ATOMIC STRUCTURE AND PERIODIC TABLE

Associate Professor & Head , Department of Chemistry
SAIVA BHANU KSHATRIYA COLLEGE
ARUPPUKOTTAI - 626101
Virudhunagar District, Tamil Nadu, India
ATOMIC STRUCTURE AND PERIODIC TABLE

The important postulates of Bohr’s theory about the atom model are
1. The electron in an atom revolve around the nucleus only in certain selected circular
orbits
2. Each orbits is associated with definite energy and therefore, they are also known as
energy levels or energy shells
3. As long as the electron remains in a particular orbit, it neither loses nor gains energy,
i.e., the energy of an electron remains constant in a particular orbit
THE BOHR’S MODEL OF THE ATOM

4. The energy levels are defined by principal quantum numbers (n = 1,2,3,4,, etc..)
starting from the nucleus and also designated by letters K, L, M, N etc.,

5. The farther the energy level from the nucleus, the greater in the energy associated with it
6. The energy of an electron cannot change continuously. It changes only as the electron jumps
from one energy level to another
7. The angular momentum of an electron moving round the nucleus is quantized i.e.,
the angular momentum of an electron in an atom can have only definite (or) discrete
values given by the expression
Angular momentum =
𝑛ℎ
2𝜋
where n is any integer (1,2,3, etc.,)
i.e., the angular momentum of an electron may be
ℎ
2𝜋
or a simple whole number
multiple of
ℎ
2𝜋
such as
2ℎ
2𝜋
,
3ℎ
2𝜋
, ……
𝑛ℎ
2𝜋

• Electron revolves around the nucleus of an atom in elliptical orbits adding to circular orbit
• There is a major axes and an minor axes having different length when electron revolves in
elliptical orbits
SOMERFIELD - BOHR ATOM MODEL
According to Somerfield – Bohr atom model

• The principal quantum number (n) and azimuthal quantum number (k) are related as
𝑛
𝑘
=
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑚𝑎𝑗𝑜𝑟 𝑎𝑥𝑒𝑠
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑚𝑖𝑛𝑜𝑟 𝑎𝑥𝑒𝑠
• When length of major axes is equal to length of minor axes, then k = n, i.e., the electron
orbit must be circular
• But, as k becomes smaller ( k < n ), the orbit become elliptical with greater and greater
eccentricity
• The number of possible value of k is equal to the principal quantum
number (n). i.e., for n = 4 , k can have four values as
shown in the diagram
SOMERFIELD - BOHR ATOM MODEL

• As the orbit broadens, the length of the two axes become closer and become equal when the
orbit become circular
• The angular momentum of the electrons revolving in an elliptical orbit is equal to
𝑘ℎ
2𝜋
, where
k is the azimuthal quantum number
• The energy of an electron depends not only principal quantum number but also azimuthal
quantum number
SOMERFIELD BOHR ATOM MODEL

• de-Broglie stated that electron can travel (X-ray) as wave and as particle. This character
is known as dual character
Derivation of de-Broglie wave equation :
• According to Einstein, the energy of an electron (X- ray) is
E = mc2 ---------(1)
Where m ------ mass of the electron
c ------ velocity of electron
• According to Plank's , the energy of light radiation (X-ray) is
E = h ----------(2)
Where h ------- Plank’s constant
 ------- Frequency of light radiation
de – BROGLIE DUAL NATURE OF ELECTRON

• Equating equation (1) and (2), we get
mc2 = h ---------(3)
• Substitute  =
𝑐

in equation (3), we get
mc2 = h
𝑐

mc =
ℎ

 =
ℎ
𝑚𝑐
This equation is known as de – Broglie wave equation
de – BROGLIE WAVE PARTICLE CONCEPT FOR ELECTRON

• The behavior of electron waves in atoms and molecules is described by the Schrödinger wave
equation
SCHRODINGER WAVE EQUATION
Where
ψ is the wave function of electron
E is the total energy of electron
V is the potential energy of electron
E-V is the kinetic energy of the electron
h is the Plank’s constant

Physical significance of the wave function:
1. The wave function Ψ has no direct physical meaning. It is a complex quality representing
the variation of a matter wave
2. The wave function Ψ (r,t) describes the position of a particle with respect to time
3. It can be considered as ‘probability amplitude’ since it is used to find the location of
the particle
SCHRODINGER WAVE EQUATION

Definition: Quantum numbers are the numbers which are used to describe completely the
state of electrons in an atom.
Four types of quantum numbers
• Principal quantum number, denoted by n
• Azimuthal quantum number, denoted by l
• Magnetic quantum number, denoted by m
• Electron spin quantum number, denoted by s
QUANTUM NUMBERS

• Principal quantum numbers describe the size and energy
level or shell of electron in an atom . It is denoted by ‘n’
• And also describe the distance between the electron and the
nucleus i.e., larger the value of principle quantum number,
greater the distance between electron and the nucleus
• The value of the principal quantum number might be any
equal to or greater than one. i.e., n = 1,2,3,….
• The value n=1 denotes the innermost electron shell of an
atom, which corresponds to the lowest energy state of an
electron and as the n value increases the energy level
increases
PRINCIPLE QUANTUM NUMBER (n)

• The azimuthal quantum number describes the sub energy level
or subshell of the electron in an atom and also describe the
shape of the electron clouds around the nucleus of an atom. It
is denoted by ‘l’
• This value depends on the value of the principal quantum
number, i.e. the value of the azimuthal quantum number
ranges between 0 and (n-1).
• For example, if n =3, the azimuthal quantum number are 0,1
and 2. When l=0, the resulting subshell is an ‘s’ subshell.
Similarly, when l=1 and l=2, the resulting subshells are ‘p’ and
‘d’ subshells (respectively). Therefore, when n=3, the three
possible subshells are 3s, 3p, and 3d.
AZIMUTHAL QUANTUM NUMBER (l)

• Magnetic quantum number describe the total number of
orbitals in a subshell and the orientation of these orbitals. It
is denoted by ‘m’.
• The value of the magnetic quantum number is dependent
on the value of the azimuthal quantum number.
• For a given value of l, the value of m ranges between the
interval -l to +l.
• For example, if l = 1 in an atom, the possible values of the
magnetic quantum number are -1, 0, +1 and the orbitals are
named as px, py and pz
MAGNETIC QUANTUM NUMBER (m)

ELECTRON SPIN QUANTUM NUMBER (s)
• The electron spin quantum number describe the spinning
nature of the electron which are revolving around the nucleus
of an atom. It is denoted by ‘s’
• The possible values of the electron spin quantum number are
+½ and -½.
• The positive value of s implies an upward spin on the electron
which is also called ‘spin up’ and is denoted by the symbol ↑.
• The negative value of s implies a downward spin on the
electron which is also called ‘spin down’ and is denoted by
the symbol ↓.

Name and Symbol Meaning and Possible Values
Principal quantum number, n Electron shell, n ≥ 1
Azimuthal quantum number, l Subshells (s=0, p=1, etc.) , (n-1) ≥ l ≥ 0
Magnetic quantum number, ml
Total number and orientation of orbitals,
l ≥ ml ≥ -l
Electron spin quantum number, ms The direction of electron spin, ms = ±½
SUMMARY OF QUANTUM NUMBER

AUFBAU PRINCIPLE
• Aufbau principle states that the orbitals are
filled in the order of their increasing
energies. That is the electrons first occupy
the lowest energy orbital available to them.
Once the lower energy orbitals are
completely filled, then the electrons enter
the next higher energy orbitals.

HUND’S RULE
• Hund’s rule state that electron pairing in any orbital is not possible until all the
available orbitals of a given subshell contains one electron each (half filled )
Eg: FOR NITROGEN ATOM

PAULI’S EXCLUSION PRINCIPLE
• Pauli Exclusion Principle states that no two electrons can be identified by the
same set of quantum numbers and the orbital can accommodate only two electrons
with opposite spin
For helium atom the electronic configuration is 1s2
The quantum numbers for the first and second electron are
First electron : n = 1, l = 0, m = 0 & s = + ½
Second electron: n = 1, l = 0, m = 0 & s = - ½

MODERN PERIODIC LAW
The modern periodic law states that the properties of the elements are a periodic
function of their atomic numbers
i.e., the elements are arranged in an increasing order of their atomic number in the periodic
table

• Repetition of properties of elements in the periodic table after a certain interval
is called periodicity of properties.
• If elements are arranged in increasing order of their atomic number in the periodic table,
then elements repeat their properties after a definite interval
PERIODICITY IN PROPERTIES
PERIODIC PROPERTIES OF THE ELEMENTS
1. Atomic radii
2. Ionization energy
3. Electron affinity
4. Electronegativity

ELECTRON AFFINITY
H1
H2
∆H = H2 – H1 = Electron affinity
Where
H1 is the energy of neutral chlorine atom
H2 is the energy of chloride ion

ELECTRON AFFINITY IN GROUP
Down the group in periodic table electron affinity decreases
because of the addition of new shell to each atom decreases is
force of attraction

ELECTRON AFFINITY IN PERIOD
In period the electron affinity increases from left to right
because successive atoms have higher nuclear charge and attract the
incoming electrons more towards itself

ELECTRONEGATIVITY
NON POLAR POLAR

ELECTRONEGATIVITY SCALE
• There are three quantitative scales used to evaluate electronegativity of an element
1. Pauling scale
2. Mulliken scale
3. Allred and Rochow scale

PAULING SCALE
• Pauling derived an electronegativity scale based on experimentally derived values of
bond energies
• According to Pauling, Bond energy of a compound A-B for pure covalency is a
geometric mean of the bond energies of A-A and B-B
i.e., Bond energy for pure covalency = [D A-A x D B-B ]1/2
• But actual experimental value D A-B is found to be greater than this expected value
i.e., D A-B (experimental) - [D A-A x D B-B ]1/2 = ∆′
• The difference, ∆′ is due to electronegativity differences between the atoms.
i.e., the electronegativity difference (XB – XA) is directly proportional to
(XB – XA)  ∆′
(XB – XA) = k ∆′

PAULING SCALE
• Where XB is the electronegativity of B
XA is the electronegativity of A
k is the proportionality constant
• When ∆′ is zero, Bonding electrons are shared equally i.e., the electronegativity of
A and B atoms are same
• In general, smaller atoms attract electron more than larger ones and therefore
more electronegative
• Atoms with nearly filled shells of electrons (example : halogens) will tends to have
higher electronegativity than those with not filled shells

MULLIKEN SCALE
• According to Mulliken, the electronegativity of an element is the arithmetic mean of
first ionization energy which measures its tendency to hold its own outer electrons,
and its electron affinity which measures its tendency to attract electron of the element
bonded with it
Electronegativity of an element =
𝑭𝒊𝒓𝒔𝒕 𝒊𝒐𝒏𝒊𝒔𝒕𝒂𝒊𝒐𝒏 𝒆𝒏𝒆𝒓𝒈𝒚+𝑬𝒍𝒆𝒄𝒕𝒓𝒐𝒏 𝒂𝒇𝒇𝒊𝒏𝒊𝒕𝒚
𝟐
• The Mulliken (M) and Pauling (P) values are related approximately as
XM
B – XM
A = 2.78 (XP
B - XP
A)

ALLRED AND ROCHOW SCALE
• Allred and Rochow defined electronegativity as the electrostatic force exerted
by the nucleus on the valence electrons
• According to them
Electronegativity = 0.359
𝒁
∗
𝒓𝟐+ 0.744
where Z* is the effective nuclear charge experienced by the electron
r is the mean radius of the orbital which can be taken equal to the covalent
radius of the atom (in A0)

EFFECTIVE NUCLEAR CHARGE
Definition
• The effective nuclear charge is the net positive charge experienced by valence electrons.
Slater proposed a formula for calculating the effective nuclear charge
Zeff = Z – S
where
Zeff is the effective nuclear charge
Z is the atomic number
S is the shielding constant
• Shielding electrons are the inner shell electrons
which are blocking the valence shell
electron attraction by the nucleus
First Inner shell
Valence shell
Second Inner shell

SLATER RULE
• Slater formulated the following rules for calculating the screening constant value for
various inner shell electrons for obtaining effective nuclear charge

APPLICATION OF SLATER RULE
APPLICATION OF SLATER RULE

POLARIZING POWER
Definition
• Polarizing power can be defined as the ability of a cation to attract the electron cloud
towards itself. Polarising power is proportional to charge/size.

ANOMALOUS BEHAVIOUR OF FIRST ELEMENT IN A GROUP
• The anomalous behaviour of first element of s and p block elements of each group
as compared to other group members is due to following reasons:
1. Small size of atom
2. Large charge/radius ratio,
3. High electronegativity
4. Non availability of d-orbitals in their valence shell

BALANCING OF REDOX EQUATION
Reduction
• Gain of electron is called reduction
Oxidation
• Loss of electron is called oxidation
Redox reaction
• Both gain and loss of electron occur in the chemical reaction is called redox reaction
Zn → Zn2+ + 2e-
Cu2+ + 2e- → Cu
4Zn + 10 HNO3 → 4Zn(NO3)2 + N2O + 5H2O
• Here Zinc is oxidized from zero state to +2 state and nitrogen is reduced from
+5 state to +2 state

There are two methods used for balancing the redox equation
1. Oxidation number method
2. Ion – electron method

Oxidation Method : Rules
1. Assign oxidation number to the atom that shows changes
2. Balance the total number of atoms undergoing the changes in oxidation state
3. Count the total number of electrons gained and lost respectively by the oxidizing agent
and reducing agent
4. Chose the proper ratio of oxidizing agent to the reducing agent so that the oxidation
number change is balanced
5. Make appropriate change in the coefficient of the products corresponding to the change
of coefficients in step 4
6. Balance the oxygen atom on bot sides by adding H2O to the side that is deficient in
oxygen

7. Balance the hydrogen atoms on both sides by adding H+ to the side that is deficient in
hydrogen
8. The equation is balanced if the reaction taking place in acidic solution. If , however the
reaction proceeds in basic solution, add sufficient number of OH- to get rid of H+ but
add equal number of OH- on both side

Example : Write the balanced equation for
Cr2O7
2- + Fe2+ + H+ → Cr3+ + Fe3+ +H2O
Solution:
1) Writing the skeleton equation
Cr2O7
2- + Fe2+ + H+ → 2Cr3+ + Fe3+ +H2O
2) Marking reducing agent and oxidizing agent. In this equation oxidation state of Fe2+ is raised to Fe3+
Therefore it is reducing agent. The oxidation state of Cr in Cr2O7
2- is reduced from -6 to +3. Hence
it is an oxidizing agent
3) Writing half reaction for oxidation of reducing agent (Fe3+) taking care of
balancing of atoms of Fe and the charge
Fe2+ → Fe3+ + e- ------------(1)
There are no oxygen or hydrogen atoms attached with the species. So question
of balancing them does not arise

4) Writing other half reaction for reduction of oxidizing agent () while balancing
i) Cr and ii) O by adding H+ ions on the oxygen exceeding side and iii) charge
by adding electrons as
Cr2O7
2- + 14 H+ + 6e- → 2Cr3+ + 7H2O ------------(2)
5) To equalize the number of electrons
6) Multiplying the half reaction (1) by 6 and adding to the half reaction (2)
6Fe2+ → 6Fe3+ +6 e-
Cr2O7
2- + 14 H+ + 6e- → 2Cr3+ + 7H2O
Cr2O7
2- + 14 H+ + 6 Fe2+ → 2Cr3+ + 6 Fe3+ 7H2O

Ion – Electron Method : Rules
1. Write the skeleton equation, showing oxidation state of the elements undergoing a change
in oxidation state
2. Mark the reducing agent ( having the atom whose oxidation number is raised) and also
the oxidizing agent ( one having the atom whose oxidation number is lowered)
3. Write down one half reaction for oxidation of the reducing agent balancing
i) the number of atoms undergoing the change in oxidation state
ii) the oxygen atoms on the two sides by adding H2O to the side deficient in oxygen or
H+ ions to the side with excess of oxygen
iii) the charge by putting the required number of electrons on R.H.S

4. In a similar manner write down the other half of the reaction for reduction of the oxidizing
agent. To balance the charge electron would now be added on the L.H.S
5. Add these two balanced half – reactions in such a way that the electrons appearing on the
right of one half-reaction and on the left of the other cancel. For this each half-reaction will
be multiplied by appropriate numbers before addition
6. If the reaction proceeds in basic solution, add enough OH- on both sides of the half-reaction
to get rid of H+ appearing there. Combine H+ and OH- to give H2O and remove H2O
duplication

Example: Write the balanced equation for
Zn + HNO3 → Zn2+ + N2O + 4H2O
Solution:
1. Assigning oxidation state to atoms that shows change in oxidation state and balancing number
of atoms balancing number of atoms showing this change on both sides (Zn and N atoms)
Zn + 2HNO3 → Zn + N2O + H2O -------------(1)
↓ ↑
2e- 4e-
2. Equalizing electrons lost = electron gained
Total number of electrons lost by one Zn = 1 x 2 = 2
Total number of electrons gained by two N atoms = 2 x 4 = 8
To equalize the electrons lost = electrons gained, we multiply Zn by 4 and 2HNO3 by 1.
4Zn + 2HNO3 → 4Zn 2+ + N2O + H2O -------------(2)

3. Balancing O-atom, the number of O atoms on right hand side is 2 while on left hand side is 6.
To balance O-atoms, add 4H2O on R.H.S
4Zn + 2HNO3 → 4Zn 2+ + N2O + 5H2O -------------(3)
4. Balancing H-atoms, in equation (3) the number of H-atoms is 8 more on R.H.S than their
number on L.H.S . Add 8H+ ions on L.H.S. By doing so the charge on both sides also
balanced.
4Zn + 2HNO3 + 8H+ → 4Zn 2+ + N2O + 5H2O
(or) 4Zn + 2NO-
3 + 10H+ → 4Zn 2+ + N2O + 5H2O

• If however it is desired to have 4Zn(NO3)2 instead of 4Zn2+ on R.H.S, we can do so by
adding 8NO3
- ions on both sides
4Zn + 2H+ +2NO-
3 + 8H+ + 8NO3
- → 4Zn2+ + 8NO3
- + N2O + 5H2O
then the molecular equation is
4Zn + 10HNO3 → 4Zn (NO3)2 + N2O + 5H2O

ATOMIC STRUCTURE AND PERIODIC TABLE

ATOMIC STRUCTURE AND PERIODIC TABLE

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