ATOMIC STRUCTURE
Atom consists of 3 sub atomic
particles
 Protons, neutrons and electrons
 Protons - 1.67 × 10-24 g, +ve
charge(1.60 × 10–19 coulomb) Nucleus
 Neutrons- 1.67 × 10-24 g, no chargeNucleus
 Electrons- 9.11 × 10-28 g, _ve charge
(– 1.60 × 10–19 coulomb)- around the
nucleus
Atomic number
Mass number
Quantum mechanical model
 Branch of physics that deals with the behavior of
matter at the atomic and subatomic level.
 Also known as wave mechanics
Properties of Waves
Light as a wave
Light as a particle
Black body radiation
Black body ?


Object that absorbs all radiations and emits radiation
perfectly
At a given temperature, of all the bodies, black body
emits max radiation
Planck’s
Quantum
Theory
Radiant energy is emitted or absorbed
discontinuously in the form of tiny bundles
–quanta
Quanta is associated with definite
amount
of
energy
E=hν
h = Planck’s constant
ν = frequency of radiation
A body can absorb or emit whole
number multiples of quantum(nhν)Quantisation
 Quantum
theory can
Photoelectric effect.
Photoelectric effect
 Each
be
used
to
explain
metal needs a minimum frequency of
incident light for ejection of electrons -Thresold
frequency
 Kinetic energy
of the ejected electrons is
independent of the intensity of the incident
radiation, Greater the intensity more will be the
electrons ejected.
 According to classical theory, energy of light
depends on its intensity, hence light of any
frequency should eject electrons. But it doesn’t
happen.
WAVE PARTICLE DUALITY
Light travels as a wave and interacts with matter
like a particle.
Einstein -1905 suggested that light has a dual
character- particle and wave
de Broglie 1929 –awarded Nobel prize in physics
for proposing that matter has dual character –
wave and particle (wavicle)
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 Bohr’s
theory – electron is a particle
 de-Broglie- matter as particle and wave,
hence electron too
 Wavelength of a particle of mass m and
velocity u is expressed as λ = h/mu
de- Broglie equation
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 Einstein’s
mass energy relation; E= mc2
 Equating this energy with energy of a
photon associated with frequency ν
 hν = mc2
 Since ν = c/λ; h c/λ = mc2
 h/mc = λ (or) λ = h/mu ; λ = h/p
 where p is the linear momentum of the
particle
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Derivation of Bohr
angular momentum
postulate from de
Broglie equation
 r = radius of the
circular orbit

If the wave is to remain
in phase, then
2πr=nλ =nh/mu
Angular momentum
 L = mur=nh/2π
This is Bohr’s postulate
 If the circumference is
smaller or larger, the
wave will no longer be
in phase.
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Heisenberg’s uncertainty principle
∆x. ∆p ≥ h/4π
The exact motion of an electron in an atom
could never be determined, which also
meant that the exact structure of the
atom could not be determined.
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SCHRODINGER WAVE EQUATION
Erwin Schrödinger, an Austrian physicist, decided to
treat the electron as a wave in accordance with de
Broglie’s matter waves.
 Schrödinger, in considering the electron as a wave,
developed an equation to describe the electron wave
behavior in three dimensions
 Suitable only for one or two electron systems

 d2ψ/dx2
+ 8π2m/h2 (E-V)ψ = 0- One
dimensional time independent wave equation
where ψ- wave function, a function of position
co-ordinates of the particle, ψ (xyz)
 - h2/8π2m (∂2 /∂x2 + ∂2 /∂y2 + ∂2 /∂z2 )ψ +Vψ] =
Eψ – Three dimensional form of Schrodinger
equation
 Ĥ ψ = E ψ where Ĥ is the Hamiltonian
operator
 Ĥ = [- h2/8π2m (∂2 /∂x2 + ∂2 /∂y2 + ∂2 /∂z2 ) +V]
SIGNIFICANCE OF Ψ AND Ψ2
ψ is a wave function and refers to the amplitude
of electron wave i.e. probability amplitude.
 It has got no physical significance. The wave
function ψ may be positive, negative or
imaginary.
 [ψ]2 is known as probability density and
determines the probability of finding an electron
at a point within the atom.

Atomic orbitals
 An atomic orbital - mathematical function
for the probability of finding any electron of
an atom around its nucleus.
 Each orbital in an atom is characterized by
three sets of quantum numbers
 principal quantum number (n), angular
momentum quantum number (l) and
magnetic quantum number (m).
 An orbital can accommodate a maximum of
two electrons and is characterized by its
spin quantum numbers.
Quantum numbers
 Quantum
numbers expresses the various
energy levels available for an electron to
reside in an atom.
 Numbers that define completely the electrons
in an atom.
They are used to
 Specify the position (or location) of an
electron in an atom.
 Predicts the direction of spin or self rotation
of the electron
 Determine
the
energy
and
angular
momentum of the electron.
Principal quantum number (n)
Shell
Number of electrons in an orbit
Energy of nth level- En = -2π2me4/n2h2
Azimuthal or subsidiary quantum number (l)
Represent the sub-shells
 The value of l is dependent on the value of n.
 l can have values from 0 to (n-1). i.e, l = 0, 1, 2, 3,
……..(n-2), (n-1). Thus l can have n values.
 Different values of ‘l’ represent the subshells which
are designated as s, p, d, f.
 The energies of the subshell in a main shell are
increasing in the order s < p < d < f…
Magnetic quantum number (m)
 Represent the orbitals of which a given sub-shell is
composed.
 m can have integral values ranging from –l to +l.
When l = 0 (s sub-shell), m = 0 (only one value)
When l = 1 (p sub-shell), m = 0, ±1 (Three values)
When l = 2 (d sub-shell), m = 0, ±1, ±2 (Five values)
When l =3 (f sub-shell), m = 0, ±1, ±2, ±3 (Seven values)
Total number of m values is (2l + 1).
Different values of m for a given value of l give us the
total number of different space orientation for the given
s, p, d etc. sub-shells.
Spin quantum number (s)
 Electron also spins on its own axis
 The direction of spin is either clockwise or anticlockwise.
 This can have values either +1/2 (for clockwise spin) or
-1/2 (for anticlockwise spin).
Spacial orientation of subshells
 The distribution of electron cloud around the nucleus
of an atom is different in different orbitals.
 They are dependent on the three quantum numbers.
s sub-shell:
l=0, m is also equal to zero
only one space orientation
p sub-shell
Three space orientations and are in three different ways
along x, y, z axes
Designated as px (m=0), py (m=+1) and pz (m=-1)
The two lobes of the p-orbital are separated by a plane
which contains the nucleus and is perpendicular to the
orbital axis.
The probability of finding an electron at the nucleus as
well as the plane is zero.
The nucleus is called the node and the plane is called the
nodal plane.
d sub-shell:
 Here l=2, have five m values -2, -1, 0, +1 and +2
 Have five different spatial orientations with same energy
(degenerate).
 They are designated as dxy (m=-2), dyz (m=-1), dxz (m=+1),
dx2-y2 (m=+2) and dz2 (m=0).
 dxz, dyz and dxz orbitals have their greatest electron
density between the axes, thus their lobes are lying
symmetrically between the axes.
 dx2-y2 and dz2 orbitals have their
electron density in the region
along the axes.
f sub-shell:
For this sub-shell l=3, thus it has seven m values and
thus seven different spatial orientations.
Trend in the periodic properties
Periodic property
Across a period
Along a group
Atomic or Ionic radii
Decreases
Increases
Ionisation Potential
Increases
Decreases
Electron Affinity
Increases
Decreases
Electronegativity
Increases
Decreases
1. A microscope using suitable photons is employed to
locate an electron in an atom within a distance of 0.1Å.
What is the uncertainty involved in measurement of
its velocity?
2. A cricket ball weighing 100 g is to be located within
0.1 Å. What is the uncertainty in its velocity?
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3. The speed of an electron is found to be 1 kms-1 within
an accuracy of 0.02%. Calculate the uncertainty in its
position
% accuracy = ∆p/p x 100 = 0.02
∆p
4. An electron moves in an electric field with kinetic
energy of 2.5 eV. What is its associated de Broglie
wavelength?
Charge x Potential = K.E= p2 / 2m
p= (2meV)1/2
λ= h/p
Radial and angular nodes
Number of radial nodes- n-l-1
Number of angular node- l
Total number of nodes = n-1
5. Calculate the number of angular and radial
nodes for the 3d orbital.