Chapter 6
Electronic Structure
of Atoms
or
“How I Learned to Stop Worrying
and Love the Electron”
Problems with the Rutherford Model
1. Classical physics says atoms should emit light
and destroy themselves - they don’t
2. Atoms can be induced to emit light, but they
give off a line spectrum, rather than a
continuous spectrum.
3. Every atom gives off different colours of light.
4. No explanation of why different atoms have
different properties, or the same properties.
Electronic
Structure
of Atoms
Let’s Talk About Light
What is Light?
• light is radiant energy.
• a better term is electromagnetic energy
(EMR)
• includes not only visible light, but many forms of
EMR we cannot see directly:
▫ heat
▫ microwaves
▫ x-rays
• light has properties of both waves and particles.
Electronic
Structure
of Atoms
Wave model of Light
• The distance between corresponding points on
adjacent waves is the wavelength
• The symbol is the Greek letter lamda ().
• The height of the wave is the amplitude. It
Electronic
corresponds to the intensity of the light
Structure
of Atoms
Waves
• The number of waves
passing a given point
per unit of time is the
frequency,
• The symbol is the Greek
letter nu ().
• The longer the
wavelength, the smaller
the frequency.
Electronic
Structure
of Atoms
Electromagnetic Radiation
• EMR is a continuous spectrum of wavelengths.
Electronic
Structure
of Atoms
Using λ and ν to determine “colour”
• “Colour” is a term used to describe visible light.
• Visible light is a very small part of the
electromagnetic spectrum:
▫ radio waves
-- ultraviolet
▫ microwaves
-- x-rays
▫ infrared
-- gamma rays
▫ visible
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Colour of Light
• we can identify light by its wavelength or
frequency:
▫ a wave 5.00 x 10-7 m is
 green
▫ a wave 6.80 x 10-7 m is
 red
▫ a wave 2.60 x 10-5 m is
 infrared
▫ a wave 7.80 x 10-10 m is
 in the x-ray region.
Electronic
Structure
of Atoms
Speed of Light
• is the one thing that is constant in the universe (sort of).
• in a vacuum, the speed of light is 3.00 x 108 m/s
• there is a relationship between wavelength and
frequency:
c  
• where
▫ c = speed of light
▫ λ = wavelength
▫ ν = frequency
Electronic
Structure
of Atoms
• Complete questions 6.13 to 6.18, even
Electronic
Structure
of Atoms
Quantized Energy and Photons
• The wave model of light is
good, but it does not explain:
▫ how an object can glow when
its temperature increases.
(Blackbody radiation)
▫ emission of electrons by
shining light on the surface of
a metal. (photoelectric effect)
▫ emission of light from
electrons of excited gas Electronic
atoms. (emission spectra)Structure
of Atoms
Blackbody Radiation
• Heated solids emit radiation (blackbody radiation)
▫ The wavelength distribution depends on the
temperature (i.e., “red hot” objects are cooler
than “white hot” objects).
▫ Why does wavelength or frequency depend on
temperature?
• Max Planck suggested a way out by assuming
that energy comes in packets called quanta.
Electronic
Structure
of Atoms
• Planck proposed a relationship between
energy and the frequency of light
quanta:
E  h
• where:
▫ E = energy in Joules
▫ h = Planck’s constant (6.6262 x 10-34 J·s)
▫ ν = frequency, in Hertz (1/s, s-1)
• as energy increases, so does frequency.
Electronic
Structure
of Atoms
• Complete questions 6.21 to 6.28
Electronic
Structure
of Atoms
The Photoelectric
Effect
Electronic
Structure
of Atoms
Photons
• Einstein used the quantum to
explain the photoelectric
effect:
▫ Light comes in particles,
called photons.
▫ The energy of each photon is
determined by Planck’s
equation.
• Light shining on the surface of
a metal can cause electrons to
be ejected from the metal.
Electronic
Structure
of Atoms
• The electrons will only be ejected if the photons
have 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.
• Complete question 6.30
Electronic
Structure
of Atoms
Line Spectra and the Bohr Model
Another mystery involved
the emission spectra
observed from energy
emitted by atoms and
molecules.
Electronic
Structure
of Atoms
The Nature of Energy
• A white light source
produces a continuous
spectrum, like a rainbow.
• When elements are
excited, only a line
spectrum of discrete
wavelengths is observed.
Electronic
Structure
of Atoms
Hydrogen Spectrum
• has line spectra in 3 regions of
the EM Spectrum:
▫ Ultraviolet – Lymann Series
▫ Visible – Balmer Series
▫ Infrared - Paschen Series
Electronic
Structure
of Atoms
The Nature of Energy
•
Niels Bohr adopted Planck’s ideas about the
quantum and applied them to the electrons
around a nucleus.
Electronic
Structure
of Atoms
The Nature of Energy
• Bohr’s model is based on three postulates:
1. Electrons in an atom can only occupy certain
permitted orbits, or quanta.
2. Electrons in permitted orbits have specific, “allowed”
energies; these energies will not be radiated from
the atom.
3. Energy is only absorbed or emitted to move an
electron from one “allowed” energy state to another;
the energy is emitted by a photon:
E = h
Electronic
Structure
of Atoms
The Nature of Energy
• An electron in its lowest permissible energy is at
ground state
• If an electron accepts a quantum of energy it
will move to a higher energy level, or excited
state.
• When the electron moves back down to ground
state it emits a photon of light of a frequency
which correlates to the energy of the quantum.
Electronic
Structure
of Atoms
The Nature of Energy
The energy absorbed or emitted from the process
of electron promotion or demotion can be
calculated by the equation:
E = −RH (
1
1
- 2
nf2
ni
)
where RH is the Rydberg constant, 2.18  10−18 J,
and ni and nf are the initial and final energy levels of
the electron.
Electronic
Structure
of Atoms
• this explains the line spectra of
hydrogen:
▫ Lyman series. High
energy, in the UV range.
Represents energy
transition from higher
quanta to ground state.
▫ Balmer series.
Intermediate energy, in the
visible range. Represents
energy transition from
higher quanta to quantum
2.
▫ Paschen series. Low
energy, in the IR range.
Represents energy
transition from higher
quanta to quantum 3.
Electronic
Structure
of Atoms
Limitations of Bohr Model
• cannot explain the spectra of atoms other
than hydrogen.
• 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
Electronic
electron from one energy level to another.
Structure
of Atoms
The Wave Nature of Matter
• Louis de Broglie posited that if light can have
material properties, matter should exhibit
wave properties.
• He demonstrated that the
relationship between mass
and wavelength was
h
 = mv
Electronic
Structure
of Atoms
What does this mean?
• electrons have wave properties.
• the orbits of electrons are multiples of the
electron wavelength
▫ the first orbit has a circumference of 1 λ, the
second is 2 λ , etc.
Electronic
Structure
of Atoms
The Uncertainty Principle
• Heisenberg showed that the more
precisely the momentum of a
particle is known, the less
precisely is its position known.
• Our uncertainty of the
whereabouts of an electron is
greater than the size of the atom
itself!
Electronic
Structure
of Atoms
Quantum Mechanics
• Erwin Schrödinger
developed a
mathematical treatment
into which both the
wave and particle
nature of matter could
be incorporated.
• It is known as quantum
mechanics.
Electronic
Structure
of Atoms
• The wave function describes the electron’s
matter wave; it gives the probability of finding
the electron.
• Electron density is another way of expressing
probability.
▫ A region of high electron density is one where
there is a high probability of finding an electron.
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Orbitals and Quantum Numbers
• Solving the wave equation gives a set of
wave functions, or orbitals, and their
corresponding energies.
• Each orbital describes a spatial distribution of
electron density.
• An orbital is described by a set of three
quantum numbers.
Electronic
Structure
of Atoms
Principal Quantum Number, n
• describes the energy level on which the
orbital resides.
• The values of n are integers ≥ 0.
• correspond to the periods on the Periodic
Table.
Electronic
Structure
of Atoms
Azimuthal Quantum Number, l
• defines the shape of the orbital.
• Allowed values of l are integers ranging from
0 to n − 1.
• letter designations communicate the different
values of l and, therefore, the shapes and
types of orbitals.
Electronic
Structure
of Atoms
Azimuthal Quantum Number, l
Value of l
0
1
2
3
Type of orbital
s
p
d
f
• Theoretical g, h, i, etc. orbitals exist, but no atoms
have been created to use them.
Electronic
Structure
of Atoms
Magnetic Quantum Number, ml
• three-dimensional orientation of the orbital.
• Values are integers ranging from -l to l :
−l ≤ ml ≤ l
• on any given energy level, there can be up
to:
▫ 1 s orbital
▫ 3 p orbitals
▫ 5 d orbitals
▫ 7 f orbitals
Electronic
Structure
of Atoms
Magnetic Quantum Number, ml
• Orbitals with the same value of n form a shell.
• Different orbital types within a shell are
subshells.
• Each subshell is designated by a number and a
letter.
▫ For example, 3p orbitals have n = 3 and l = 1.
Electronic
Structure
of Atoms
In Summary
Electronic
Structure
of Atoms
s Orbitals
• Value of l = 0.
• Spherical in shape.
• Radius of sphere increases
with increasing value of n.
Electronic
Structure
of Atoms
p Orbitals
• Value of l = 1.
• Have two lobes with a node between them.
• The letters correspond to allowed the values
of ml of –1, 0, and +1.
Electronic
Structure
of Atoms
d Orbitals
• Value of l is 2.
• Four of the five
orbitals have 4 lobes;
the other resembles a
p orbital with a
doughnut around the
center.
• The letters correspond
to allowed the values
of ml of -2, –1, 0, +1
and +2.
Electronic
Structure
of Atoms
f orbitals
• Value of l is 3.
• 7 possible shapes,
including 8 lobes
and 2 doughnuts.
• The letters
correspond to
allowed the values
of ml of -3, -2, –1,
0, +1, +2 and +3.
Electronic
Structure
of Atoms
Energies of Orbitals
• Orbitals of the same
energy are
degenerate.
Electronic
Structure
of Atoms
Spin Quantum Number, ms
• two electrons in the
same orbital do not have
exactly the same energy.
• The “spin” of an
electron describes its
magnetic field, which
affects its energy.
Electronic
Structure
of Atoms
Spin Quantum Number, ms
• There is a spin quantum
number, ms.
• has only 2 allowed
values: +1/2 and −1/2.
Electronic
Structure
of Atoms
Pauli Exclusion Principle
• No two electrons in the
same atom can have
exactly the same energy.
• Therefore, no two
electrons in the same
atom can have identical
sets of quantum
numbers.
Electronic
Structure
of Atoms
Electron Configurations
• Distribution of all electrons in an atom
• Tell us how the electrons are distributed
among the various orbitals of an atom.
• Consist of
▫ Number denoting the energy level
Electronic
Structure
of Atoms
Electron Configurations
• Distribution of all electrons in an atom
• Tell us how the electrons are distributed
among the various orbitals of an atom.
• Consist of
▫ Number denoting the energy level
▫ Letter denoting the type of orbital
Electronic
Structure
of Atoms
Electron Configurations
• Distribution of all electrons in an atom.
• Tell us how the electrons are distributed
among the various orbitals of an atom.
• Consist of
▫ Number denoting the energy level.
▫ Letter denoting the type of orbital.
▫ Superscript denoting the number of electrons
in those orbitals.
Electronic
Structure
of Atoms
Electron Configurations
• Electrons tend to occupy the lowest
energy orbitals at ground state.
• Thus the electron configuration of an
atom is the arrangement of the electrons
from the lowest energy level to the
highest.
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Electron Configurations
• For any atom or ion:
▫ find total number of electrons
▫ start with the 1s electrons and fill each orbital in order
of energy
▫ watch the order of filling; energy is all important
• For instance:
▫ Iron (Fe) – contains 26 electrons
▫ 1s22s22p63s23p64s23d6
Electronic
Structure
of Atoms
Electron Configuration of Period 2 Elements
Element
Electron configuration
lithium
beryllium
boron
carbon
nitrogen
oxygen
fluorine
neon
1s22s1
1s22s2
1s22s22p1
1s22s22p2
1s22s22p3
1s22s22p4
1s22s22p5
1s22s22p6
Electronic
Structure
of Atoms
Examples:
• Potassium - 19 electrons
▫ 1s22s22p63s23p64s1
• Silver - 47 electrons
▫ 1s22s22p63s23p64s23d104p65s24d9
• Tungsten - 74 electrons
▫ 1s22s22p63s23p64s23d104p65s24d105p66s24f14
5d4
• Plutonium - 94 electrons
▫ 1s22s22p63s23p64s23d104p65s24d105p66s24f14
5d106p67s25f6
Electronic
Structure
of Atoms
• Write the correct electron configuration for the
following:
▫ S, P, As, Fe, Br, At, U, Na1+, O2-, Ne, Kr, Si,
Al, Ca
Electronic
Structure
of Atoms
Electron Configuration
•
•
•
•
•
•
•
•
•
•
•
•
•
•
S - 16 e1- 1s22s22p63s23p4
P - 15 e1- 1s22s22p63s23p3
As - 33 e1- 1s22s22p63s23p64s23d104p3
Fe - 26 e1- 1s22s22p63s23p64s23d6
Br - 35 e1- 1s22s22p63s23p64s23d104p5
At - 85 e11s22s22p63s23p64s23d104p65s24d105p66s24f145d106p5
U - 92 e11s22s22p63s23p64s23d104p65s24d105p66s24f145d106p6
7s25f4
Na1+ -10 e1- 1s22s22p6
O2- - 10 e1- 1s22s22p6
Ne - 10 e1- 1s22s22p6
Kr - 36 e1- 1s22s22p63s23p64s23d104p6
Si - 14 e1- 1s22s22p63s13p3
Electronic
Al - 13 e1- 1s22s22p63s13p2
Structure
of Atoms
Ca - 20 e1- 1s22s22p63s23p64s14p1
Electron Promotion
• movement of an outer ‘s’ electron to the
adjacent ‘p’ orbital at the same energy level.
• turns non-bonding electrons into bonding
electrons
• allows atoms to make more chemical bonds and
achieve a lower energy
• applies to elements from groups 2, 13 and 14
only
Electronic
• for these elements promotion is the rule
Structure
of Atoms
Electron Promotion
Element
Unhybridized Hybridized
beryllium
1s22s2
1s22s12p1
boron
1s22s22p1
1s22s12p2
carbon
1s22s22p2
1s22s12p3
Electronic
Structure
of Atoms
Orbital Diagrams
• are another way to illustrate the position of electrons.
• They are best learned by comparison with electron
configuration:
•
•
Na (11 protons, 11 electrons)
electron configuration:
1s22s22p63s1
•
orbital diagram:
1s
2s
2p
3s
↑↓
↑↓
↑↓ ↑↓ ↑↓
↑
Electronic
Structure
of Atoms
Orbital Diagrams
• Each line represents
one orbital.
• Arrows represent the
electrons.
• The direction of the
arrow represents the
spin of the electron.
Electronic
Structure
of Atoms
Hund’s Rule
“In any orbital with
more than 1 suborbital electrons will
half-fill each suborbital before
pairing up.”
Electronic
Structure
of Atoms
Orbital Diagrams
Representative
Group Element
Electron configuration
Orbital Diagram
1
lithium
1s22s1
1s
↑↓
2s
↑
2p
2
beryllium
1s22s12p1
↑↓
↑
↑
13
boron
1s22s12p2
↑↓
↑
↑ ↑
14
carbon
1s22s12p3
↑↓
↑
↑ ↑ ↑
15
nitrogen
1s22s22p3
↑↓
↑↓
↑ ↑ ↑
16
oxygen
1s22s22p4
↑↓
↑↓
↑↓ ↑ ↑
17
fluorine
1s22s22p5
↑↓
↑↓
↑↓ ↑↓ ↑
18
neon
1s22s22p6
↑↓
↑↓
↑↓ ↑↓ ↑↓
Note the electron promotion for the elements from groups 2, 13 &
Electronic
14Structure
of Atoms
• Repeat the last assignment, giving the
orbital diagrams for the elements.
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
• these are examples of electron promotion
Electronic
Structure
of Atoms
Condensed Electron Configurations
• Looks mainly at electrons with the highest
energy:
▫ find element on the Periodic Table.
▫ find noble gas with lower atomic number
▫ write electron configuration from that point.
• Example:
▫ P is 1s22s22p63s23p3,
▫ but Ne is 1s22s22p6.
▫ Therefore, P is [Ne]3s23p3.
Electronic
Structure
of Atoms
Electron Configuration 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 1 & 2 - s block
Groups 13 to 18 - p block
Groups 3 – 12 – d block
The lanthanides and actinides - f block
• Watch the order of filling!
Electronic
Structure
of Atoms
Electronic
Structure
of Atoms
Some Anomalies
Some
irregularities
occur when there
are enough
electrons to halffill s and d
orbitals on a
given row.
Electronic
Structure
of Atoms
Some Anomalies
For instance, the
electron
configuration for
copper is
[Ar] 4s1 3d5
rather than the
expected
[Ar] 4s2 3d4.
Electronic
Structure
of Atoms
Some Anomalies
• This occurs
because the 4s
and 3d orbitals
are very close in
energy.
• These anomalies
occur in f-block
atoms, as well.
Electronic
Structure
of Atoms