Chapter 3, Problem 3.104QP

Determine the number of unpaired electrons in each of the following atoms in the ground state and identify each as diamagnetic or paramagnetic: (a) C, (b) S, (c) Cu, (d) Pb, (e) Ti.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms with its diamagnetic or paramagnetic behaviour 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 $\text{C}$ and get its magnetic behavior

Answer to Problem 3.104QP

The number of unpaired electrons in $\text{C}$ is 2.  It is paramagnetic in nature

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.

The noble gas core for $\text{C}$ is $\left[\text{He}\right]$, where atomic number of $\text{He}$ is 2.  So, the order of filling beyond the noble gas core is $2s\text{ and }2p$. The electrons in $\text{C}$ beyond its noble gas core are $\left(\text{6 – 2}\right)=\text{ 4}$ electrons.  The four electrons enter into the $2s\text{ and }2p$-subshells.

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

The 4 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 4 electrons are going into $2s$-atomic orbitals which are again followed by $2p$-atomic orbitals.  Blue colored orbital corresponds to $2s$-atomic orbital.  Red colored orbital corresponds to $2p$-atomic orbitals.

The unpaired electrons are present in $2p$-atomic orbital.  There are two unpaired electrons in $2p$-atomic orbital in the case of $\text{C}$-atom.  Therefore, $\text{C}$ is paramagnetic in nature.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms with its diamagnetic or paramagnetic behavior 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 $\text{S}$ and get its magnetic behavior

Answer to Problem 3.104QP

The number of unpaired electron in $\text{S}$ is 2.  It is paramagnetic in nature

Explanation of Solution

$\text{S}$ is placed in VIA group of the periodic table. Its atomic number is 16.  Therefore, $\text{S}$ has 16 electrons in its shells.  $\text{S}$ is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell.

The noble gas core for $\text{S}$ is $\left[\text{Ne}\right]$, where atomic number of $\text{Ne}$ is 10.  So, the order of filling beyond the noble gas core is $3s\text{ and }3p$. The electrons in $\text{S}$ beyond its noble gas core are $\left(\text{16 – 10}\right)=\text{ 6}$ electrons.  These 6 electrons enter into the $3s\text{ and }3p$ subshells.

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

All the 6 electrons of $\text{S}$ 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 $3s$-atomic orbitals first, followed by $3p$-atomic orbitals.  Blue colored orbital corresponds to $3s$-atomic orbital.  Red colored orbital corresponds to $3p$-atomic orbitals.

The unpaired electrons are present in $3p$-atomic orbital.  There are two unpaired electrons in $3p$-atomic orbital in the case of $\text{S}$-atom.  Therefore, $\text{S}$ is paramagnetic in nature.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms with its diamagnetic or paramagnetic behavior 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 $\text{Cu}$ and get its magnetic behavior

Answer to Problem 3.104QP

The number of unpaired electron in $\text{Cu}$ is 1.  It is paramagnetic in nature

Explanation of Solution

$\text{Cu}$ is placed in IB group of the periodic table. Its atomic number is 29.  Therefore, $\text{Cu}$ has 29 electrons in its shells.  $\text{Cu}$ is a $d$-block element.  So, its outermost electrons are located in a $d$-subshell.

The noble gas core for $\text{Cu}$ 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 $\text{Cu}$ beyond its noble gas core are $\left(\text{29 – 18}\right)=\text{ 11}$ electrons.  These 11 electrons enter into the $4s\text{ and }3d$ subshells.

Put all the 11 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 11 electrons of $\text{Cu}$ 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 11 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.  One of the electrons in $4s$-atomic orbital is jumped into $3d$-atomic orbital because completely filled $3d$-atomic orbital is more stable.

The unpaired electron is present in $4s$-atomic orbital.  There is only one unpaired electron in $4s$-atomic orbital in the case of $\text{Cu}$-atom.  Therefore, $\text{Cu}$ is paramagnetic in nature.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms with its diamagnetic or paramagnetic behavior 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 $\text{Pb}$ and get its magnetic behavior

Answer to Problem 3.104QP

The number of unpaired electron in $\text{Pb}$ is 2.  It is paramagnetic in nature

Explanation of Solution

$\text{Pb}$ is placed in IVA group of the periodic table.  Its atomic number is 82.  Therefore, $\text{Pb}$ has 82 electrons in its shells.  $\text{Pb}$ is a $p$-block element.  So, its outermost electrons are located in a $p$-subshell.

The noble gas core for $\text{Pb}$ 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 $\text{Pb}$ beyond its noble gas core are $\left(\text{82 – 54}\right)=\text{ 28}$ electrons.  These 28 electrons enter into the $4f,6s,5d\text{ and }6p$ subshells.

Put all the 28 electrons in the atomic orbitals by following Aufbau principle, Pauli exclusion principle and Hund’s rule.

All the 28 electrons of $\text{Pb}$ 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 28 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.

The unpaired electrons are present in $6p$-atomic orbital.  There are two unpaired electrons in $6p$-atomic orbital in the case of $\text{Pb}$ -atom.  Therefore, $\text{Pb}$ is paramagnetic in nature.

Interpretation Introduction

Interpretation:

The number of unpaired electrons in the given atoms with its diamagnetic or paramagnetic behavior 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 $\text{Ti}$ and get its magnetic behavior

Answer to Problem 3.104QP

The number of unpaired electron in $\text{Ti}$ is 2.  It is paramagnetic in nature

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 are $\left(\text{22 – 18}\right)=\text{ 4}$ electrons.  The four electrons enter into the $4s\text{ and }3d$-subshells.

Put all the electrons 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.  Therefore, $\text{Ti}$ is paramagnetic in nature.