ch6 outline
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
Chapter 6
Electronic Structureof Atoms
Chemistry, The Central Science, 11th editionTheodore L. Brown; H. Eugene LeMay, Jr.;
and Bruce E. Bursten
John D. BookstaverSt. Charles Community College
Cottleville, MO
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
Waves
To understand the electronic structure ofatoms, one must understand the nature of
electromagnetic radiation.
The distance between corresponding pointson adjacent waves is the wavelength ().
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
Waves
The number of wavespassing a given point perunit of time is the
frequency(). For waves traveling atthe same velocity, thelonger the wavelength,
the smaller thefrequency.
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
Electromagnetic Radiation
All electromagneticradiation travels at thesame velocity: thespeed of light (c),
3.00 108 m/s.
Therefore,
c=
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
The wave nature of lightdoes not explain howan object can glow
when its temperatureincreases.
Max Planck explained itby assuming that
energy comes inpackets called quanta.
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
Einstein used thisassumption to explain thephotoelectric effect.
He concluded that energy isproportional to frequency:
E= h
where h is Plancksconstant, 6.626 1034 J-s.
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
Therefore, if one knows thewavelength of light, onecan calculate the energy inone photon, or packet, ofthat light:
c= E= h
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
Another mystery inthe early 20thcentury involved theemission spectraobserved fromenergy emitted byatoms andmolecules.
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
For atoms andmolecules one doesnot observe acontinuous spectrum,as one gets from awhite light source.
Only a line spectrum ofdiscrete wavelengthsis observed.
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
Niels Bohr adopted Plancksassumption and explainedthese phenomena in thisway:
1. Electrons in an atom can onlyoccupy certain orbits(corresponding to certain
energies).
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ElectronicStructure
of Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
Niels Bohr adopted Plancksassumption and explainedthese phenomena in thisway:
1. Electrons in permitted orbitshave specific, allowedenergies; these energies will
not be radiated from theatom.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
Niels Bohr adopted Plancksassumption and explainedthese phenomena in thisway:
1. Energy is only absorbed oremitted in such a way as tomove an electron from one
allowed energy state toanother; the energy is definedby
E= h
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
The Nature of Energy
The energy absorbed or emittedfrom the process of electronpromotion or demotion can be
calculated by the equation:
E= RH ( )1nf21ni2
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whereRH is the Rydberg constant,2.18 1018 J, and ni and nf are theinitial and final energy levels of theelectron.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
The Wave Nature of Matter
Louis de Broglie posited that if light canhave material properties, matter should
exhibit wave properties. He demonstrated that the relationship
between mass and wavelength was
=h
mv
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
The Uncertainty Principle
Heisenberg showed that the more preciselythe momentum of a particle is known, the lessprecisely is its position known:
In many cases, our uncertainty of the
whereabouts of an electron is greater than thesize of the atom itself!
(x) (mv) h
4
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Quantum Mechanics
Erwin Schrdingerdeveloped amathematical treatmentinto which both the waveand particle nature ofmatter could beincorporated.
It is known as quantummechanics.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Quantum Mechanics
The wave equation isdesignated with a lowercase Greekpsi().
The square of the waveequation, 2, gives aprobability density map of
where an electron has acertain statistical likelihoodof being at any given instantin time.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Quantum Numbers
Solving the wave equation gives a setof wave functions, ororbitals, and their
corresponding energies. Each orbital describes a spatial
distribution of electron density.
An orbital is described by a set of threequantum numbers.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Principal Quantum Number (n)
The principal quantum number, n,describes the energy level on which the
orbital resides. The values ofn are integers 1.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Angular Momentum QuantumNumber (l)
This quantum number defines theshape of the orbital.
Allowed values oflare integers rangingfrom 0 to n 1.
We use letter designations to
communicate the different values ofland, therefore, the shapes and types oforbitals.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Angular Momentum QuantumNumber (l)
Value ofl 0 1 2 3
Value ofl 0 1 2 3
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Magnetic Quantum Number (ml)
The magnetic quantum numberdescribes the three-dimensional
orientation of the orbital. Allowed values ofmlare integers
ranging from -lto l:
l ml l.
Therefore, on any given energy level,there can be up to 1 s orbital, 3porbitals, 5 dorbitals, 7 forbitals, etc.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Magnetic Quantum Number (ml)
Orbitals with the same value ofn form a shell.
Different orbital types within a shell are
subshells.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
s Orbitals
The value oflforsorbitals is 0.
They are spherical inshape.
The radius of thesphere increases with
the value ofn.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
s Orbitals
Observing a graph ofprobabilities of findingan electron versus
distance from thenucleus, we see that sorbitals possess n1nodes, or regions
where there is 0probability of finding anelectron.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
p Orbitals
The value oflforp orbitals is 1.
They have two lobes with a node between
them.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
dOrbitals
The value oflfor adorbital is 2.
Four of the five d
orbitals have 4lobes; the otherresembles aporbital with a
doughnut aroundthe center.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Energies of Orbitals
For a one-electronhydrogen atom,orbitals on the sameenergy level havethe same energy.
That is, they are
degenerate.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Energies of Orbitals
As the number ofelectrons increases,though, so does the
repulsion betweenthem.
Therefore, in many-electron atoms,
orbitals on the sameenergy level are nolonger degenerate.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Spin Quantum Number, ms
In the 1920s, it wasdiscovered that twoelectrons in the sameorbital do not haveexactly the same energy.
The spin of an electron
describes its magneticfield, which affects itsenergy.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Spin Quantum Number, ms
This led to a fourthquantum number, thespin quantum number,ms.
The spin quantumnumber has only 2
allowed values: +1/2and 1/2.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Pauli Exclusion Principle
No two electrons in thesame atom can haveexactly the same energy.
Therefore, no twoelectrons in the sameatom can have identical
sets of quantumnumbers.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Electron Configurations
This shows thedistribution of allelectrons in an atom.
Each componentconsists of A number denoting the
energy level,
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Electron Configurations
This shows thedistribution of allelectrons in an atom
Each componentconsists of A number denoting the
energy level,
A letter denoting the typeof orbital,
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Electron Configurations
This shows thedistribution of allelectrons in an atom.
Each componentconsists of A number denoting the
energy level,
A letter denoting the typeof orbital,
A superscript denotingthe number of electronsin those orbitals.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Orbital Diagrams
Each box in thediagram representsone orbital.
Half-arrows representthe electrons.
The direction of the
arrow represents therelative spin of theelectron.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Hunds Rule
For degenerateorbitals, the lowestenergy is attainedwhen the number ofelectrons with thesame spin ismaximized.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Periodic Table
We fill orbitals inincreasing order ofenergy.
Different blocks on theperiodic table (shadedin different colors in
this chart) correspondto different types oforbitals.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Some Anomalies
Someirregularitiesoccur when thereare enoughelectrons to half-fill s and dorbitals on a
given row.
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ElectronicStructureof Atoms
2009, Prentice-Hall, Inc.
Some Anomalies
For instance, theelectronconfiguration forcopper is
[Ar] 4s1 3d5
rather than the
expected[Ar] 4s2 3d4.
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ElectronicStructureof Atoms
Some Anomalies
This occursbecause the 4sand 3dorbitalsare very close inenergy.
These anomaliesoccur in f-blockatoms, as well.