ch6 outline

7/30/2019 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


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


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


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


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



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



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



Another mystery inthe early 20thcentury involved theemission spectraobserved fromenergy emitted byatoms andmolecules.


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ElectronicStructure

of Atoms



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



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




1. Electrons in permitted orbitshave specific, allowedenergies; these energies will

not be radiated from theatom.


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ElectronicStructureof Atoms




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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The energy absorbed or emittedfrom the process of electronpromotion or demotion can be

calculated by the equation:

E= RH ( )1nf21ni2

-

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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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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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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Quantum Mechanics

Erwin Schrdingerdeveloped amathematical treatmentinto which both the waveand particle nature ofmatter could beincorporated.

It is known as quantummechanics.


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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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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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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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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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Angular Momentum QuantumNumber (l)

Value ofl 0 1 2 3

Value ofl 0 1 2 3


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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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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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s Orbitals

The value oflforsorbitals is 0.

They are spherical inshape.

The radius of thesphere increases with

the value ofn.


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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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p Orbitals

The value oflforp orbitals is 1.

They have two lobes with a node between

them.


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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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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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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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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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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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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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Electron Configurations

This shows thedistribution of allelectrons in an atom.

Each componentconsists of A number denoting the

energy level,


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This shows thedistribution of allelectrons in an atom


energy level,

A letter denoting the typeof orbital,


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This shows thedistribution of allelectrons in an atom.


energy level,

A letter denoting the typeof orbital,

A superscript denotingthe number of electronsin those orbitals.


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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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Hunds Rule

For degenerateorbitals, the lowestenergy is attainedwhen the number ofelectrons with thesame spin ismaximized.


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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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Some Anomalies

Someirregularitiesoccur when thereare enoughelectrons to half-fill s and dorbitals on a

given row.


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Some Anomalies

For instance, theelectronconfiguration forcopper is

[Ar] 4s1 3d5

rather than the

expected[Ar] 4s2 3d4.


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Some Anomalies

This occursbecause the 4sand 3dorbitalsare very close inenergy.

These anomaliesoccur in f-blockatoms, as well.

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