Chapter 7, Problem 7.90QP

(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 $\text{Ge}$

Answer to Problem 7.90QP

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

Explanation of Solution

$\text{Ge}$ is placed in IVA group of the periodic table. Its atomic number is 32.  Therefore, $\text{Ge}$ has 32 electrons in its shells.  $\text{Ge}$ is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell. 

The noble gas core for $\text{Ge}$ 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 $\text{Ge}$ beyond its noble gas core are $\left(\text{32 – 18}\right)=\text{ 14}$ electrons.  These 14 electrons enter into the $4s,3d\text{ and }4p$ subshells.

Put all the 14 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

All the 14 electrons of $\text{Ge}$ 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 14 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 two electrons in $4p$-atomic orbitals.  Therefore, the ground-state electron configuration for $\text{Ge}$ is $\left[\text{Ar}\right]3d^{10}4s^{2}4p^2$.

(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 $\text{Fe}$

Answer to Problem 7.90QP

The ground-state electron configuration for $\text{Fe}$ is $\left[\text{Ar}\right]3d^{6}4s^2$

Explanation of Solution

$\text{Fe}$ is placed in VIIIB group of the periodic table. Its atomic number is 26.  Therefore, $\text{Fe}$ has 26 electrons in its shells.  $\text{Fe}$ is a $d$-block element.  So, its outermost electrons are located in a $d$-subshell. 

The noble gas core for $\text{Fe}$ 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 $\text{Fe}$ beyond its noble gas core are $\left(\text{26 – 18}\right)=\text{ 8}$ electrons.  These 8 electrons enter into the $4s\text{ and }3d$ subshells.

Put all the 8 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 8 electrons of $\text{Fe}$ 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 8 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, six electrons in $3d$-atomic orbital.  Therefore, the ground-state electron configuration for $\text{Fe}$ is $\left[\text{Ar}\right]3d^{6}4s^2$.

(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 $\text{Zn}$

Answer to Problem 7.90QP

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

Explanation of Solution

$\text{Zn}$ is placed in IIB group of the periodic table. Its atomic number is 30.  Therefore, $\text{Zn}$ has 30 electrons in its shells.  $\text{Zn}$ is a $d$-block element.  So, its outermost electrons are located in a $d$-subshell. 

The noble gas core for $\text{Zn}$ 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 $\text{Zn}$ beyond its noble gas core are $\left(\text{30 – 18}\right)=\text{ 12}$ electrons.  These 12 electrons enter into the $4s\text{ and }3d$ subshells.

Put all the 12 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 12 electrons of $\text{Zn}$ 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 12 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, ten electrons in $3d$-atomic orbital.  Therefore, the ground-state electron configuration for $\text{Zn}$ is $\left[\text{Ar}\right]3d^{10}4s^2$.

(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 $\text{Ni}$

Answer to Problem 7.90QP

The ground-state electron configuration for $\text{Ni}$ is $\left[\text{Ar}\right]3d^{8}4s^2$

Explanation of Solution

$\text{Ni}$ is placed in VIIIB group of the periodic table. Its atomic number is 28.  Therefore, $\text{Ni}$ has 28 electrons in its shells.  $\text{Ni}$ is a $d$-block element.  So, its outermost electrons are located in a $d$-subshell. 

The noble gas core for $\text{Ni}$ 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 $\text{Ni}$ beyond its noble gas core are $\left(\text{28 – 18}\right)=\text{ 10}$ electrons.  These 10 electrons enter into the $4s\text{ and }3d$ subshells.

Put all the 10 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

All the 10 electrons of $\text{Ni}$ 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 12 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, eight electrons in $3d$-atomic orbital.  Therefore, the ground-state electron configuration for $\text{Ni}$ is $\left[\text{Ar}\right]3d^{8}4s^2$.

(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 $\text{W}$

Answer to Problem 7.90QP

The ground-state electron configuration for $\text{W}$ is $\left[\text{Xe}\right]4f^{14}5d^{4}6s^2$

Explanation of Solution

$\text{W}$ is placed in VIB group of the periodic table.  Its atomic number is 74.  Therefore, $\text{W}$ has 74 electrons in its shells.  $\text{W}$ is a $d$-block element.  So, its outermost electrons are located in a $d$-subshell. 

The noble gas core for $\text{W}$ 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 $\text{W}$ beyond its noble gas core are $\left(\text{74 – 54}\right)=\text{ 20}$ electrons.  These 20 electrons enter into the $4f,5d\text{ and }6s$ subshells.

Put all the 20 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

All the 20 electrons of $\text{W}$ 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 20 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.

There are 14 electrons present in $4f$-atomic orbital, two electrons in $6s$-atomic orbital and four electrons in $5d$-atomic orbital.  Therefore, the ground-state electron configuration of $\text{W}$ is $\left[\text{Xe}\right]4f^{14}5d^{4}6s^2$.

(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 $\text{Tl}$

Answer to Problem 7.90QP

The ground-state electron configuration for $\text{Tl}$ is $\left[\text{Xe}\right]4f^{14}5d^{10}6s^{2}6p^1$

Explanation of Solution

$\text{Tl}$ is placed in IIIA group of the periodic table.  Its atomic number is 81.  Therefore, $\text{Tl}$ has 81 electrons in its shells.  $\text{Tl}$ is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell. 

The noble gas core for $\text{Tl}$ is $\left[\text{Xe}\right]$, where atomic number of $\text{Xe}$ is 54.  So, the order of filling beyond the noble gas core is $4f,6s,5d\text{ and }6p$. The electrons in $\text{Tl}$ beyond its noble gas core are $\left(\text{81 – 54}\right)=\text{ 27}$ electrons.  These 27 electrons enter into the $4f,6s,5d\text{ and }6p$ subshells.

Put all the 27 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

All the 27 electrons of $\text{Tl}$ 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 whereas $f$-atomic orbitals have seven sub-shells.  The 27 electrons are going into the $4f$ -atomic orbitals first, followed by $6s$-atomic orbitals which are again followed by $5d$-atomic orbitals and $6p$-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.  Red colored orbital corresponds to $6p$-atomic orbital.

There are 14 electrons present in $4f$-atomic orbital, two electrons in $6s$-atomic orbital, ten electrons in $5d$-atomic orbital and one electron in $6p$-atomic orbital.  Therefore, the ground-state electron configuration of $\text{Tl}$ is $\left[\text{Xe}\right]4f^{14}5d^{10}6s^{2}6p^1$.