Chapter 6
Electronic Structure
of Atoms
Electronic
Structure
of Atoms
Waves
Electronic
Structure
of Atoms
Waves
• The number of waves
passing a given point per
unit of time is the
frequency (ν).
• For waves traveling at
the same velocity, the
longer the wavelength,
the smaller the
frequency.
Electronic
Structure
of Atoms
Electromagnetic Radiation
Continuous spectrum
• All electromagnetic radiation travels at the same velocity:
the speed of light (c), 3.00x108 m/s
• Therefore,
Electronic
Structure
c = 
of Atoms
The Nature of Energy
• Max Planck explained it by assuming that energy comes in
packets called quanta.
Energy
Energy
Intensity
We assume that energy
increases in a continuous
stream. When we add heat
to a pot of water it slowly
gets warmer and it will
eventually boil.
Intensity
In the micro world energy
increases in discrete units. It
increases by a full quantum or not
at all. Even when energy is applied
to the electron, it will never be
ejected from the atom unless the
quantum of energy is applied.
Electronic
Structure
of Atoms
The Photoelectric Effect
• The energy is carried out by
particles of light called
photons.
• He concluded that energy is
proportional to frequency:
E = h
where h is Planck’s constant
6.63x10-34 Js
Electronic
Structure
of Atoms
The Photoelectric Effect
• Fact # 1: Highly intense low frequency light does not
eject any electrons, even if it shines on the metal surface
for several days.
• Fact # 2: Only when the threshold frequency is reached
is that electrons will be ejected from the metal.
• Fact # 3: Increasing the intensity of the light at a
frequency that will cause electrons to eject results in a
higher ejection rate, but all ejected electrons share the
same velocity.
• Fact # 4: Increasing the frequency of the light increases
the velocity of the ejected electrons, but all ejected
electrons share the same velocity.
Electronic
Structure
of Atoms
Einstein Theory 1905
• A beam of light is a stream of particles called photons.
• The energy of the photon is related to its frequency
according to E = h
• The quantum of Planck is a particle – a photon.
• If the frequency of a photon is below a certain
threshold, no electrons are ejected.
• All these supports the idea that there must be a one to
one relationship of electron to photon.
Electronic
Structure
of Atoms
The Nature of Energy
• Therefore, if one knows the
wavelength of light, one
can calculate the energy in
one photon, or packet, of
that light:
c = 
E = h
Electronic
Structure
of Atoms
Bohr’s Model
•
Niels Bohr adopted Planck’s assumption and
explained these phenomena in this way:
1. Electrons in an atom can only occupy certain orbits
(corresponding to certain energies).
n=4
n=3
n=2
n=1
Electronic
Structure
of Atoms
Bohr’s Model
2. Electrons in permitted orbits have specific, “allowed”
energies; these energies will not be radiated from the
atom.
The force of attraction between the electrons and the
nucleus (protons) determine the distance between the
energy levels and the nucleus and therefore the distance
between the outermost electrons and the nucleus.
(atomic radius)
F = k q1 q2 Coulomb’s Law
d2
Electronic
Structure
of Atoms
Bohr’s Model
3. Energy is only absorbed or emitted in such a way as
to move an electron from one “allowed” energy state
to another; the energy is defined by
E = h
Electronic
Structure
of Atoms
Bohr’s Model
The energy absorbed or emitted from the process of
electron promotion or demotion can be calculated
by the equation:
E = −RH
(
1
1
nf2
ni2
)
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
Line spectra and how it explains
energy levels
Electronic
Structure
of Atoms
Line spectrum and energy levels
• Each line represents a wavelength/frequency of
an electron transition. This transition is
associated to an energy.
• The separation between the lines corresponds to
the difference in energy between energy levels.
• Since all lines are not separated equally, not all
transitions happen within the same energy levels
and not all energy levels are equally separated.
• These facts support Bohr model of the atom.
Electronic
Structure
of Atoms
Bohr’s Model see animation
•
•
•
•
Based on the hydrogen atom.
The diagram shows the transitions
of the electron in hydrogen as it
moves from higher energy levels to
energy level 1, 2, and 3.
The transitions to energy level 1
will release the greatest amount of
energy. This energy forms a group
of lines in the UV section of the
spectrum.
Similarly the transitions to energy
level 3 fall in the IR and the ones to
energy level 2 fall in the Visible. Electronic
Structure
of Atoms
The Shell Model of the Atom
• Ionization energy suggests that electrons are arranged
in shells.
• In this model electrons move in 3D shells. Each shell is
an exact set distance from the nucleus, so electrons that
remain in a given shell of a neutral atom are always the
same distance from the nucleus.
hydrogen
helium
lithium
Electronic
Structure
of Atoms
The Shell Model of the Atom
• It requires much less energy to
remove the most loosely held electron
from Li because that electron is farther
from the nucleus than the electrons in
H and He.
• The trend in the ionization energies
suggests that n=2 can hold 8 electrons
(Li  Ne)
• The most loosely held electron in Na
must be in another shell since its IE
drops.
Li
Be
B
C
N
O
F
Ne
Electronic
Structure
of Atoms
The Shell Model of the Atom
Unexplained problems:
• The 1st IE for boron (B)
is less than for beryllium
(Be).
• The trend repeats in
shell n=3 with Mg and
Al
Electronic
Structure
of Atoms
Inner Core and Valence Electrons
Inner core
electrons are
contained in the
inner shells
Valence electrons
are contained in
the outer shells
Electronic
Structure
of Atoms
Photoelectron Spectroscopy PES
• High energy photons remove electrons from atoms.
• Only one electron is removed from each atom, but
that electron can come from any shell.
• When the photon absorbs the electron, it is provided
with the energy required to be ejected from the atom
(IE) and the KE associated with its velocity after it
has left the atom.
• The IE for each ejected electron can be calculated by
subtracting the KE of the ejected electron from the
energy contained by the photon.
Electronic
Structure
of Atoms
Photoelectron Spectroscopy PES
Relative number of electrons
H
1.31
He
2.37
Li
6.26
0.52
Be
11.5
0.90
 Ionization Energy (MJ/mol)
• The Ionization energy
decreases from left to right.
• The greater the IE the
closer the electrons are to
the nucleus.
• The height of the peaks
corresponds to the number
of electrons with that IE.
H: 1 electron in n = 1
He: 2 electrons in n = 1
Li: 2 electrons in n = 1 and 1 electrons in n = 2
Be: 2 electrons in n = 1 and 2 electrons in n = 2
Electronic
Structure
of Atoms
Photoelectron Spectroscopy PES
Relative number of electrons
H
1.31
He
2.37
Li
6.26
0.52
Be
11.5
0.90
B
19.3
1.36
 Ionization Energy (MJ/mol)
0.80
• The shell model does not
separate the 8 electrons in n = 2.
But The PES for boron does not
support that.
• PES data tells us that the
model must be revised, as the n
= 2 shell must contain 2
subshells with different IE.
• Each peak corresponds to a
subshell or sublevel.
H: 1 electron in n = 1
He: 2 electrons in n = 1
Li: 2 electrons in n = 1 and 1 electrons in n = 2
Be: 2 electrons in n = 1 and 2 electrons in n = 2
Electronic
B: 2 electrons in n = 1, 2 electrons in n = 2, 2s and 1 electron in 2pStructure
of Atoms
Photoelectron Spectroscopy PES
Relative number of electrons
C
28.6
N
1.72
39.6
2.45
1.09
1.40
O
52.6
3.12
1.31
F
67.2
3.88
1.67
Ne
84.0
4.68
2.08
 Ionization Energy (MJ/mol)
C: 1s2 2s2 2p2
N: 1s2 2s2 2p3
O: 1s2 2s2 2p4
F: 1s2 2s2 2p5
Ne:1s2 2s2 2p6
three peaks
three peaks
three peaks
three peaks
three peaks
In all cases the size of the first
2 peaks is the same, but the
third one gets larger due to the
presence of more electrons in
that subshell.
The IE increases from C to Ne for
the same peak, except between N
and O. (will be discussed later)
Electronic
Structure
of Atoms
Photoelectron Spectroscopy PES
Problem 1. How many peaks can you predict for the elements
• Na through Ar?
• K and Ca?
• Sc?
Electronic
Structure
of Atoms
Chemical models of the atom
• Since atoms are very small, models must be used
to explain them.
• When models are not consistent with the
experimental data, they need to be refined or
replaced by a new one that fits the experimental
data.
• The shell model of the atom constructed through
ionization energy was replaced with the quantum
mechanical model as additional information was
considered.
Electronic
Structure
of Atoms
Chemical models of the atom so far
• Dalton’s model is incorrect. (Mass spec demonstrates
evidence that the atom is NOT indivisible and all atoms of the same element
are NOT identical).
• Bohr model – electrons follow circular orbits that
are at exact distances from the nucleus. (the
equations that predicted the energy levels of the orbits only worked for
hydrogen)
• Shell model – electrons circulate on the
perimeters of spheres that are at exact distances
from the nucleus. (PES data indicates that there are subshells
within each shell)
Electronic
Structure
of Atoms
Quantum Mechanics
• Electrons do not follow orbits.
• 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
Quantum Numbers
• Solving the wave equation gives a set of
wave functions, or orbitals, and their
corresponding energies.
• An orbital graphically describes the space
that an electron occupies 90% of the time.
• An orbital is described by a set of three
quantum numbers.
• Every electron within a given subshell of a
given atom is at the same quantized
Electronic
Structure
energy level.
of Atoms
s Orbitals
Electronic
Structure
of Atoms
p Orbitals
Electronic
Structure
of Atoms
d Orbitals
Electronic
Structure
of Atoms
Energies of Orbitals
• For a one-electron
hydrogen atom,
orbitals on the same
energy level have
the same energy.
• That is, they are
degenerate.
Electronic
Structure
of Atoms
Energies of Orbitals
• As the number of
electrons increases,
though, so does the
repulsion between
them.
• Therefore, in manyelectron atoms,
orbitals on the same
energy level are no
longer degenerate Electronic
Structure
and they split.
of Atoms
Spin Quantum Number, ms
• In the 1920s, it was
discovered that 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
Pauli Exclusion Principle
• No two electrons in the
same atom can have
exactly the same energy.
• For example, no two
electrons in the same
atom can have identical
sets of quantum
numbers.
Electronic
Structure
of Atoms
Electron Configurations
5
4p
• Distribution of all electrons in
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
Orbital Diagrams
• Each box represents one
orbital.
• Half-arrows represent
the electrons.
• The direction of the
arrow represents the
spin of the electron.
Electronic
Structure
of Atoms
Hund’s Rule
“For degenerate
orbitals, the lowest
energy is attained
when the number of
electrons with the
same spin is
maximized.”
Electronic
Structure
of Atoms
Periodic Table
• We fill orbitals in
increasing order of
energy.
• Different blocks on
the periodic table,
then correspond to
different types of
orbitals.
Electronic
Structure
of Atoms
Electron Configurations
• Orbital diagram.
• Complete electron configuration.
• Noble gas notation. It uses the previous
noble gas.
Electronic
Structure
of Atoms
Periodic Table and Electron Configurations
Electronic
Structure
of Atoms
Paramagnetism and Diamagnetism
• Paramagnetism: Atoms with one or more
unpaired electrons are attracted to a
magnetic field.
• Diamagnetism: Atoms with all electrons
paired will have no magnetic moment since
the magnetic moments generated by each
electron cancels out when they are paired.
Electronic
• Orbital diagram
Structure
of Atoms