five sub-shells.  $f$-atomic orbitals have seven sub-shells.  The 25 electrons are going into the $4f$ -atomic orbitals first, followed by $6s$-atomic orbitals which are again followed by $5d$-atomic orbitals.  Green colored orbital corresponds to $4f$-atomic orbitals.  Blue colored orbital corresponds to $6s$-atomic orbital.  Black colored orbital corresponds to $5d$-atomic orbital.  One electron in $6s$-orbital is jumped into the $5d$-orbital because completely filled $d$-orbitals are more stable.

There are 14 electrons present in $4f$-atomic orbital, one electron in $6s$-atomic orbital and ten electrons in $5d$-atomic orbital.  Therefore, the ground-state electron configuration of gold ($\text{Au}$) is $\left[\text{Xe}\right]4f^{14}5d^{10}6s^1$.