Chapter 3, Problem 3.103QP

Determine the number of impaired electrons in each of the following atoms in the ground state and identify each as diamagnetic or paramagnetic: (a) Rb, (b) As, (c) I, (d) Cr, (e) Zn.

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 $\text{Rb}$ and get its magnetic behavior

Answer to Problem 3.103QP

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

Explanation of Solution

$\text{Rb}$ is placed in IA group of the periodic table.  Its atomic number is 37.  Therefore, $\text{Rb}$ has 37 electrons in its shells.  $\text{Rb}$ is a $s$-block element.  So, its outermost electrons are located in $s$-shell.

The noble gas core for $\text{Rb}$ is $\left[\text{Kr}\right]$, where atomic number of $\text{Kr}$ is 36.  So, the order of filling beyond the noble gas core is $5s$. The electrons in $\text{Rb}$ beyond its noble gas core are $\left(\text{37 – 36}\right)=\text{ 1}$ electron.  The one electron enters into the $5s$-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 $\text{Rb}$ 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 $5s$-atomic orbital.  Blue colored orbital corresponds to $5s$-atomic orbital.

The unpaired electron is present in $5s$-atomic orbital.  There is only one unpaired electron in $5s$-atomic orbital in the case of $\text{Rb}$-atom.  Therefore, $\text{Rb}$ is paramagnetic in nature.

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 $\text{As}$ and get its magnetic behavior

Answer to Problem 3.103QP

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

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.

The unpaired electrons are present in $4p$-atomic orbital.  There are three unpaired electrons in $4p$-atomic orbital in the case of $\text{As}$-atom.  Therefore, $\text{As}$ is paramagnetic in nature.

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 $\text{I}$ and get its magnetic behaviour

Answer to Problem 3.103QP

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

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.

The unpaired electron is present in $5p$-atomic orbital.  There is only one unpaired electron in $5p$-atomic orbital in the case of $\text{I}$-atom.  Therefore, $\text{I}$ is paramagnetic in nature.

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 $\text{Cr}$ and get its magnetic behavior

Answer to Problem 3.103QP

The number of unpaired electron in $\text{Cr}$ is 6.  It is paramagnetic in nature

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 $d$-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 are $\left(\text{24 – 18}\right)=\text{ 6}$ electrons.  The six 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 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.  Therefore, $\text{Cr}$ is paramagnetic in nature.

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 $\text{Zn}$ and get its magnetic behavior

Answer to Problem 3.103QP

There is no unpaired electron in $\text{Zn}$.  It is diamagnetic in nature

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 is no unpaired electron present in $4s$ and $3d$-atomic orbitals.  Therefore, $\text{Zn}$ is diamagnetic in nature.