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CHAPTER 6
ELECTRONIC STRUCTURE
AND PERIODIC PROPERTIES OF
ELEMENTS
OpenStax
Chemistry
Joseph DePasquale
Review
• Chapter 2: Structure of the Atom
• Nucleus: Contains protons and neutrons
• Electron cloud: Surrounds the nucleus. Contains the
electrons.
• Chapter 6 will focus on the arrangement of electrons
in the electron cloud.
• Energy levels
• Spatial locations – orbitals
CH. 6 Outline
6.1 Electromagnetic Energy
6.2 The Bohr Model
6.3 Development of Quantum Theory
6.4 Electronic Structure of Atoms (Electron
Configurations)
6.5 Periodic Variations in Element Properties
6.1: Electromagnetic Energy
• It was originally thought that light only behaved as a
wave.
• Wave – An oscillation or periodic movement that can
transport energy from one point in space to another.
• Eventually it became apparent that light also possess
particle like properties.
• Visible light belongs to a vast spectrum of radiation known
as electromagnetic radiation.
6.1: Electromagnetic Energy
• Characteristics of Waves:
1) Wavelength (λ)
• Distance between two consecutive crests or troughs.
2) Frequency (n)
• Number of successive crests or troughs (wave cycles)
that pass a given point in a unit time.
3) Amplitude
• One half the distance between the peaks and troughs.
Frequency
• If 109 cycles of a wave pass a particular point in one
second then,
n=
• The frequency unit of inverse second (s-1) is given the
name hertz (Hz).
• Sometimes we use the term megahertz (MHz) when a
large number of cycles passes in a unit time.
Wavelength-Frequency Relationship
• The speed at which a wave moves through space is
found by multiplying the wavelength by the
frequency:
ln = c
• c is the speed of light in a vacuum, 2.998 X 108 m/s
• When using this equation:
• Frequency must be in s-1
• Wavelength must be in m
Wavelength and Frequency
ln = c
Wavelength and Frequency
ln = c
• One-dimensional sinusoidal waves show the relationship among wavelength,
frequency, and speed. The wave with the shortest wavelength has the highest
frequency. Amplitude is one-half the height of the wave from peak to trough.
Electromagnetic Radiation
• Visible light is a type of Electromagnetic Radiation.
• Different types of electromagnetic radiation are classified
by their respective λ and n.
• The human eye can only see a small fraction of the
different types of electromagnetic radiation, covering only
a narrow region of the electromagnetic spectrum.
• Only λ between 400 and 700 nm.
• But in chemistry we work with light of all
wavelengths.
The Electromagnetic Spectrum
•
Portions of the electromagnetic spectrum are shown in order of decreasing frequency and increasing wavelength. Examples
of some applications for various wavelengths include positron emission tomography (PET)scans, X-ray imaging, remote
controls, wireless Internet, cellular telephones, and radios. (credit “Cosmic ray”: modification of work by NASA; credit “PET
scan": modification of work by the National Institute of Health; credit “X-ray”: modification of work by Dr. Jochen Lengerke;
credit “Dental curing": modification of work by the Department of the Navy; credit “Night vision": modification of work by the
Department of the Army; credit “Remote": modification of work by Emilian Robert Vicol; credit “Cell phone": modification of
work by Brett Jordan; credit “Microwave oven”: modification of work by Billy Mabray; credit “Ultrasound": modification of work
by Jane Whitney; credit “AM radio”: modification of work by Dave Clausen)
The Visible Spectrum
Blackbody spectral distribution curves are shown for some representative
temperatures.
The Particle Nature of Light; Photon Energies
• Just 100 years ago, everyone thought light could be
explained in terms of wave behavior.
• Experiments from 1900-1910 by Max Planck and Albert
Einstein showed that light has properties not explained
by waves.
• Today, we consider light to also behave as a stream of
particles called photons, with energy, E, given by
• h is Planck’s constant: 6.626 X 10-34 J·s
Energy and Wavelength
• Note that energy and wavelength are inversely
related
• Long wavelength, low energy
• Short wavelength, high energy
Continuous Spectrum
• Matter can absorb energy in the form of
electromagnetic radiation.
• Matter can also absorb energy in the form of heat
(Ch. 5).
• The matter releases some of this excess energy in the
form of electromagnetic radiation.
• When solids, liquids, or high concentration gases
are heated to high temperature, this emitted
radiation can be passed through a prism to produce
a continuous spectrum.
Continuous Spectrum
• A continuous spectrum is unbroken for the entire
visible spectrum (400 to 700 nm).
• White light from the sun also produces a continuous
spectrum.
Gaseous Elements: Line Spectra
• When dilute gas phase elements are heated they also
radiate energy in the form of electromagnetic radiation.
• The emitted light is NOT continuous
• Rather the emitted light is only of single, discrete
wavelengths.
• Consider sodium
• Two strong lines at 589.0 and 589.6 nm are emitted.
• The light is yellow.
• Light of discrete wavelength is also of discrete energy!
Continuous Spectra vs. Line Spectra
Compare the two types of emission spectra: continuous spectrum of white light (top)
and the line spectra of the light from excited sodium, hydrogen, calcium, and mercury
atoms.
Neon signs operate by exciting a gas at low partial pressure using an electrical current.
This sign show the elaborate artistic effects that can be achieved. (credit: Dave Shaver)
Line Spectra and Electron Arrangement
• The emitted light of single, discrete wavelength
has a corresponding discrete energy!
E = hn =
hc
l
• Why do elements emit light of single wavelength?
• Why do different elements emit light of different
wavelengths?
6.2: The Bohr Model
• Niels Bohr (1885-1962)
• Theoretical explanation of the hydrogen line spectrum
• 1922 Nobel Prize in physics
• The Bohr Model
• Hydrogen consists of a central proton about which moves an
electron in a circular orbit.
• Electrostatic attraction of the proton for the electron and
centrifugal force keeps the electron in orbit.
• The electron can only occupy fixed orbits around the nucleus.
• These orbits have fixed, discrete energies.
• As the orbit gets farther from the nucleus, the energy
increases.
The Bohr Model
• The atom emits or absorbs a photon if its electron moves to a
different orbit.
• The energy of the photon absorbed or emitted is equal to the
difference in energy between the final orbit (Ef) and initial
orbit (Ei) that the electron traveled between.
• Since the electron can only reside in orbits of discrete energy,
the atoms can only absorb or emit photons of discrete
energy, and therefore discrete wavelength.
Mathematics of the Bohr Model
• The energy of the hydrogen electron can be calculated
with
• En is the energy of the electron when in orbit n
• RH is the Rydberg constant, 2.179 X 10-18 J
• n corresponds to the orbit occupied by the electron.
• n is called the principal quantum number.
• n can take on any positive integer value.
Notes on the Bohr Model of Hydrogen
1. The ground state, where n = 1, is the lowest energy
state for the electron. The electron is in an orbit closest
to the nucleus. Any n value above 1 corresponds to
an excited state.
2. When the atom absorbs energy, the electron moves
from an orbit with a lower n to a higher n.
3. When an electron falls from an orbit with a higher n to a
lower n, energy is emitted.
The energy emitted is in the form of a photon of specific
wavelength.
• The wavelength of the light absorbed or emitted can be related
to the orbits (n) that the electron transitioned between.
æ
ö
1 RH 1
1
çç 2 - 2 ÷÷
=
l hc è n i n f ø
The horizontal lines show the relative energy of orbits in the Bohr model of the
hydrogen atom, and the vertical arrows depict the energy of photons absorbed (left) or
emitted (right) as electrons move between these orbits.
æ
ö
1 RH 1
1
çç 2 - 2 ÷÷
=
l hc è n i n f ø
6.3: Development of Quantum Theory
• Accomplishments of the Bohr Model:
• Explains the structure of the hydrogen atom very well.
• Indicated that the location of an electron in an atom is
restricted to fixed locations!
• But when applied to atoms with two or more
electrons, the theory deviates significantly from
that observed by experiment.
Development of Quantum Theory
• Classical physics sufficiently explains what happens in our
macroscopic world.
• But by the 1920’s it became clear that very small pieces of
matter, such at atoms and electrons follow a different set of
rules.
• Early 20th century:
• Louis de Broglie – If light can be treated as a particle,
then a particle, such as an electron, can be treated as
a wave.
• This thinking ushered in Quantum Theory.
Development of Quantum Theory
• Heisenberg Uncertainty Principle: It is fundamentally
impossible to determine simultaneously and exactly both
the momentum and the position of a particle.
• Erwin Schrodinger (1926): Schrodinger equation
• We can only specify the probability of finding an
electron in a particular region of space known as an
orbital.
Quantum Numbers
• Every electron in an atom has its own unique set of four
quantum numbers.
• Three of these quantum numbers are used to described
the region of space (orbital) that the electron occupies.
•n
•ℓ
• mℓ
• The fourth quantum number, ms, is associated with the
electron’s spin.
Principle Quantum Number, n
• Principle quantum number (n) – Defines the location of
the orbital.
• Essentially the same concept as n in the Bohr Model.
• n is also called the shell number.
• n = 1, 2, 3, 4, …
• n = 1 is the first shell
• n = 2 is the second shell, and so on …
• As the value of n increases, the distance the electron is
from the nucleus increases, and the energy of the electron
increases.
Principle Quantum Number, n
• Different shells are numbered by principle
quantum numbers.
Angular Momentum Quantum Number, ℓ
• Angular momentum quantum number (ℓ) – Defines
the shape of the orbital.
• The larger the value of ℓ the more complex the shape of
the orbital.
• The value of ℓ is derived from the value of n.
• In the nth principal level, there are n sublevels
ℓ = 0, 1, 2 … (n-1)
Angular Momentum Quantum Number, ℓ
• Instead of using numbers, the shapes of orbitals
are often designated by letters.
• For ℓ = 0: s orbital
• For ℓ = 1: p prbital
• For ℓ= 2: d orbital
• For ℓ = 3: f orbital
Shapes of s orbitals (ℓ= 0)
• Shapes of s, p, d, and f orbitals. They
can be constructed and described by
(a) the values of the magnetic quantum
number or (b) with the axis that defines
their orientation.
Shapes of p orbitals (ℓ= 1)
• Shapes of s, p, d, and f orbitals. They can
be constructed and described by (a) the
values of the magnetic quantum number or
(b) with the axis that defines their
orientation.
Shapes of d orbitals (ℓ= 2)
• Shapes of s, p, d, and f orbitals. They
can be constructed and described by
(a) the values of the magnetic quantum
number or (b) with the axis that defines
their orientation.
Shapes of f orbitals (ℓ= 3)
Shapes of s, p, d, and f
orbitals. They can be
constructed and described by
(a) the values of the magnetic
quantum number or (b) with
the axis that defines their
orientation.
Combining n and ℓ
• When referring to an orbital, usually both the n
and ℓ values are reported.
• Examples:
• 1s means n = 1 and ℓ =0
• 2s means n = 2 and ℓ = 0
• 3p means n = 3 and ℓ = 1
Relative Energy
• As n increases, energy increases
• Example: 2s is higher in energy than 1s
• But for atoms with more than one electron, the energy is
dependent on both n and ℓ
• Within a given shell (same value of n), as ℓ increases, the
energy of the orbital also increases.
ns < np < nd < nf
Magnetic Quantum Number, mℓ
• Magnetic Quantum Number (mℓ) – Determines
the direction in space (orientation) of the
orbital and the number of possible orbitals for
that ℓ value.
• The value of mℓ depends on ℓ
• mℓ = -ℓ … -1, 0, +1, … +ℓ
• There are 2ℓ + 1 orbitals with the same nℓ value.
Spin Quantum Number: ms
• The fourth quantum number, ms, is associated with
electron spin, not the orbital.
• Two spins are possible, clockwise and counterclockwise
• There are two values of ms, + ½ and – ½
Electrons with spin values ±1/2 in an external magnetic field.
The Pauli Exclusion Principle
• Pauli Exclusion Principle - No two electrons in the
same atom can have exactly the same set of all four
quantum numbers.
• A maximum of TWO electrons may occupy the same exact
orbital and therefore have the same n, ℓ, and mℓ numbers.
• But these electrons will differ in spin and therefore have
different ms numbers.
• One will be ms = + ½
• The other will be ms = – ½
• We say these two electrons have “opposite” spins.
6.4: Electronic Structure of Atoms (Electron
Configurations)
• Electron Configuration - Arrangement of electrons in the
orbitals of an atom.
• Example of an electron configuration: 1s22s22p5
• Coefficient (number) represents n
• Letter represents ℓ
• Superscript is the number of electrons in that particular
orbital.
Predicting Electron Configurations
Generalized energy-level diagram for atomic orbitals in an atom with two or more
electrons (not to scale).
Orbitals fill with electrons in order of increasing energy.
The lowest energy orbitals fill first.
Predicting Electron Configurations
• Once the order of orbital filling is known, the electron
configuration is readily obtained.
• Typically, an orbital is completely filled before electrons
start to occupy the next orbital.
• Be careful there are exceptions…
• This process is known as the “Aufbau Principle”
Predicting Electron Configurations
• We must know the number of each type of orbital
as indicated by the mℓ quantum number.
• Remember that each orbital can hold a maximum
of 2 electrons.
Predicting Electron Configurations
The arrow leads through each subshell in the appropriate filling order for electron
configurations. This chart is straightforward to construct. Simply make a column for all the s
orbitals with each n shell on a separate row. Repeat for p, d, and f. Be sure to only include
orbitals allowed by the quantum numbers (no 1p or 2d, and so forth). Finally, draw diagonal
lines from top to bottom as shown.
Filling of Orbitals and the Periodic Table
• Being familiar with the periodic table on the next slide
makes it possible to quickly write an electron
configuration for any element.
This periodic table shows the electron
configuration for each subshell. By “building
up” from hydrogen, this table can be used to
determine the electron configuration for any
atom on the periodic table.
Notes on The Periodic Table
1. For s and p sublevels, the value of n is equal to the period
number.
2. Elements in Group 1 and 2 add electrons last to an s orbital
3. Elements in Groups 13-18 add electrons last to a p orbital
(exception being He)
4. Transition metal elements add electrons last to a d orbital,
with “n” value that is one less than the period number.
5. The two sets of 14 elements each at the bottom of the
periodic table add electrons last to an f orbital with a “n”
value that is two less than the period number.
Electron Configuration and Orbital Diagram of H,
He, Li, Be
Orbital Diagrams of Atoms
• Orbital Diagram – Pictorial representation of the
electron configuration, showing the individual
orbitals and the pairing arrangement of electrons.
• Parentheses or boxes represent individual orbitals.
• Arrows, up and down, indicate electrons (↑↓)
• One electron in an orbital has ms = + ½ and the other
has ms = - ½ (Pauli Exclusion Principle).
• Orbital diagrams provide more detailed information
than electron configurations alone.
Orbital Diagrams of Atoms
• Hund’s Rule: The lowest-energy configuration for an
atom with electrons within a set of degenerate orbitals
is that having the maximum number of unpaired
electrons.
• Degenerate Orbitals - orbitals with the same energy.
• Only after all degenerate orbitals are half-filled will
electrons begin to pair with opposite spins.
Valence Electrons and Core Electrons
• Valence Electrons – Electrons occupying orbitals
in the outermost shell (highest n value).
• Core Electrons – Electrons occupying orbitals in
the inner shell(s) (not the highest n value).
Abbreviated Electron Configurations
• To save writing, abbreviated electron configurations
are written.
• This type of configuration is also called a “condensed”
electron configuration.
• Core electrons shown as the noble gas they represent in
brackets.
• Only the configuration of valence electrons are shown.
• N:
• Cl:
Exceptions
• Some transition metals have electron configurations
that contradict the rules we just discussed.
• The difference is usually by a shift of just one
electron to an orbital of similar energy.
• These difference arise because
• The orbitals are close to each other in energy.
• There is sometimes a gain in stability by producing a
half-filled or fully-filled orbital.
Exceptions
• Two exceptions: Cr and Cu
Electron Configuration of monoatomic ions
• In forming a cation, electrons are removed from
orbitals in the highest energy shell (n).
• For a main group cation, electrons added last are the first
removed.
• For a transition metal cation, electrons are always
removed from an s orbital before a d orbital.
• In forming an anion, electrons are added to orbitals
according to the Aufbau principle.
• Add electrons to available orbitals of lowest energy.
Electron Configurations of Select Ions
6.5: Periodic Variations in Element
Properties
• Elements in the same group exhibit similar chemical and
physical properties.
• This is because elements in the same group have similar
valence electron configurations.
• We will examine four physical and chemical properties and
how they vary within groups and periods.
1) Size – Atomic radius (covalent radius) and ionic radius
2) Ionization energy
3) Electron affinity
This version of the periodic table shows the
outer-shell electron configuration of each
element. Note that down each group, the
configuration is often similar.
Atomic Radius
• The “size” of an atom is a difficult term to define, as the
electron cloud does not have a defined boundary.
• The radius of an atom can be defined and measured,
assuming the atom is a sphere.
• Atomic Radius (or Covalent Radius) – One half the
distance between the nuclei of two identical atoms
when they are joined by a covalent bond.
• The larger the radius, the larger the atom
Atomic Radius
Atomic Radius Trends in the Periodic Table
• Radii increase down a group.
• The outermost electrons (valence electrons)
are in a shell of higher “n” value and therefore
farther from the atom’s nucleus.
• Radii decrease left to right across a period.
• The reason is a little more complex…
Within each period, the trend in atomic radius decreases as Z increases; for example,
from K to Kr. Within each group (e.g., the alkali metals shown in purple), the trend is
that atomic radius increases as Z increases.
Trend in Atomic Radius Explained
• The observed trend in atomic radius within a period can
be explained by electron shielding and effective
nuclear charge (Zeff).
• In a neutral atom there is 1 proton for every 1 electron.
• The proton(s) “pull” the electron(s) towards the nucleus.
• The outermost electrons (valence electrons)
are“shielded” from some of the positive charge of the
nucleus by other electrons.
• Core electrons are very good at shielding valence
electrons.
• Valence electrons slightly shield other valence
electrons.
Trend in Atomic Radius Explained
• Effective Nuclear Charge – The positive, nuclear charge
felt by the outermost electron(s).
• The more an electron is shielded, the lower the effective
nuclear charge.
• As effective nuclear charge increases, the outermost
electrons are pulled in more tightly, and the atomic
radius decreases.
Trend in Atomic Radius Explained
• Decrease in radius left to right across a period
• Moving across a period, electrons are being added to the
same shell so the number of valence electrons increases.
• The number of core electrons stays the same.
• Therefore, as you move across a period the number of
protons increases but the amount of shielding only slightly
increases.
• Result: The effective nuclear charge increases left to
right across a period and the atomic radius decreases.
Ionic Radius
• Cations are smaller than the atoms from which they
are derived.
• Loss of electron(s) results in an excess of protons
relative to electrons.
• Valence electrons are now pulled closer to the nucleus.
• Anions are larger than the atoms from which they are
derived.
• Gain of electron(s) results in a deficiency of protons
relative to electrons.
• Also, increased electron repulsion.
• Valence electrons are now held less tightly to the
nucleus.
Ionic Radius
• The more positive the charge
of the cation, the smaller the
ionic radii.
Ionization Energy
• First Ionization energy (IE1) – The amount of energy required
to remove the most loosely bound electron from a gaseous
atom in its ground state.
• The energy required to remove the second most loosely
bound electron is called the Second Ionization energy (IE2).
• Energy must always be absorbed in order for ionization to
occur.
• The ionization process is always endothermic.
• Ionization energies are always positive quantities.
First Ionization Energy
M (g)  M+ (g) + e• The trend in first ionization energies is the inverse of
atomic radius.
• As the radius gets smaller, the outer electrons are held
more tightly to the nucleus, therefore the electron becomes
more difficult to remove, and ionization energy increases.
• Ionization energy increases across a period from left to
right.
• Ionization energy decreases down a group from top to
bottom.
First Ionization Energy Trend
First Ionization Energy Trend
Note there are
some
exceptions to
the trend
The first ionization energy of the elements in the first five periods are plotted against
their atomic number.
IE1 Trend Exceptions
• IE1 (Group 2) > IE1 (Group 3)
• It is easier to remove an electron from a p orbital than
an s orbital with the same principal quantum number
(n), because the p orbital is of higher energy.
Group 2
Group
3
80
IE1 Trend Exceptions
• IE1 (Group 5) > IE1 (Group 6)
• Within a p subshell, it is easier to remove an electron
from an an orbital that already contains an electron
than from an empty orbital.
• This is due to repulsive forces between electrons.
Group 5
Group 81
6
Successive IE Values
• Successive ionization energies always increase.
• Greater electrostatic attraction between the electron and
positive cation.
• There is a large jump in energy for the removal of a core
electron.
Blue indicates core electrons
Electron Affinity
• Electron affinity (EA) – The energy change for the
process of adding an electron to a gaseous atom to form
an anion.
• This process can be either
• Endothermic
• Exothermic
84
Electron Affinity Trend
• It becomes easier to add electrons to elements moving
left to right across a period.
 Easier to add an electron as the Zeff increases.
• In general, electron affinity becomes more negative
from left to right across a period.
• There are some exceptions.
• The trend in electron affinity is less clear down a
group.
85
Electron Affinity Trend
This version of the periodic table displays the electron affinity values (in kJ/mol) for
selected elements.