Download Unit 6 1 Quantum Mechanics

NAME __________________________________ UNIT 6 (1): QUANTUM MECHANICAL MODEL
Big Idea 1: The chemical elements are fundamental building materials of
matter, and, all matter can be understood in terms of arrangements of
atoms. These atoms retain their identity in chemical reactions.
Enduring understanding 1.A: All matter is Essential knowledge 1.A.1: Molecules are composed of
made of atoms. There are a limited number specific combinations of atoms; different molecules are
of types of atoms; these are the elements.
composed of combinations of different elements and of
combinations of the same elements in differing amounts and
proportions.
Essential knowledge 1.A.2: Chemical analysis provides a
method for determining the relative number of atoms in a
substance, which can be used to identify the substance or
determine its purity.
Essential knowledge 1.A.3: The mole is the fundamental unit
for counting numbers of particles on the macroscopic level
and allows quantitative connections to be drawn between
laboratory experiments, which occur at the macroscopic
level, and chemical processes, which occur at the atomic
level.
Enduring understanding 1.B: The atoms
of each element have unique structures
arising from interactions between electrons
and nuclei.
Essential knowledge 1.B.1: The atom is composed of
negatively charged electrons, which can leave the atom, and
a positively charged nucleus that is made of protons and
neutrons. The attraction of the electrons to the nucleus is the
basis of the structure of the atom. Coulomb’s law is
qualitatively useful for understanding the structure of the
atom.
Essential knowledge 1.B.2: The electronic structure of the
atom can be described using an electron configuration that
reflects the concept of electrons in quantized energy levels or
shells; the energetics of the electrons in the atom can be
understood by consideration of Coulomb’s law.
Enduring understanding 1.C: Elements
display periodicity in their properties when
the elements are organized according to
increasing atomic number. This periodicity
can be explained by the regular variations
that occur in the electronic structures of
atoms. Periodicity is a useful principle for
understanding properties and predicting
trends in properties. Its modern-day uses
range from examining the composition of
materials to generating ideas for designing
new materials.
Essential knowledge 1.C.1: Many properties of atoms
exhibit periodic trends that are reflective of the periodicity of
electronic structure.
Essential knowledge 1.C.2: The currently accepted best
model of the atom is based on the quantum mechanical
model.
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Enduring understanding 1.D: Atoms are so
small that they are difficult to study directly;
atomic models are constructed to explain
experimental data on collections of atoms.
Essential knowledge 1.D.1: As is the case with all scientific models,
any model of the atom is subject to refinement and change in response
to new experimental results. In that sense, an atomic model is not
regarded as an exact description of the atom, but rather a theoretical
construct that fits a set of experimental data.
Essential knowledge 1.D.2: An early model of the atom stated that all
atoms of an element are identical. Mass spectrometry data
demonstrate evidence that contradicts this early model….e.g.
ISOTOPES!!!!
Essential knowledge 1.D.3: The interaction of electromagnetic
waves or light with matter is a powerful means to probe the structure
of atoms and molecules, and to measure their concentration. e.g. PES
and Spectrophotometry
Enduring understanding 1.E: Atoms are
Essential knowledge 1.E.1: Physical and chemical processes can be
conserved in physical and chemical processes. depicted symbolically; when this is done, the illustration must
conserve all atoms of all types.
Essential knowledge 1.E.2: Conservation of atoms makes it possible
to compute the masses of substances involved in physical and
chemical processes. Chemical processes result in the formation of
new substances, and the amount of these depends on the number and
the types and masses of elements in the reactants, as well as the
efficiency of the transformation.
Learning objective 1.1 The student can justify the observation that the ratio of the masses of the constituent elements in any pure sample of that
compound is always identical on the basis of the atomic molecular theory. [See SP 6.1; Essential knowledge 1.A.1]
Learning objective 1.2 The student is able to select and apply mathematical routines to mass data to identify or infer the composition of pure
substances and/or mixtures. [See SP 2.2; Essential knowledge 1.A.2]
Learning objective 1.3 The student is able to select and apply mathematical relationships to mass data in order to justify a claim regarding the
identity and/or estimated purity of a substance. [See SP 2.2, 6.1; Essential knowledge 1.A.2]
Learning objective 1.4 The student is able to connect the number of particles, moles, mass, and volume of substances to one another, both
qualitatively and quantitatively. [See SP 7.1; Essential knowledge 1.A.3]
Learning objective 1.5 The student is able to explain the distribution of electrons in an atom or ion based upon data. [See SP 1.5, 6.2; Essential
knowledge 1.B.1]
Learning objective 1.6 The student is able to analyze data relating to electron energies for patterns and relationships. [See SP 5.1; Essential
knowledge 1.B.1]
Learning objective 1.7 The student is able to describe the electronic structure of the atom, using PES data, ionization energy data, and/or
Coulomb’s law to construct explanations of how the energies of electrons within shells in atoms vary. [SP 5.1, 6.2; Essential knowledge 1.B.2]
Learning objective 1.8 The student is able to explain the distribution of electrons using Coulomb’s law to analyze measured energies. [See SP
6.2; Essential knowledge 1.B.2]
Learning objective 1.9 The student is able to predict and/or justify trends in atomic properties based on location on the periodic table and/or the
shell model. [See SP 6.4; Essential knowledge 1.C.1]
Learning objective 1.10 Students can justify with evidence the arrangement of the periodic table and can apply periodic properties to chemical
reactivity. [See SP 6.1; Essential knowledge 1.C.1]
Learning objective 1.11 The student can analyze data, based on periodicity and the properties of binary compounds, to identify patterns and
generate hypotheses related to the molecular design of compounds for which data are not supplied. [SP 3.1, 5.1; Essential knowledge 1.C.1]
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Learning objective 1.12 The student is able to explain why a given set of data suggests, or does not suggest, the need to refine the atomic model
from a classical shell model with the quantum mechanical model. [See SP 6.3; Essential knowledge 1.C.2]
Learning objective 1.13 Given information about a particular model of the atom, the student is able to determine if the model is consistent with
specified evidence. [See SP 5.3; Essential knowledge 1.D.1]
Learning objective 1.14 The student is able to use data from mass spectrometry to identify the elements and the masses of individual atoms of a
specific element. [See SP 1.4, 1.5; Essential knowledge 1.D.2]
Learning objective 1.15 The student can justify the selection of a particular type of spectroscopy to measure properties associated with vibrational
or electronic motions of molecules. [See SP 4.1, 6.4; Essential knowledge 1.D.3]
Learning objective 1.16 The student can design and/or interpret the results of an experiment regarding the absorption of light to determine the
concentration of an absorbing species in a solution. [See SP 4.2, 5.1; Essential knowledge 1.D.3]
Learning objective 1.17 The student is able to express the law of conservation of mass quantitatively and qualitatively using symbolic
representations and particulate drawings. [See SP 1.5; Essential knowledge 1.E.1]
Learning objective 1.18 The student is able to apply conservation of atoms to the rearrangement of atoms in various processes. [See SP 1.4;
Essential knowledge 1.E.2]
Learning objective 1.19 The student can design, and/or interpret data from, an experiment that uses gravimetric analysis to determine the
concentration of an analyte in a solution. [See SP 4.2, 5.1, 6.4; Essential knowledge 1.E.2]
Learning objective 1.20 The student can design, and/or interpret data from, an experiment that uses titration to determine the concentration of an
analyte in a solution. [See SP 4.2, 5.1, 6.4; Essential knowledge 1.E.2]
Review and Diagnostic Work …. http://www.bozemanscience.com/ap-chem-007-quantum-mechanical-model
Quantum Mechanics is essentially a theory developed to explain or to predict, as best as possible, the
behavior of light and atoms. Throughout this review section our goals will be, in part, to understand the
meaning and implications of a ground state configuration such as that for an atom of iron (Fe):
1s2 2s2 2p6 3s2 3p6 3d6 4s2 OR
[Ar] 3d6 4s2
First, study the following to review what is meant by principal energy level, sublevel, and orbital:
Superscripts indicate the number of e- occupying the orbitals of the specific sublevel
1s22s22p5
Large integers indicate the PEL (n)
Recall that every orbital can hold a
maximum of 2 e-, in opposite “spins”.
•Every s sublevel has 1 orbital.
•Every p sublevel has 3 (*degenerate) orbitals
•Every d sublevel has 5 (degenerate) orbitals
•Every f sublevel has 7 (degenerate) orbitals
the small-case letters represent sublevels
that are divided into orbitals, with e-
The Aufbau Diagram (listed here up to 5f)., helps
to place (configure) electrons, but does NOT help
to interpret the “why” of the configuration
1s
2s
3s
4s
5s
2p
3p 3d
4p 4d 4f
5p 5d 5f
*degenerate orbitals are orbitals equal in
energy to each other
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Here a few other ideas to keep in mind…. The following ideas are generalizations …
The total number of electrons in any Principle Energy Level (n) equals 2n2
Heisenberg Uncertainty Principle: We cannot know with certainty the position and the momentum of an
electron, simultaneously.
The Heisenberg Uncertainty Principle tosses out the idea of Bohr’s “orbits”, and replaces it with orbitals
Orbitals represent a shaped volume of space (thus, in essence, an energy) surrounding the nucleus.
An orbital may hold 0, 1 , or a maximum 2 electrons.
Aufbau Principle: Electrons are ordered (configured) from lowest energy levels to higher energy levels.
The diagonal rule (prior page) helps to explain the order of filling – but it is limited and
NOT absolute. There are exceptions to the Aufbau Principle, although these exceptions
are not tested on the AP exam.
Hund’s Rule: When a sublevel contains degenerate orbitals, electrons are configured into the orbitals, one
at a time, and are paired only when energy concerns become dominant.
Pauli Exclusion Principle: No two electrons may share the exact same quantum numbers – hence, when two
electrons occupy a single orbital, their spins are in opposition to each other.
Now, using the ground state electron configuration representing an atom of the element Fe0, with
26 electrons and thus 26 protons, answer the following questions a - n to the best of your abilities.
This is NOT graded. Ten of fourteen is outstanding … 7 of fourteen is solid…
1s2 2s2 2p6 3s2 3p6 3d6 4s2 OR
[Ar] 3d6 4s2
a. What is meant by “the ground state electron configuration” * The electrons are organized so that
they represent that order, at their lowest energy levels.
b. The element, will be found in period * 4
of the periodic table
c. Based solely upon the configuration Fe, a transition metal (hint) is in group *8
periodic table
of the
d. Based upon the configuration, iron is a member of the family called the *transition metals
you can infer this because of the configuration’s * incomplete d sublevel
e. The atom appears to have * 4
(a number) incomplete or half-filled orbitals, in the ground state
f. The first two electrons used in bonding are probably from the *4s
oxidation state of 2+
sublevel, creating an
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g. The oxidation state of 3+ is a possibility, due to the possibility that *one 3d electron can be
used/lost
h. The electron configuration of the 2+ oxidation state species is: * [Ar] 3d6
i. The electron configuration of the 3+ oxidation state species is: *[Ar] 3d5
j. The atom has electron shells completely filled up through the *2nd
level.
k. The configuration implies that while occupied, the * 3rd and 4th
NOT filled.
principal energy
principal energy levels are
l. The loss of the 4s2 electrons is best explained in that these electrons (select one)
*ii)
i) are the least shielded electrons from the nuclear attractive force, thus are held more tightly
to the nucleus
ii) experience the greatest shielding effect, relative to the nuclear attractive force, and are
bound less tightly to the nucleus
iii) are the only possible electrons to form bonds due to their excessively low level of
energy, relative to the rest of the electrons of the atom
iv) provides the resulting ion with a stable valence octet
m. The arrangement of the 3 d electrons: 3d ↑↓ ↑ ↑ ↑ ↑
with multiple inner d electrons exhibiting similar spins suggests that iron
i)
ii)
iii)
iv)
Keep Going….
*iv
is more easily oxidized than atoms of sodium
has a greater electronegativity than atoms of sulfur
can be easily melted
exhibits (ferro)magnetism
n. As electrons are removed from the 4s and then from the 3d sublevel of an iron atom which of
the following occurs?
e.g.) as Fe4+ is formed from Fe3+
*iv
i) the radius of the resulting ion becomes smaller
ii) the ionization energy required for the removal of the next electron is greater
iii) the tendency to attract electrons increases
iv) all of the above
ASSIGNMENT: Seriously check out Bozeman Science … a favorite http://www.youtube.com/watch?v=2AFPfg0Como
It is 10 minutes well spent….it will introduce you to Coulomb’s Law and remind you of all you have learned
from last year… It will begin to blend quantum and periodic trends.
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I) Energy can travel through space by electromagnetic radiation, which are those forms of energy represented
on the electromagnetic spectrum. All forms travel at the speed of light (in a vacuum) and exhibit a similar
type of wavelike behavior; with wavelength, frequency and amplitude.
All forms of electromagnetic radiation exhibit: wavelength (λ), frequency (ѵ measured in Hertz), and speed.
Wavelength is just that …when measured from crest to crest or trough to trough
Frequency is the number of cycles or waves per second that pass a given point in space. Small
wavelength radiation has a high frequency; longer wavelength radiation has a lower frequency. This
inverse relationship is expressed as: λѵ = c Where c is the speed of light in a vacuum. This equation
is on your reference tables.
You can compare the relationships by studying the following diagrams from Zumdahl (p 297)
A) Keep in mind: shorter wavelengths = greater frequencies (a greater number of waves occur in 1 sec = greater
frequency, but that must equate to a smaller wavelength)
longer wavelengths = lower frequencies
Recall: Converting from Hertz (Hz) to Megahertz (MHz), using Dimensional Analysis:
1) conversion factor:
1 megahertz (MHz) = 1 x 106 (or 1 million hertz)
2) Microwaves have a frequency of 2.5 x 109 Hz. Use dimensional analysis to calculate the
equivalent of that frequency in MHz
MHz = * 2.5 x 109 Hz | 1 MHz | = 2.5 x 103 MHz
1 x 106
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3) Max Planck, the grandmaster of quantum, found, in the very late 19th century that:

energy is quantized, and can only occur in whole number units equal to hѵ … See the
work on standing waves and Schrodinger / De Broglie (about pages 515-16)

where h is known as Planck’s constant of 6.626 x 10-34 J•s.

Each small unit of exchanged energy was called a quantum. (plural = quanta)

Energy must be transferred in whole “packets”… thus energy has some commonality
to “particle” behavior as well as wave properties!
(This is on your tables)
B) Enter Einstein and the Photoelectric Effect …Einstein embraces Planck’s work:
1) Einstein assumed that the radiant energy striking a metal surface behaves like a stream of tiny
packets of energy … He called these quanta of energy: photons.
Using Planck’s work (and constant) he determined that a minimum frequency of light,
different for different metals is required for to kick off (or emit) electrons. For instance, that
frequency of light which will cause cesium metal to emit electrons must be equal to or greater
than 4.60 x 1014s-1
Thus, electromagnetic radiation is itself quantized and can be seen as a stream of particles
called photons. The energy of a photon is directly proportional to its frequency …
2) Ephoton = hc
λ
Where:
E = the energy of the EM radiation
c = 2.998 x 108 m/s
h = 6.626 x 10-34 J•s (Planck’s constant)
λ = the wavelength of EM radiation in meters
e.g.) What is the energy of blue light with a wavelength of 450.0 nanometer?
Where 1 nanometer = 1 x 10-9 meter
a) Convert to meters:
meters = *450.0 nm | 1 x 10-9 m | =4.50 x 10-7 meter
1 nm
b) Then use the equation:
E = hc
λ
-34
* E = (6.626 x 10 J•s )( 2.998 x 108 m/s) = 4.41 x 10-19J
4.50 x 10-7 m

EM radiation can be reflected (bounced off something, like a silver mirror), refracted
(as it passes through water …it can become bent)

Humans can generally detect, visually the wavelengths in the visible spectrum (700 nm
to 400 nm)
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
Humans and other organisms (e.g honey bees) can also detect UV radiation (Humans
cannot see UV light, but bio-molecules (DNA) can react to it….therefore detect it,
passively) Also certain drugs taken internally (e.g. tetracycline) or applied externally
(salicylic acid) can absorb UV radiation, and then releases it into the skin, killing
cells. This is why those using acne medications, must be careful about sun exposure
Salicylic acid
TRY THIS!!!
Brown & Lemay 216
a.k.a 2-hydroxybenzoic acid: a beta-hydroxy acid
essentially, helps to remove or the outer skin layer
(the epidermis) which absorbs the vast amount of UV
radiation) revealing the far more sensitive dermis
layer to the power of UV. It additionally can absorb UV
radiation, creating skin cell death.

The colors of a butterfly are due in large part to specialized protein structures,
trapping or bending light interacting with those protein structures.

EMS radiation can also interact with the electrons of the atoms, and thus the bonds
made between atoms, by the sharing or transfer of electrons.

Think of a fairly simplified means of explaining the color of a blouse or shirt or the
changing colors of leaves, in the autumn.
The yellow light given off by a sodium vapor lamp used for public lighting, and those lamps
found along the highway, has a wavelength of 589 nm.
a) What is the frequency of this radiation?
*convert to meters: meters = 589 nm| 1 x 10-9 m |
1 nm
*use: λѵ = c or:
ѵ = c/λ
*ѵ = (2.998 x 108 m/s) = 5.09 x 1014
5.89 x 10-7 m
Hint1: *Convert nm to meters.
Hint 2: *You are asked for
frequency, and given
wavelength. You know of an
equation using both variables …
It is in your reference tables.
ans: 5.09 x 10
b) What is the most correct unit for the answer? *s-1
Assignment: Read over, in Brown and LeMay p. 219-23 … Line Spectra and the Bohr Model
For Fun: The Big Bang Theory: Schrodinger’s Cat: https://www.youtube.com/watch?v=pNTMYNj2Ulk
It’s pretty right on track ….a nice “every person’s” explanation.
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II) Enter: Werner Heisenberg and The Uncertainty Principle: When applied to the electrons in an atom,
the Uncertainty principle states that it is impossible for us to know simultaneously both the exact momentum
of an electron and its exact location in space.
A) Your Brown and LeMay text runs you through a neat little calculation on page 225. It shows that
the level of uncertainty in position for an electron in a H atom is 1 x 10-9 m
Given that the diameter of a hydrogen atom is about 1 x 10-10 m, you will note that the uncertainty
factor is greater than the diameter of the atom! Hence …we are clueless as to the location.
1) Between Louis De Broglie’s wave-particle duality concept (Nobel Prize in 1929), and
Heisenberg’s Uncertainty Principle (Nobel Prize in 1932), Erwin Schrodinger’s wavefunction equation and Paul Dirac’s re-working of it to meet relativistic issues (resulting in a
shared Nobel Prize in 1933) … the wave nature of the electron is embraced … & we begin to
speak of the energy of the electron while describing its location, in terms of probabilities.
Exit, Einstein.
II) Atomic Orbitals: Due to the inferences made using the Uncertainty Principle, we can’t identify the exact
location of an individual electron around the nucleus to which it is bound.
We speak therefore of the probability of an electron being in a region of space around
the nucleus ….
A) (psi)2 or ψ2 = probability distribution (or electron density), represents the probability that an
electron will be found in a region of space.
B) The solution of the Schrodinger equation
does not give us a line …as we might assume.
Rather it gives us a set of wave functions which
describe the e- bound to a specific nucleus
ψ (psi) represents a wave function and ψ2 provides
information about the e-‘s location when it is
in an allowed energy state.
Think of these diagrams as a stop-motion
set of photos envisioning in 3D the travels of an eThe term, atomic orbital, is often envisioned
in this manner.
Brown & Lemay p 227
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C) De Broglie and Schrodinger treated the electron in a hydrogen atom like a standing wave.
(one that does not travel through space)
The oft used analogy is a plucked guitar string. … The plucked guitar string produces a
standing wave that has a fundamental frequency and higher overtones … Schrodinger
envisioned something similar for the electron … which exhibits both a lowest-energy
standing wave, and higher energy ones. There are also NODES … where the magnitude
of the wave is zero … meaning that there is a 0 probability of finding the electron.
Nodes and Standing Waves (Brown and LeMay p 226)
I have used the example of a rope tied to a tree in the past:
https://joulespersecond.wordpress.com/
Check out: https://www.allaboutcircuits.com/textbook/semiconductors/chpt-2/quantum-physics/
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Another means of visualizing the electron as “standing wave”
String vibrating at resonant frequency between two fixed points forms standing wave.
The atom according to de Broglie consisted of electrons existing as standing waves, a phenomenon well
known to physicists in a variety of forms. As the plucked string of a musical instrument (Figure above)
vibrating at a resonant frequency, with “nodes” and “antinodes” at stable positions along its length.
De Broglie envisioned electrons around atoms standing as waves bent around a circle as in Figure below.
“Orbiting” electron as standing wave around the nucleus, (a) two cycles per orbit, (b) three cycles per orbit.
Electrons only could exist in certain, definite “orbits” around the nucleus because those were the only
distances where the wave ends would match. In any other radius, the wave should destructively interfere
with itself and thus cease to exist.
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There are other means by which this is envisioned. We may “see” it as a radial probability
distribution
Most
probable
distance
from the
nucleus.
Zumdahl 9th ed. p. 312
Check out: YouTube: Cassiopeia Project segment on radial probability: http://www.youtube.com/watch?v=Fw6dI7cguCg&feature=related
More Cassiopeia Project https://www.youtube.com/watch?v=n4LnvLAjmcU At 12 minutes (Bohr Model), 16 min de Broglie
18 min Heisenberg, particle as wave: 20 min, Schrodinger 21.30, Heisenberg and radial probability 23 min, spin 29 min
III) Quantum Numbers: n, ℓ, mℓ, ms
A) The solution to the Schrodinger equation for the hydrogen atom yields a set of wave functions called
ORBITALS (not orbits …as in the Bohr Model)

*each orbital has a characteristic shape and energy
1) The quantum mechanical model uses 3 quantum numbers n, l, ml to describe an orbital.

a 4th quantum number ms is used to describe the intrinsic property of the electron(s) of an
orbital. This property is electron spin … we’ll see this when we re-visit the Pauli
Exclusion Principle
2) The 3 quantum numbers used to describe the orbital are:
a) n = principal quantum number
i) n may equal positive integral values of 1, 2, 3, 4…

as n increases the orbital becomes larger and the electron spends more
time farther from the nucleus.

as n increases, the electron has a higher energy and is therefore *less
tightly bound to the nucleus.
b) l = angular (azimuthal) momentum quantum number.
i) l may have integral values from 0 to (n-l), for each value of n.

l defines the *shape of the orbital.

the value of l is generally designated by the letters s, p, d, f which
correspond to l values of 0, 1, 2 and 3 … or rather 0 to n-1
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Hence:
value of l 0 1 2 3 4 5
symbol
s p d f g h
c) mℓ = magnetic quantum number with integral values between – l to l, including 0

This quantum number indicates the orbital’s orientation in space
3) The collection of orbitals with the same value of n is called an electron shell.
The set of orbitals that have the same n and l values is called a subshell … designated by
an integer for n and a letter (s, p, d, f) for l
SUMMARY OF QUANTUM NUMBERS:
In essence for quantum number work: n = 1 -7
l = 0 to (n-1) I have memorized: where s = 0, p = 1, d = 2, f = 3
mℓ = - l to l
ms = ½ or -½
Quantum Numbers
Name
Designation Property of the Orbital
Related to the size and energy of the orbital
Principal quantum number
n
May be any positive integer 1, 2, 3, 4, ….
Related to the shape of the orbital (s, p, d, f)
Angular momentum quantum number
l
Magnetic quantum number
Electron spin quantum number
ml
ms
Related to the position of the orbital in space
in relation to other orbitals.
For instance, this deals with px, py, pz or those positions
related with the d sublevel and/or f sublevel.
Related to the spin of the electron, which can be only
one of two values +1/2 or -1/2
Based essentially in the Pauli exclusion principle.
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SUMMARY OF ALLOWED QUANTUM NUMBERS
n
l
ml
1 0
0
2 0
0
1
-1, 0, +1
3 0
0
1
-1, 0, +1
2
-2, -1, 0, +1, +2
4 0
0
1
-1, 0, +1
2
-2, -1, 0, +1, +2
3 -3, -2, -1, 0, +1, +2, +3
Number of
orbitals
Orbital
Name
Number of
electrons
1
1
3
1
3
5
1
3
5
7
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
2
2
6
2
6
10
2
6
10
14
http://www.angelo.edu/faculty/kboudrea/general/quantum_numbers/Quantum_Numbers.htm
For a very nice summary (with practice problems) on quantum numbers try:
I also really like:
https://www.youtube.com/watch?v=kS-U0R3Kx8E
https://www.allaboutcircuits.com/textbook/semiconductors/chpt-2/quantum-physics/
Reading: Take a look at the table and readings on page 229 of your Brown and LeMay text, for more.
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IV) Representations of Orbitals:
A) You’ll recall from Honors, that every s subshell is spherical … differing in volume, as we move
from 1s to 2s to 3s ….
http://www.dlt.ncssm.edu/tiger/diagrams/structure/s-orbitals_3-up.jpg
B) No one will forget the “dumbbell” shaped p orbitals traveling oriented along the x, y, z axes.
surface boundary representation
3 possible "p" orbitals and orientation in space
Probability Distributions
http://wps.prenhall.com/wps/media/objects/724/741576/Instructor_Resources/Chapter_01/Text_Images/FG01_0139UN.JPG
https://www2.bwdsb.on.ca/~f_schlenker/4U/4U%20quantum%20chemistry/university%20website/imgres_files/a.htm
http://upload.wikimedia.org/wikipedia/commons/1/1b/Eixos.jpg
http://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Px_py_pz_orbitals.png/525px-Px_py_pz_orbitals.png
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Shapes of three of the five d orbitals
Checkout!!
YouTube: http://www.youtube.com/watch?v=45KGS1Ro-sc
Synthesis of Bohr/Heisenberg Particles with Schrodinger Waves
YouTube: https://www.youtube.com/watch?v=F-xLQ1WBIlQ
Shape of orbitals (not bad! …narration is a bit tougher, but good)
YouTube: http://www.youtube.com/watch?v=VfBcfYR1VQo
Shape of s, p
YouTube: http://www.youtube.com/watch?v=sMt5Dcex0kg
Scandium configuration
Assignment: Take about 20 minutes to go through the
4 video clips from YouTube … just to re-familiarize
yourself with the general concepts.
Assignment: Get to page 231 of the text and read over
pages 230 (bottom of) – 231. Try the “Go Figure”. It is
a nice little exercise in analysis … nothing grand … the
answer is on page A-39.
C) Remember that the electrons of any “p” sublevel are equal in energy to each other… That is
they are degenerate.
1) Orbitals which are degenerate are those of a common subshell … having the same energy.
Hence the orbitals of 2p are degenerate. The orbitals of 3d are degenerate.
2) This holds true for the electrons of a specific “d” or “f” sublevel as well.
3) If we get to the Actinides and Lanthanides … we’ll see that configuration into the d and f
sublevels play a significant role…. Mind you … it is one of the reasons as to why those
elements have been pulled out of the main table.
* e.g. Lanthanide series: Period 6: 6s2 stabilizes while 4f is filled (or rarely 5d..Ce, Gd, Lu)
521
D) Up to now your text has dealt exclusively with hydrogen atoms … but many-electron atoms have
a few twists and turns worth reviewing. There are NO SURPRISES here … It may be worded a bit
more formally than that to which we are familiar … but it is all the same tune….

In a many-electron atom, for a given value of n, the energy of an orbital increase with
increasing value of l… e.g. 3s < 3p < 3d. The CONVERSE of this idea may be used to
help explain the ionization (or oxidation) of species … in that we must recognize that
electrons that are closer to the nucleus experience greater coulombic forces of attraction
and therefore require more energy to be removed.

In a hydrogen atom the energy of an orbital depends only on n … but in many-electron
atoms, there is electron – electron repulsion (leading to shielding effect) … and this
repulsion leads to the various sublevels being different in terms of energy.
E) Pauli Exclusion Principle (ms) Recall that a moving charge creates a magnetic field … and e- have
“spin”
Essentially, no 2 e- may have all 4 quantum numbers, exactly the same) AND * have the same
same directional spin. So the 2 e- of any single orbital must have opposite spins.
(Translation: When 2 e- occupy the same orbital they must have opposite “spins” because
this lessens the effects of the magnetic fields developed by moving charges
1) However, it is important to note that this pairing is not as stable a lone e-, because paired
(correlated) electrons have more energy, than unpaired eAccording to Pauli, electrons of “like spin” tend to get as far from each other as
is possible. This concept has been the most influential factor in determining
the shapes and properties of molecules. Organic Chemistry Morrison & Boyd 3 ed p 8 (see Lewis Structures Unit 5)
rd
let : 1 e- be symbolized by or so a filled orbital = 
or a filled orbital =

2) But, the Pauli Exclusion Principle is the basis for our belief that an orbital may only hold a
maximum of 2 electrons.
a) For a given orbital, the values of n, l ml are fixed. If we want to put more than one
electron in an orbital and satisfy the Pauli Exclusion Principle, we must assign a
different ms value (-1/2 or +1/2). There IS NOT THIRD OPTION! Hence an orbital
can only hold a maximum of two electrons.
522
3) The Pauli Exclusion Principle answers one of the more basic questions of physics,
chemistry & biology: Why does matter have volume? First, there are 2 types of
fundamental particles:
Fermions and
Bosons
spin: odd half integral spin 1/2, 3/2
spin: whole integral spin 0,1,2
Characteristics: may be elementary or
composite particles but, only 1 can exist per
quantum state ... Obey Dirac-Fermi Equations
and Pauli Exclusion Principle
Characteristics: may be elementary or
composite particles but, many may occur in the
same quantum states (which helps explains,
lasers, for instance) ... Obey Bose-Einstein
equations and do NOT obey Pauli Exclusion
Principle
e.g.) quarks, electrons, protons, neutrons,
neutrinos, and nuclei with an odd number of
fermions like a nucleus of 7Li)
e.g.) all force carriers, like photons & gluons
citations: Look up these for more information....
http://www.particleadventure.org/fermibos.html
http://en.wikipedia.org/wiki/Boson
http://www.pa.msu.edu/courses/1997spring/phy232/lectures/atomic/bosons.html
http://sciencepark.etacude.com/particle/forces2.php
eg.) mesons, any nucleus with an even number
of fermions like 4He or 12C.
Thus: Matter has volume (but energy does not) because...
... Photons are bosons, not fermions, and as such do not obey the Pauli Exclusion Principle. They can and do
travel "through" other photons. Fermions are particles such as Protons, Neutrons, and Electrons. The exclusion
principle describes the observation that no two of those particles can occupy the same spot in space AND have the
same Quantum Numbers. (Which describe the properties of each particle, such as energy level and spin) It is a
direct result of that principle that matter has volume. Most of the atoms that make up all matter is simply
empty space. It only has volume because the electrons cannot occupy the same spots and cannot get close to the
nucleus on average. http://www.physicsforums.com/showthread.php?t=513639
4) (I believe) ... by 1924 - 1926 Pauli had used such results to develop what is now called the
Exclusion Principle. The Exclusion Principle directly underpins the construction of
the periodic table. It is that important to chemistry...
5) Around 1930 Pauli proposed the existence of the neutrino.
The neutrino as a fundamental particle was confirmed in 1956, by Reines and Cowan.
Professor Charles P Enz was Pauli's last research assistant and his biographer. According to
Enz's book, No Time To Be Brief when Pauli was written with the news confirming the
existence of the neutrino, Pauli cabled back:
"Thanks for message. Everything comes to him who knows how to wait. Pauli."
6) Pauli was awarded the Nobel Prize in Physics for his contributions to the field in 1945
523
F) Hund's Rule: When accounting for the e- in sublevels with multiple orbitals the electrons fill each
orbital one at a time and then pair up using Pauli Exclusion Principle (Bus Rule)
p _____ ______ _______
not
p ______ _______ _______
1) In sublevels with multiple orbitals (such as : p,d,f) , the orbitals of the sublevel are ...
degenerate (equal in energy) (e.g. px energy = py energy = pz energy ) thus, making the electrons
of those orbitals of the specific sublevel EQUAL in energy to each other.
a) e.g. the electrons of 2px  2py  2pz  .
are equal in energy to each other
2) Translation: My friend Elaine Battaglino explained this using the Battaglino Bus Rule:
When boarding a bus, all the seats are equal, and passengers fill seats of equal energy
one at a time... and double up only when each seat has one passenger already (but the
second passenger/seat must sit upside down to obey the Pauli Exclusion Principle :-)
Or, you could look at it like a movie theater... All the seats (orbitals) of a specific row
(sublevel) in a movie theater give you the same view (have equal energy).
3) According to Hund:
A symmetric spin state (multiple electrons in separate orbitals) forces an anti-symmetric
spatial state (e.g. the different spatial directions of x,y,z) where the electrons are on
average further apart and provide less shielding for each other, yielding a lower energy.
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
a) What Hund was stating is very important...The electrons entering a degenerate
sublevel (a sublevel containing more than one orbital (like p,d,f sublevels)), will have
THE MOST STABLE arrangement when the electrons occupy the orbitals singly,
rather than in pairs.
4) The lessening of this shielding effect becomes important in our next unit ... But essentially, a
lesser (lower) shielding effect, helps to stabilize an atom
a) Shielding effect the interference for the nucleus’s pull on a valence electron, due to
the "inner (or core) electrons". The lessening of the shielding effect, (that is, allowing
the nucleus to attract the electron as maximally as possible) creates a more stable
electron configuration and greater chemical stability, because the electron(s) is/are at
lower energy
524
H) Condensed Quantum Electron Configurations
Recall that there are the inner (core) electrons and the outer valence electrons. We are beginning
to see that the valence electrons are NOT the only electrons that can take part in a chemical
reactions … Rather, with the transition metals especially, it is not uncommon to see the inner d
electrons play some sort of role in bonding.
What then, are the valence electrons? Frankly and simply, valence electrons are the outermost
electrons. In the case of transition metals, the valence electrons and the inner d electrons can be
very close in energy to each other.
The inner core electrons comprise the levels of electron configuration equal to the noble gas
prior to the element. For instance, when dealing with iron, as we did in our diagnostic:
1s2 2s2 2p6 3s2 3p6 3d6 4s2 OR
[Ar] 3d6 4s2
The core configuration is that of argon … the noble gas capping Period 3, and built upon for
iron, found in period 4.
Hence for ruthenium, in period 5 and just below iron, it is not surprising to see the configuration
abbreviated as: [Kr] 4d7 5s1
Ru atoms have the same e- configuration up to an atom of Krypton, but extends beyond the
stable octet of krypton, to the 4d and 5s sublevel.
Now, because configurations can become so long ... we often abbreviate a configuration, by
using the symbol of the noble gas of the element's prior period ... and then finish up
the configuration with inner d (or f electrons), and of course, the valence electrons in an
"s" or "s and p" set of orbitals.
TRY THIS!!!: Use only your periodic table and your grasp of the concepts. You may use the condensed
configuration (or not) …
1) Write the ground state electron configuration for an atom of titanium (atomic # 22)
*1s2 2s22p6 3s23p63d2 4s2 or [Ar] 3d2 4s2
2) Write the electron configuration for an atom of nickel (atomic # 28)
*1s2 2s22p6 3s23p63d8 4s2 or [Ar] 3d8 4s2
3) Write the electron configuration for an atom of zinc (atomic #30)
*1s2 2s22p6 3s23p63d10 4s2
or [Ar] 3d10 4s2
a) Zinc will react with Cl2 to produce ZnCl2. From which sublevel are the electrons of zinc
most likely lost? *4s
525
TRY THIS!!!
Condensed Configurations for the Alkaline-Earth Metals
Alkaline- Earth Symbol Atomic
Electron Configuration
Number
Using the Condensed Method
Beryllium
Be
4
[He] 2s2 Be has the inner core of He plus 2s2
Magnesium
Mg
12
[Ne] 3s2 Mg has the inner core of Ne, plus 3s2
Calcium
Ca
20
[Ar] 4s2
Strontium
Sr
38
[Kr] 5s2
Barium
Ba
56
[Xe] 6s2
Radium
Ra
88
[Rn] 7s2
1) When given the ground state configuration: [Rn] 5f 36d1 7s2 the atom is of the element: *uranium
2) When given the ground state configuration: [Ar] 3d10 4s2 4p5 the atom is of the element *bromine
3) When given the ground state configuration: [He] 2s2 2p5 the atom is of the element *fluorine
4) When given the ground state configuration: [Ar] 3d10 4s1 the atom is of the element *copper
5) When given the ground state configuration: [Ne] 3s2 3p4 the atom is of the element *sulfur
answers: uranium, bromine, fluorine, copper, sulfur
H) Quantum Odds & Ends:
Before we begin to actually interpret configurations I want to re-state that the Aufbau Principle is great
and handy for writing configurations, but it really does not help explain some of the seeming
inconsistencies. (Remind me, to discuss Cr vs. W. There’s a mind-bender!!...or you can let Dr E Scerri
do it, when you tackle one of the references)
For anyone interested in going further I would like to suggest a slow, studied read of the following, and
of a few of the provided references.
Quantum theory shows that each atom's electronic structure is a unique compromise between several
different effects. Electronic configurations of the fourth period elements can be appreciated by
considering these effects. These issues surround what I have already included in your notes.
Inconsistencies can be explained by connecting (yet recognizing them as competing) ideas such as:
lessening of shielding effect (or increasing ENC)
the relative restrictive pathways of some sublevels (like d) compared to the more “open” s,
the natural closeness in energies of some sublevels (such as 3d and 4s), along with the fact that the
sublevels shift positions (and thus change in their energies), as the effects of added electrons are
exhibited. Recall … subshells start repelling each other, generating a shielding effect and this
affects the energies of the subshells!!!
Check out:
http://employees.oneonta.edu/viningwj/sims/atomic_electron_configurations_s1.html
526
Or, according to Dr. Fred Senese: http://antoine.frostburg.edu/chem/senese/101/electrons/faq/4s-3d.shtml
Raising n raises orbital energy. Electrons are attracted to the nucleus. To pull an electron farther away
from the nucleus, you have to work against that attraction. That means an electron farther from the
nucleus has more energy than electron closer in; energy is required to move the electron out, and energy
can be released when the electron moves in. So we expect outer shells to have higher energies than inner
shells, because increasing n increases the average distance between the nucleus and the electron.
For atoms heavier than copper this effect dominates, and 4s electrons have higher energy than 3d
electrons.
Raising l raises orbital energy. Higher l values result in orbitals with more nuclear nodes (a node
being a place where the probability of finding the electron is zero). We say high-l orbitals are "less
penetrating" because their electrons have a lower probability of being found at or near the nucleus. That
gives high-l orbitals (like d orbitals) more energy than low- l orbitals (like s orbitals) within the same
shell.
This effect causes 4s orbitals to have lower energy than 3d orbitals for elements lighter than copper.
(Although for hydrogen, the unoccupied 4s and 3d orbitals have nearly identical energies).
Within a subshell, more unpaired spins means a lower overall energy. Quantum mechanics predicts
that the motions of electrons with paired spins are "correlated". Paired electrons move together, while
electrons with unpaired spins can stay farther away from each other on average. Since electrons repel
each other, paired electrons have more energy than unpaired electrons, all other things being equal. This
spin correlation effect explains why Cr has a [Ar] 4s13d5 configuration rather than a [Ar]4s23d4
configuration- the former has more unpaired electron interactions than the latter.
Other references are:
1) http://www.chemguide.co.uk/atoms/properties/3d4sproblem.html
2) http://ericscerri.blogspot.com/2012/06/trouble-with-using-aufbau-to-find.html
3) http://crescentok.com/staff/jaskew/ISR/chemistry/class4.htm
4) W. H. Eugen Schwarz: The Full Story of the Electron Configurations of the Transition Elements: Journal of Chemical
Education, Vol. 87 No. 4 April 2010 (copies available)
5) R. N. Keller: Textbook errors Energy Level Diagrams and Extranuclear Building of the Elements: J. Chem. Educ., 1962,
39 (6), p 289, published June 1962) (copies available)
6) Quantum numbers and Orbital diagrams: https://www.youtube.com/watch?v=nexoMIZK7cE
For a peak at the de Broglie-Bohm model, check out: http://www.spaceandmotion.com/Physics-DavidBohm-Holographic-Universe.htm and look at the section called Bohmian Mechanics.
527
V) Writing Ground State Configurations (Note, in AP Chemistry e- configurations are NOT on your tables)
DIRECTIONS: I have asked a number of questions which will require you to interpret and re-write a number of orbital
notations.
Diagonal Rule (Aufbau)
7s
6s
5s
4s
3s
2s
1s
7p
6p
5p
4p
3p
2p
7d
6d
5d
4d
3d
7f
6f
5f
4f
For questions 1 - 5 use the orbital configuration: 1s22s22p63s23p4
You may re-write it like this ...
(re-write the configuration, using the "arrows" first)
or like this vertical design
1s _____ 2s _____ 2p _____ _____ _____ 3s _____ 3p _____ _____ _____
low energy
high energy
_____ 1. What is the total number of electrons found in this atom?
_____ 2. Which principal energy level is considered
the valence principal energy level ?
_____ 3. How many electrons are in the
valence principal energy level?
_____ 4. How many orbitals are only half - filled?
_____ 5. How many sublevels are filled completely?
http://www.nlcs.k12.in.us/bnlhs/staff/coy/notes/c1notes/l32.pdf
For questions 6 - 12 use the orbital configuration: 1s22s22p63s23p63d34s2
1s ___ 2s ___ 2p ___ ___ ___ 3s ___ 3p ___ ___ ___ 3d ___ ___ ___ ___ ___ 4s ___
low energy
high energy
_____ 6. What is the total number of electrons found in this atom?
_____ 7. Which principal energy level is considered
the valence principal energy level ?
_____ 8. How many electrons are in the
valence principal energy level?
_____ 9. How many orbitals are half - filled?
_____ 10. How many sublevels are filled completely?
_____ 11. What is the group number in which
this element is found?
_____ 12. In what period of the periodic table is this element found?
528
For questions 13-20 use the orbital configuration:
1s22s22p63s23p63d104s24p3
1s ___ 2s ___ 2p ___ ___ ___ 3s ___ 3p ___ ___ ___ 3d ___ ___ ___ ___ ___ 4s ___ 4p ___ ___ ___
low energy
high energy
_____ 13. What is the total number of electrons found in this atom?
_____ 14. Which principal energy level is considered
the valence principal energy level ?
_____ 15. How many electrons are in the
valence principal energy level?
_____ 16. How many orbitals are only half - filled?
_____ 17. How many sublevels are filled completely?
_____ 18. The above atom is representative of
which element ? (Write the symbol)
_____ 19. What is the group number in which
this element is found?
_____ 20. In what period of the periodic table
is this element found?
529
VI) Periodic Table and Wave-Mechanic Model
A) Using quantum, the elements are organized, beyond groups and periods, into "blocks". The block
of an element is determined by the last orbital to be used to configure an electron. That is, the block
corresponds to the angular momentum quantum number (l)
1) Now, don't confuse the "block"-designation with the valence level. Recall Aufbau...
For instance, it is accurate to say that the s-block elements do have a Valence Principal
Energy Level with an s sublevel e.g. Lithium: 1s  2s 
The p block elements do indeed have s and p orbitals in the Valence Principal Energy
Level .... eg.) Fluorine: 1s  2s  2p   
However, while the transition metals are in the d block, they have a valence level with an
s sublevel. . . BUT, the last configured electron(s) go into an orbital of a d sublevel
e.g.) Iron: [Ar] 3d      4s 
these are the last to be configured
BUT!! These are the valence e-
s block
p block
d block
f block
http://www.mikeblaber.org/oldwine/chm1045/notes/Struct/EPeriod/Struct09.htm
2) As stated by Dr. Fred Senese at http://antoine.frostburg.edu/chem/senese/101/periodic/
Each block contains a number of columns equal to the number of electrons that can occupy that sublevel
The s-block has 2 columns, because a maximum of 2 electrons can occupy the single orbital
The p-block has 6 columns, because a maximum of 6 electrons can occupy the three p orbitals
The d-block has 10 columns, because a maximum of 10 electrons can occupy the five d orbitals.
The f-block has 14 columns, because a maximum of 14 electrons of the seven orbitals in a f-sublevel.
530
VII) Quantum helps to answer questions regarding a number of topics: from magnetism to chemical reactivity
to the natural production of (or lack thereof) certain ions.
A) For example:





How is iron seen as being ferromagnetic ... but copper, is not?
Why is sulfur more chemically stable as an anion, of S2-, than as an atom, S0?
How do we explain carbon atoms making 4 equal covalent bonds to atoms such as H, and not
just two?
What seems to be the explanation for multiple oxidation states of some transition metals,
such as Fe3+ ions and Fe2+ but only on stable oxidation state of sodium ion, Na1+?
We have evidence of Na1+ & Mg2+ cations, but why is there so little evidence of Mg1+ ions?
B) Quantum can help explain phenomena that are related to far more difficult questions such as:





Why is mercury, in the liquid phase, at STP?
How can we account for the non-white (non-silver) color of solid gold and the (lesser, but
still evident) golden-hue of metallic cesium?
How can we account for the smaller-than-predicted atomic radii of francium and radium?
Why is gold so resistant to oxidation?
Why is lead metal (group 14), not found in tetrahedral crystals, like carbon (diamonds)?
First, recognize that the chemical and physical properties of any atom is due to the energies and spatial
distributions of the electrons, of the atom.
Secondly, as atoms become larger in nuclear charge, Einstein's Theory of Special Relativity can be
employed to explain certain issues. To this end, we need to assume two issues:
 Special Relativity states that the mass of any moving object changes as its velocity changes! Under most
"normal" circumstances, this velocity is so small that any relativistic issues are minimal (ridiculously
so...), thus elements of Periods 1 -4 are really not an issue. (Thayer J. Chem. Educ., 2005, 82 (11)
 As the mass of the atoms increases (as with the atoms of the elements in periods 6 and 7), the velocity
of the electrons increases to far more important levels, approaching the speed of light. (To help
simplify the issue, recall that Bohr showed that all electrons exist around a nucleus in the same amount
of time, thus supporting the idea that valence electrons have greater kinetic (and potential energies.
Perhaps a more sophisticated and correct view is that the standing waves of the electrons are exhibited
around the nucleus simultaneously). Anyway, with the increase in mass relativistic causations /
explanations of main group chemistry are valuable.
The relativistic effects are not explained by solutions to the Schrodinger Equation(s). It was Paul Dirac
that added or adjusted the equations to deal with these relativistic issues of the very heavy atoms (with,
perhaps the initiating force of Wolfgang Pauli...but that is debated). The following page addresses only
a few specific issues - but it hopefully offers you enough intriguing thoughts to see why some men and
women just love this field.
As a bit of advice... keep this mind: When considering the relativistic effects, I think there is a domino
effect essentially ... I am sometimes lost in a "which came first chicken/egg” issue. This is evidenced
in the following ideas that the velocity of electrons increase, causing shrinkage of orbitals in terms of
the s and p, and size increases at the d and f ...etc. To start putting these ideas together, read on…
531
The relativistic phenomena exist primarily due to a large nuclear charge, causing an increase in electron
velocity. Thus, a nucleus with a large charge (lots of protons) will cause an electron to have a high velocity.
A higher electron velocity means an increased electron relativistic mass, as a result the electrons will be
near the nucleus more of the time and thereby contract the radius for the smaller principal energy levels
(e.g... n =1,2). http://en.wikipedia.org/wiki/Relativistic_quantum_chemistry
When we begin to look at the electrons of these Period 6 species, the velocity of the "s" electrons are
approaching 58% of the speed of light. At such terrific velocities a few things occur:
 s-orbitals decrease substantially in energy as do the p-orbitals (but to a lesser extent) & this decrease
in energy is due to an increase of the relativistic mass of the e- and a contraction of the s and p orbitals
& a complimentary increase in electron cloud density of these energy levels. (Thayer J. Chem. Educ., 2005, 82 (11),
p 1721)
 These factors increase shielding effect, causing an increase in the energy of the d and f orbitals.
These changes in orbital energies (due to orbital contraction of the s and p orbitals), affect bond lengths
and inter-atomic separations (Thayer J. Chem. Educ., 2005, 82 (11), p 1721)
This phenomenon is seen in the color of gold. The 5d electrons, shift towards those wavelengths
required for their excitation, due to the orbital contraction of the 6s.
The liquidity of mercury at STP results from the lowered energy of the 6s electrons, weakening the
Hg-Hg interatomic bonds (Norrby, LJ JCE Volume 68 Number 2 February 1991), thus ostensibly, increasing the
potential energy between the bonded atoms shifting it towards values that are exhibited by other metals
in the liquid phase.
Other Terrific Articles and Websites:
1) I happen to have a copy of Lars J Norrby's: Why is Mercury a Liquid? (JCE Volume 68 Number 2
February 1991) If you wish for a copy …just you ask .. and you got it
2) I also have a copy of Dr. JS Thayer's chapter titled: Relativistic Effects and the Chemistry of the Heavier
Main Group Elements. (JCE Volume 82, Number 11) 2005, p 1721) Or, p.66 of the Chapter 2 piece, of the same title, and author
Ask me to get you a copy, if you are interested.
3) As a final visualization, you may find this link helpful.... http://tinyurl.com/668g8 or,
http://www.colorado.edu/physics/2000/applets/a2.html You may wish to re-visit this visualization after some
practice with orbital notation
4) As a helpful alternative voice for explaining the issues, you may find http://tinyurl.com/249bk6r or
http://www.mhhe.com/physsci/chemistry/chang7/ssg/chap07_8sg.html , meaningful.
TRY THIS!!!
___1 Which of the following notations best represent the valence principal energy level of a silicon atom,
in the ground state ?
a)
b)
c)
d)
3s 
3s 
3s 
3s 
3p
3p
3p
3p




 



532
___2 How many orbitals are completely filled in an atom of lithium in the ground state ?
a) 1
b) 2
c) 3
d) 4
___3 Which of the following notations best represents the valence principal energy level of an oxygen atom,
in the ground state ?
a)
b)
c)
d)
2s 
2s 
2s 
2s 
2p
2p
2p
2p
For 4 – 7 use choices
a) alkali metal
b) alkaline-earth metal







 .
__
.
.
__
c) halogen
d) noble gas
___4 An atom with the electron configuration of 1s2 2s2 2p6 3s23p6 4s2 is best classified as a(n)
___5 An atom with the electron configuration of
1s2
___6 An atom with the electron configuration of
1s2 2s2 2p5 is best classified as a(n)
is best classified as a(n)
___7 Which is the electron configuration of a fluorine atom in the ground state?
a) 1s22s22p4
b) 1s22s22p5
c) 1s22s22p63s1
d) 1s22s22p63s2
___8 The formation of an aluminum ion occurs when 3 electrons are removed. Which electron would
require the most energy to remove?
a)
b)
c)
d)
3s because it is filled before 3p
3p because it is farther from the nucleus
3p because it only has 1 electron in the orbital
3s because it experiences higher attractive forces
___9 Why does chlorine gain an electron to become a chloride ion?
a) It has only 7 valence electrons
b) Less shielding means there is room for another electron
c) Adding an electron completely fills the s and p orbitals of energy level 3
d) An electron is attracted to the large effective nuclear charge of the atom.
______10 How many electrons can occupy the 5d sublevel?
______11 How many electrons may occupy any one of the orbitals in 3p?
Answers: 1) c Si is in group 14 with 4 valence e- 2) a 3) b 4) b 5) d 6) c 7) b 8) d 9) d 10) 10 (5 orbitals, with a max.
number of 2 e-) 11) 2 … no orbital may hold more than 2 e-
Assignment: Scan pages 240 -245 of your text for questions or issues which you would like to have
addressed.
533
VIII) Electron Configuration and Magnetic Properties of Ions
A) Magnetism: The attractive power of magnets. It's caused by electron spin in materials containing
unpaired electrons.
http://www.engineering-timelines.com/how/electricity/definitions.asp
Most of us should recall that an unpaired electron (a charged particle) generates a
magnetic field. http://www.fao.org/docrep/003/t0355e/t0355e02.htm
This phenomenon links us to the electromagnetic spectrum and radio waves. Thus, moving electrons create radio
waves & astronomers "listen" to areas of space with radio telescopes (as with the Very Large Array [VLA]),
analyzing the waves for coherent, organized, patterned activity trying to verify observational data, supernovae
activity, gravitational lenses (a large celestial body, capable of bending light...) and even intelligent life(???)
Back to Magnetism: "Although known about since
antiquity as with, for example, the lodestone
(a natural magnet), explanations of magnetism tended to
be descriptive. Even in the 19th century, magnetism
was ascribed as a property of its lines of force. Michael
Faraday showed that all matter, including gases,
possesses magnetic properties." http://www.engineeringtimelines.com/how/electricity/definitions.asp
http://jpkc.whut.edu.cn/web18/main/wangluo/webelements/webelements/elements/text/bi/key.html
All atoms have inherent sources of magnetism because electron spin contributes a magnetic
field and electron orbits act as current loops which produce a magnetic field.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/magpr.html#c1
As an important aside to this is that the presence, or absence, of unpaired electrons is detected
experimentally by the behavior of a element when placed in a magnetic field… hence the two issues,
paired/unpaired e- and magnetism are intertwined!
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B) 3 forms of magnetism:
Diamagnetism
Paramagnetism
weakest
Ferromagnetism
strongest (overwhelms the other forms)
When materials fail to react perceptively to an applied magnetic field, we tend to rate the
materials as "non-magnetic" ... when really, the materials are probably diamagnetic or
paramagnetic, but very weakly so....
On this issue, let’s just Cut To The Chase
Personally, diamagnetic and paramagnetic substances drive me batty… (okay, battier)
There is a good deal of gunk out there on the web… but the lowdown is this:
Essentially, diamagnetism is associated with * paired electrons.
and paramagnetism is associated with * unpaired electrons.
Any substance
which has both unpaired and paired electrons will skew towards a net paramagnetism, since
the effect is much stronger than diamagnetism.
1) Diamagnetism: All of the electrons in an atom are paired. …Thus diamagnetism is caused by
only the orbital motion of electrons creates tiny atomic current loops, which produce
magnetic fields. Diamagnetic substances have only paired electrons.
When an external magnetic field is applied to a material, these current loops will tend to align
in such a way as to oppose the applied field.
Translation: Diamagnetism is the property of repulsion of a material by a magnetic field.
http://www.mhhe.com/physsci/chemistry/chang7/ssg/chap07_8sg.html
Hence, any superconductor (such as the materials we hope to use in maglev trains) would be
a superior diamagnetic material (because the goal is to oppose any magnetic disturbance ... and thus "push away
and float") ....(note: this is highly simplified …. issues re: Lenz's Law and the Meissner Effect and the London Equation are
each involved) See: http://hyperphysics.phy-astr.gsu.edu/hbase/solids/magpr.html#c1 or http://tinyurl.com/27d9fna)
http://msnbcmedia4.msn.com/j/msnbc/Components/Photo_StoryLevel/080619/urban%20maglev.hlarge.jpg
http://www.fzu.cz/~jirsa/htm/principles.htm
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a) Some diamagnetic substances are:
dihydrogen (H2(g)), ammonia (NH3(g)), mercury (Hg(l)), water (H2O),
Ne(g), He(g), Zn0 AND Zn2+
TRY THIS!!!
Given: Zn0 has a ground state electron configuration of [Ar] 4s2 3d10
Use electron configurations to prove the diamagnetic nature of Zn0 and Zn2+. Use the
definition of diamagnetism to support your answer.
* remove the box for an answer
A species which is diamagnetic has only paired electrons. Both species of zinc have only
paired electrons. For instance: Zinc atom: [Ar] 4s ↑↓ 3d ↑↓ ↑↓ ↑↓ ↑↓ ↑↓
Because the 4s2 electrons will be lost first from the atom, upon ionization, yielding a Zn2+ ion,
it too is diamagnetic … for Zn2+ ion: [Ar] 4s___ 3d ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ All electrons are
still paired.
2) Paramagnetism: Some materials exhibit a magnetization which is proportional to the applied
magnetic field in which the material is placed... In most materials the
magnetic moments of the electrons cancel, but in materials which are
classified as paramagnetic, the cancelation is incomplete.
Translation: Paramagnetism is the property of attraction to a magnetic field, in
proportion to the field. The atoms of a paramagnetic substance
contain UNpaired e-. The property is not permanent, in that the
material cannot be “magnetized”, and disappears once the magnetic
field is removed.
a) Some paramagnetic substances are: Uranium, Platinum, Tungsten, and Aluminum
FeO (iron (II) oxide), and dioxygen gas (O2)
O
O
& this little fact, creates a real problem, when considering
the double bond between oxygen of a dioxygen molecule
But this reasoning is found in molecular orbital theory
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch8/mo.html
b) When weighed in a magnetic field, paramagnetic substances appear to weigh more
they do, when not in a magnetic field (a diamagnetic material appears to weigh less)
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TRY THIS!!!
Given: Al3+, S2- and Fe3+. Use electron configurations for each ion to determine whether
each is paramagnetic or diamagnetic.
Hint:* Draw orbital diagrams
(using arrows) to illustrate
the configuration of the ions.
Apply the definitions.
ans: * Al3+ and S2- are
diamagnetic … they end up
being isoelectronic to a noble
gas …no unpaired e-!
Fe3+ is paramagnetic.
http://www.bozemanscience.com/ap-chem-007-quantum-mechanical-model/
Assignment: Please prep for the work on periodic trends, by going to the Trivedi flash and messing
about with 7.22 re: size, electron affinity and ionization energy.
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