Chapter 3, Problem 3.102QP

Determine the number of unpaired electrons in each atom: K, Ca, Sc, Ti, V, Cr, Mn.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms should be given by knowing their ground-state electron configurations.

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.  If all the atomic orbitals are filled by electrons, then the atom is diamagnetic in nature.  Diamagnetic atoms are repelled by the magnetic field.  If one or more unpaired electrons are present in an atom, then that atom is paramagnetic in nature.  Paramagnetic atoms are attracted to the magnetic field.

To find: Count the number of unpaired electrons in $\text{K}$

Answer to Problem 3.102QP

The number of unpaired electron in $\text{K}$ is 1

Explanation of Solution

$\text{K}$ is placed in IA group of the periodic table.  Its atomic number is 19.  Therefore, $\text{K}$ has 19 electrons in its shells.  $\text{K}$ is a s-block element.  So, its outermost electrons are located in $s$-shell.

The noble gas core for $\text{K}$ is $\left[\text{Ar}\right]$, where atomic number of $\text{Ar}$ is 18.  So, the order of filling beyond the noble gas core is $4s$. The electrons in $\text{K}$ beyond its noble gas core is $\left(\text{19 – 18}\right)=\text{ 1}$ electron.  The one electron enters into the $4s$-shell.

All the electrons are placed in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

The one electron of $\text{K}$ 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.  The one electron is going into the $4s$-atomic orbital.  Blue colored orbital corresponds to $4s$-atomic orbital.

The unpaired electrons are present in $4s$-atomic orbitals.  There is only one unpaired electron in $4s$-atomic orbital in the case of $\text{K}$-atom.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms should be given by knowing their ground-state electron configurations.

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.  If all the atomic orbitals are filled by electrons, then the atom is diamagnetic in nature.  Diamagnetic atoms are repelled by the magnetic field.  If one or more unpaired electrons are present in an atom, then that atom is paramagnetic in nature.  Paramagnetic atoms are attracted to the magnetic field.

To find: Count the number of unpaired electrons in $\text{Ca}$

Answer to Problem 3.102QP

There is no unpaired electron in  $\text{Ca}$

Explanation of Solution

$\text{Ca}$ is placed in IIA group of the periodic table.  Its atomic number is 20.  Therefore, $\text{Ca}$ has 20 electrons in its shells.  $\text{Ca}$ is a $s$-block element.  So, its outermost electrons are located in $s$-shell.

The noble gas core for $\text{Ca}$ is $\left[\text{Ar}\right]$, where atomic number of $\text{Ar}$ is 18.  So, the order of filling beyond the noble gas core is $4s$. The electrons in $\text{Ca}$ beyond its noble gas core is $\left(\text{20 – 18}\right)=\text{ 2}$ electrons.  The two electrons enter into the $4s$-shell.

All the electrons are placed in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

The two electrons of $\text{Ca}$ 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.  The two electrons are going into the $4s$-atomic orbital.  Blue colored orbital corresponds to $4s$-atomic orbital.

There is no unpaired electron present in $4s$-atomic orbital in the case of $\text{Ca}$-atom.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms should be given by knowing their ground-state electron configurations.

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.  If all the atomic orbitals are filled by electrons, then the atom is diamagnetic in nature.  Diamagnetic atoms are repelled by the magnetic field.  If one or more unpaired electrons are present in an atom, then that atom is paramagnetic in nature.  Paramagnetic atoms are attracted to the magnetic field.

To find: Count the number of unpaired electrons in $\text{Sc}$

Answer to Problem 3.102QP

The number of unpaired electron in $\text{Sc}$  is 1

Explanation of Solution

$\text{Sc}$ is placed in IIIB group of the periodic table.  Its atomic number is 21.  Therefore, $\text{Sc}$ has 21 electrons in its shells.  $\text{Sc}$ is a $d$-block element.  So, its outermost electrons are located in $d$-subshells.

The noble gas core for $\text{Sc}$ 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 $\text{Sc}$ beyond its noble gas core is $\left(\text{21 – 18}\right)=\text{ 3}$ electrons.  The three electrons enter into the $4s\text{ and }3d$-subshells.

All the electrons are placed in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

The three electrons of $\text{Sc}$ 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 subshells.  The three electrons are going into the $4s$-atomic orbital followed by $3d$-atomic orbital.  Blue colored orbital corresponds to $4s$-atomic orbital.  Black colored orbital corresponds to $3d$-atomic orbital.

The unpaired electrons are present in $3d$-atomic orbitals.  There is only one unpaired electron in $3d$-atomic orbital in the case of $\text{Sc}$-atom.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms should be given by knowing their ground-state electron configurations.

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.  If all the atomic orbitals are filled by electrons, then the atom is diamagnetic in nature.  Diamagnetic atoms are repelled by the magnetic field.  If one or more unpaired electrons are present in an atom, then that atom is paramagnetic in nature.  Paramagnetic atoms are attracted to the magnetic field.

To find: Count the number of unpaired electrons in $\text{Ti}$

Answer to Problem 3.102QP

The number of unpaired electrons in $\text{Ti}$ is 2

Explanation of Solution

$\text{Ti}$ is placed in IVB group of the periodic table.  Its atomic number is 22.  Therefore, $\text{Ti}$ has 22 electrons in its shells.  $\text{Ti}$ is a $d$-block element.  So, its outermost electrons are located in $d$-subshells.

The noble gas core for $\text{Ti}$ 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 $\text{Ti}$ beyond its noble gas core is $\left(\text{22 – 18}\right)=\text{ 4}$ electrons.  The four electrons enter into the $4s\text{ and }3d$-subshells.

All the electrons are placed in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

The four electrons of $\text{Ti}$ 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 subshells.  The four electrons are going into the $4s$-atomic orbital followed by $3d$-atomic orbital.  Blue colored orbital corresponds to $4s$-atomic orbital.  Black colored orbital corresponds to $3d$-atomic orbital.

The unpaired electrons are present in $3d$-atomic orbitals.  There are two unpaired electrons in $3d$-atomic orbital in the case of $\text{Ti}$-atom.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms should be given by knowing their ground-state electron configurations.

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.  If all the atomic orbitals are filled by electrons, then the atom is diamagnetic in nature.  Diamagnetic atoms are repelled by the magnetic field.  If one or more unpaired electrons are present in an atom, then that atom is paramagnetic in nature.  Paramagnetic atoms are attracted to the magnetic field.

To find: Count the number of unpaired electrons in $\text{V}$

Answer to Problem 3.102QP

The number of unpaired electrons in $\text{V}$ is 3

Explanation of Solution

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

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 is $\left(\text{23 – 18}\right)=\text{ 5}$ electrons.  The five electrons enter into the $4s\text{ and }3d$-subshells.

All the electrons are placed in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule

The five electrons of $\text{V}$ 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 subshells.  The five electrons are going into the $4s$-atomic orbital followed by $3d$-atomic orbital.  Blue colored orbital corresponds to $4s$-atomic orbital.  Black colored orbital corresponds to $3d$-atomic orbital.

The unpaired electrons are present in $3d$-atomic orbitals.  There are three unpaired electrons in $3d$-atomic orbital in the case of $\text{V}$-atom.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms should be given by knowing their ground-state electron configurations.

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.  If all the atomic orbitals are filled by electrons, then the atom is diamagnetic in nature.  Diamagnetic atoms are repelled by the magnetic field.  If one or more unpaired electrons are present in an atom, then that atom is paramagnetic in nature.  Paramagnetic atoms are attracted to the magnetic field.

To find: Count the number of unpaired electrons in $\text{Cr}$

Answer to Problem 3.102QP

The number of unpaired electrons in $\text{Cr}$ is 6

Explanation of Solution

$\text{Cr}$ is placed in VIB group of the periodic table.  Its atomic number is 24.  Therefore, $\text{Cr}$ has 24 electrons in its shells.  $\text{Cr}$ is a $d$-block element.  So, its outermost electrons are located in $d$-subshells.

The noble gas core for $\text{Cr}$ 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 $\text{Cr}$ beyond its noble gas core is $\left(\text{24 – 18}\right)=\text{ 6}$ electrons.  The six electrons enter into the $4s\text{ and }3d$-subshells.

All the electrons are placed in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

The six electrons of $\text{Cr}$ 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 subshells.  The six electrons are going into the $4s$-atomic orbital followed by $3d$-atomic orbital.  Blue colored orbital corresponds to $4s$-atomic orbital.  Black colored orbital corresponds to $3d$-atomic orbital.  One of the electrons present in $4s$-atomic orbital is jumped into the $3d$-atomic orbital because half-filled $3d$-atomic orbital is more stable.

The unpaired electrons are present in $4s$- and $3d$-atomic orbitals.  There are six unpaired electrons in the case of $\text{Cr}$-atom.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms should be given by knowing their ground-state electron configurations.

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.  If all the atomic orbitals are filled by electrons, then the atom is diamagnetic in nature.  Diamagnetic atoms are repelled by the magnetic field.  If one or more unpaired electrons are present in an atom, then that atom is paramagnetic in nature.  Paramagnetic atoms are attracted to the magnetic field.

To find: Count the number of unpaired electrons in $\text{Mn}$

Answer to Problem 3.102QP

The number of unpaired electrons in $\text{Mn}$ is 5

Explanation of Solution

$\text{Mn}$ is placed in VIIB group of the periodic table.  Its atomic number is 25.  Therefore, $\text{Mn}$ has 25 electrons in its shells.  $\text{Mn}$ is a $d$-block element.  So, its outermost electrons are located in $d$-subshells.

The noble gas core for $\text{Mn}$ 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 $\text{Mn}$ beyond its noble gas core is $\left(\text{25 – 18}\right)=\text{ 7}$ electrons.  The seven electrons enter into the $4s\text{ and }3d$-subshells.

All the electrons are placed in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

The seven electrons of $\text{Mn}$ 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 subshells.  The seven electrons are going into the $4s$-atomic orbital followed by $3d$-atomic orbital.  Blue colored orbital corresponds to $4s$-atomic orbital.  Black colored orbital corresponds to $3d$-atomic orbital.

The unpaired electrons are present in $3d$-atomic orbitals.  There are five unpaired electrons in $3d$-atomic orbital in the case of $\text{Mn}$-atom.