Spring 2017
Chapter 6
Electronic Structure
of Atoms
Table of Contents
 6.1.
 6.2.
 6.3.
 6.4.
 6.5.
 6.6.
 6.7.
The Wave Nature of Light
Quantized Energy and Photons
Line Spectra and the Bohr Model
The Wave Behavior of Matter
Many-Electron Atoms
Electron Configurations
Electron Configurations and the
Periodic Table
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Aim
 Describe the development of the quantum theory and
how it led to a consistent description of the electronic
structure of the elements.
 Quantum theory:
Branch of physics which deals with physical phenomena at
microscopic scales.
Quantum theory is the theoretical basis of modern physics
that explains the nature and behavior of matter and energy
on the atomic and subatomic level.
It provides a mathematical description of much of the
behavior and interactions of energy and matter.
The Wave Nature of Light
 The electronic structure of an atom refers to
the arrangement of electrons.
 Interaction of light (electromagnetic radiation)
with matter has provided us with a lot of
information about the electronic structure of
atoms.
 Visible light is a form of electromagnetic
radiation, or radiant energy.
 Radiation carries energy through space.
 Electromagnetic radiation is characterized by its
wave nature
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 All waves have a characteristic wavelength,
l(lambda), amplitude, A and frequency n.
 The speed of a wave is given by its
frequency (hertz) multiplied by its
wavelength.
 For light, speed is c = n l
Electromagnetic radiation moves through a vacuum
with a speed of 3.00 x 108 m/s.
Modern atomic theory arose out of studies of
the interaction of radiation with matter.
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 The electromagnetic spectrum is a display
of the various types of electromagnetic
radiation arranged in order of increasing
wavelength.
 Example: visible radiation has wavelengths
between 400 nm (violet) and 750 nm (red).
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Hot Objects and the Quantization of
Energy
 Heated solids emit radiation (blackbody
radiation)
 The wavelength distribution depends on
the temperature (i.e., “red hot” objects are
cooler than “blue hot” objects).
Temp.
Light emitted
Blue
Yellow
Orange
Red
Infra Red
Infra Red Night Vision
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Temp.
Light emitted
Blue
Yellow
Orange
Red
Infra Red
Quantized Energy and Photons
 Planck investigated black body radiation.
He proposed that energy can only be
absorbed or released from atoms in
certain amounts called quanta.
 A quantum is the smallest amount of
energy that can be emitted or absorbed
as electromagnetic radiation.
 The energy of a single quantum:
E =hn where h = 6.626×10-34 J.s (Planck’s constant)
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The photoelectric effect
Phenomenon explained by Albert Einstein (Nobel prize, 1921)
The photoelectric effect
If light shines on a metal surface, there is a point at
which electrons are ejected from the metal
(photoelectric effect).
 The electrons will only be ejected if the light source has
sufficient energy:
 Below the threshold frequency no electrons are ejected.
 Above the threshold frequency, the excess energy appears
as the kinetic energy of the ejected electrons.
 Light has wave-like AND particle-like
properties
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 Einstein assumed that light traveled in
energy packets called photons.
 The energy of one photon:
E =hn
Line Spectra and Bohr Model
 Radiation composed of only one
wavelength is called monochromatic.
 Radiation that spans a whole array of
different wavelengths is called continuous.
 When radiation from a light source, such
as a light bulb, is separated into its
different wavelength components, a
spectrum is produced.
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Continuous Spectrum
White light can be separated into a continuous spectrum of colors.
A rainbow is a continuous spectrum of light produced by the
dispersal of sunlight by raindrops
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Line Spectra
Line Spectra Of Na and H
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Bohr’s Model
 Bohr noted the line spectra of certain
elements and assumed the electrons
were confined to specific energy states.
These were called orbits.
Bohr’s Model
 Bohr’s model is based on three postulates:
1. Only orbits of specific radii, corresponding
to certain definite energies, are permitted for
electrons in an atom.
2. An electron in a permitted orbit has a
specific energy and is in an "allowed" energy
state.
3. Energy is only emitted or absorbed by an
electron as it moves from one allowed
energy state to another.
(The energy is gained or lost as a photon).
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Energy States of the Hydrogen Atom
 Colors from excited gases arise because
electrons move between energy states in the
atom.
 Since the energy states are quantized, the
light emitted from excited atoms must be
quantized and appear as line spectra.
Energy States of the Hydrogen Atom
Bohr showed mathematically that:
 1
 1
E  (hcRH ) 2   (2.18x1018 J ) 2 
n 
n 
The product hcRH = 2.18 x 10-18 J
n is called the principal quantum number
The first orbit in the Bohr model has n = 1 and is closest to the
nucleus. This is the most stable state and is called ground state.
The second, third …. orbit in the Bohr model has n=2, 3, 4,5…
(excited states)
As n gets infinite the energy gets closer to zero. (electron is
removed from the nucleus).
h: Planck’s constant
6.626 x 10 J-s
-34
c:
speed of light
RH : Rydberg constant
3x
108
m/s
1.096776 x 107 m-1
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Energy Level in Hydrogen Atom
Energy states in Hydrogen Atom
 Balmer: discovered that the lines in the visible
line spectrum of hydrogen fit a simple equation.
 1
1
E  Ef  Ei  hν -2.18 x10 18 J  2  2 
n

 f ni 
If nf is smaller than ni, the electron moves closer to the nucleus,
and E is negative. The atom releases energy.
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Limitations of the Bohr Model
 The Bohr Model has several limitations:
 It cannot explain the spectra of atoms other than
hydrogen.
 Electrons do not move about the nucleus in
circular orbits.
However, the model introduces two important
ideas:
 The energy of an electron is quantized:
electrons exist only in certain energy levels
described by quantum numbers.
 Energy gain or loss is involved in moving an
electron from one energy level to another.
The Wave Behavior of Matter
 Knowing that light has a particle nature, it seems
reasonable to ask whether matter has a wave
nature.
 This question was answered by Louis deBroglie.
 Using Einstein’s and Planck’s equations,
deBroglie derived:
h
l
mn
 The momentum, mv, is a particle property,
whereas l is a wave property
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Matter waves
 Matter waves is the term used to describe wave
characteristics of material particles.
 Therefore, in one equation deBroglie
summarized the concepts of waves and particles
as they apply to low-mass, high-speed objects.
applications: X-ray diffraction, electron microscopy
The Uncertainty Principle
Heisenberg’s uncertainty principle:
 we cannot determine the exact position,
direction of motion, and speed of
subatomic particles simultaneously.
 Heisenberg: For electrons: we cannot
determine their momentum and position
simultaneously: x x mn > h/4p
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Quantum Mechanics and Atomic Orbitals
 Schrödinger proposed an equation containing both wave
and particle terms.
Solving the equation leads to wave functions
 The wave function describes the electron’s matter wave.
 The square of the wave function,  2, gives the
probability of finding the electron.
That is,  2 gives the electron density for the atom.
  2 is called the probability density.
Electron density
A region of high electron density is one
where there is a high probability of finding
an electron.
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Quantum Numbers
 Schrödinger’s equation requires three
quantum numbers:
1.Principal quantum number, n. This is the
same as Bohr’s n.
As n becomes larger, the atom becomes
larger and the electron is further from the
nucleus.
Quantum Numbers
2. Second quantum number, l. This
quantum number depends on the value of
n.
 The values of l begin at 0 and increase to
n – 1.
We usually use letters for l (s, p, d and f for l
= 0, 1, 2, and 3).
This quantum number defines the shape of
the orbital.
also named “azimuthal” or “angular momentum” quantum number
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Quantum Numbers
3.Magnetic quantum number, ml.
This quantum number depends on l.
The magnetic quantum number has integer
values between –l and +l.
Magnetic quantum numbers give the threedimensional orientation of each orbital.
 A collection of orbitals with the same value
of n is called an electron shell.
 A set of orbitals with the same n and l is
called a subshell.
 Each subshell is designated by a number
and a letter.
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Possible Values of quantum Numbers
Representations of Orbitals
 All s orbitals are spherical.
 As n increases, the s orbitals get larger.
 As n increases, the number of nodes increases.
 A node is a region in space where the probability
of finding an electron is zero.2 = 0 at a node.
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Representation of S Orbital
The p Orbitals
 There are three p orbitals: px, py and pz.
 The three p orbitals lie along the x-, y-, and zaxes of a Cartesian system.
 The letters correspond to the allowed values of
ml ( –1, 0, and +1).
 The orbitals are dumbbell shaped; each has two
lobes.
 As n increases, the p orbitals get larger.
 All p orbitals have a node at the nucleus.
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The p Orbitals
The d Orbitals
 There are five d orbitals
 Three of the d orbitals lie in a plane
bisecting the x-, y-, and z-axes.
 Two of the d orbitals lie in a plane aligned
along the x-, y-, and z-axes.
 Four of the d orbitals have four lobes
each.
 One d orbital has two lobes and a collar.
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The d Orbitals
F orbitals
 When n is equal to 4 or larger, there are seven f
orbitals for which l=3.
 The shape of f orbitals are very complicated than
those of d orbitals
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Many-Electron Atoms
Orbitals and Their Energies
 In a many-electron atom, for a given value
of n, the energy of an orbital increases
with increasing value of l (2s and 2p).
 Orbitals of the same energy are said to be
degenerate.
Ordering of Orbital energy levels
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Electron Spin
 Line spectra of many-electron atoms show
each line as a closely spaced pair of lines.
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Magnetic Quantum Number
 Electron is a tiny sphere spinning around its
own axis.
 Electron spin is said to be quantized
 ms = spin magnetic quantum number = ± ½.
Pauli’s Exclusion Principle
 Pauli’s exclusion principle states that no
two electrons in the same orbital can have
the same set of four quantum numbers.
Therefore, two electrons in the same orbital
must have opposite spins.
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Electron Configurations
 Electron configurations tell us how the
electrons are distributed among the
various orbitals of an atom.
 The most stable configuration, or ground
state, is that in which the electrons are in
the lowest possible energy state.
 When writing ground-state electronic
configurations:
 electrons fill orbitals in order of increasing
energy with no more than two electrons per
orbital.
 no two electrons can fill one orbital with the
same spin (Pauli).
 for degenerate orbitals, electrons fill each
orbital singly before any orbital gets a
second electron (Hund’s rule).
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 How do we show spin?
An arrow pointing upwards has ms = + ½
(spin up).
An arrow pointing downwards has ms = – ½
(spin down).
Hund's Rule
 for degenerate orbitals, the lowest energy
is attained when the number of electrons
with the same spin is maximized. Thus,
electrons fill each orbital singly with their
spins parallel before any orbital gets a
second electron.
 By placing electrons in different orbitals,
electron-electron repulsions are
minimized.
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Summary For Quantum Mechanical
Model For The Atom
 Every electron in an atom has a probability
region in which it resides.
 Probability region is described by wave
function and a wave equation
 Solving the wave equation produces four
Quantum Numbers.
 The complete set of four Quantum Numbers
most adequately describes the physical
features of the probability region.
Principle Quantum Number (n)
 n the energy level of orbitals.
 Allowable values of n = 1,2,3,4....
 Maximum number of electrons in a
given shell is 2n2
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Azimuthal Quantum Number (l)
 It defines the shape of the orbital
 Allowable values- l = 0,1,2.....n-1
 l=0 called an "S" region. It can have a maximum of 2
electrons assigned to it, and is shaped spherical
 l=1 called a "P" region. It can have a maximum of 6
electrons assigned to it, and is shaped double lobed
(two spheres tangent to one another.
 l=2 called a “d" region. It can have a maximum of 10
electrons assigned to it, and is shaped as an quadralobed region.
 l=3 called an “f" region. It can have a maximum of 14
electrons assigned to it, and is shaped as an octa
lobed region.
Magnetic Quantum Number (ml)
 It defines the direction the region
extends to
 Allowable values for ml = -l< ml <+l
 What values of "m" are possible for a
probability region that is partially
described by an l=3 value?
 ml = -3, -2, -1, 0, +1, +2, +3
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Spin Quantum Number (s)
 It defines the direction of spin electron
particle may have
 Allowable values- +1/2 or -1/2
Pauli Exclusion Principle
 No two electrons can have the same
exact set of quantum numbers (ie:
electrons must have paired spins in the
same orbital)
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Hund’s Rule
 For degenerate orbitals, the lowest
energy is attained when the number of
electrons with the same spin is
maximized.
Octet Rule
 The most stable atoms are those whose
valence outermost regions have eight
electrons. Exceptions are Hydrogen
and Helium atoms which have 1 and 2
respectively)
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Assigning Electronic Configuration of
a given atom
 The following sequence is used:
 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f, 5d,
6p,7s,5f,6d.....
 You begin with the first orbital, 1s, and
add electrons until the maximum
number for that orbital is reached,
Assigning Electronic Configuration of
a given atom
 1s
2s 2p
3s 3p
4s 3d 4p
5s 4d 5p
6s 4f 5d 6p
7s 5f 6d 7p
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Energy ordering rule
Klechkowski’s rule
Madelung’s rule
“n+l rule”
Electron Configuration of Lighter
Elements
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Condensed Electron Configurations
 Electron configurations may be written
using a shorthand notation (condensed
electron configuration):
Condensed Electron Configurations
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Transition Metals
 After Ar the d orbitals begin to fill.
 After the 3d orbitals are full the 4p orbitals
begin to fill.
 The ten elements between Sc and Zn are
called the transition metals, or transition
elements.
Transition Metals
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Lanthanide and Actinide Elements
 The 15 elements corresponding to the
filling of 4f orbitals are called lanthanide
elements (or rare earth elements).
 The 15 elements corresponding to the
filling of 5f orbitals are called actinide
elements.
 Most actinides are not found in nature
(they are synthesized).
Electron Configurations and the Periodic
Table
 The periodic table can be used as a guide
for electron configurations.
 The period number is the value of n.
 Groups 1A and 2A have their s orbitals
being filled.
 Groups 3A – 8A have their p orbitals being
filled.
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 The s-block and p-block of the periodic table
contain the representative, or main-group,
elements.
 Transition metals have their d orbitals being
filled.
 The lanthanides and actinides have their f
orbitals being filled.
 The actinides and lanthanide elements are
collectively referred to as the f-block metals.
 Note that the 3d orbitals fill after the 4s orbital.
Similarly, the 4f orbitals fill after the 5d orbitals.
Electron Configuration of lanthanide
 La [Xe] 6s2 5d1 4f 0
Lu [Xe] 6s2 5d1 4f 14
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Anomalous Electron Configurations
 There are many elements that appear to
violate the electron configuration guidelines.
 Examples:
 Chromium is [Ar]3d54s1 instead of [Ar]3d44s2.
 Copper is [Ar]3d104s1 instead of [Ar]3d94s2.
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