Chapter 6 Electronic Structure of Atoms - Yolaholcombslab.yolasite.com/resources/WCU Inorganic...

6/3/2012

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Electronic

Structure

of Atoms

© 2009, Prentice-Hall, Inc.

Chapter 6

Electronic Structure

of Atoms

Chemistry, The Central Science, 11th edition

Theodore L. Brown; H. Eugene LeMay, Jr.;

and Bruce E. Bursten

John D. Bookstaver

St. Charles Community College

Cottleville, MO

Electronic

Structure

of Atoms


Chapter 6 Problems

• Problems 13, 15, 21, 33, 35, 47, 51, 53,

63, 65, 67, 71, 73

Electronic

Structure

of Atoms


Electronic Structure of Atoms

• To understand the electronic structure

of atoms, one must understand the

nature of electromagnetic radiation.

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Electronic

Structure

of Atoms


Electromagnetic Radiation

• Electric and magnetic

fields propagate as waves

through empty space or

through a medium.

• A wave transmits energy.

Electronic

Structure

of Atoms


Waves

• The distance between corresponding points

on adjacent waves is the wavelength ().

Electronic

Structure

of Atoms


Waves

• The number of waves

passing a given point per

unit of time is the

frequency ().

• For waves traveling at

the same velocity, the

longer the wavelength,

the smaller the

frequency.

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Electronic

Structure

of Atoms


EM Radiation

Low

High

Electronic

Structure

of Atoms


• Waves have a frequency • Use the Greek letter “nu”, , for frequency,

and units are “cycles per sec” • All radiation: • = c • c = velocity of light = 3.00 x 108 m/sec

• Long wavelength --> small frequency

• Short wavelength --> high frequency

= c/λ


Electronic

Structure

of Atoms


Red light has = 700 nm. Calculate the

frequency. = c/λ

Freq = 3.00 x 108 m/s

7.00 x 10-7 m 4.29 x 1014 sec-1

700 nm • 1 x 10 -9 m

1 nm = 7.00 x 10 -7 m


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Electronic

Structure

of Atoms



• All electromagnetic radiation travels at the same velocity: the speed of light (c),

3.00 108 m/s.

• Therefore,

c =

Electronic

Structure

of Atoms


Electromagnetic Spectrum

Electronic

Structure

of Atoms


Constructive and Destructive

Interference

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Electronic

Structure

of Atoms


The Nature of Energy

• The wave nature of light

does not explain how

an object can glow

when its temperature

increases.

• Max Planck explained it

by assuming that

energy comes in

packets called quanta.

Electronic

Structure

of Atoms


Black Body Radiation

Electronic

Structure

of Atoms


Quantum Theory Blackbody Radiation:

Max Planck, 1900

є = h Energy, like matter, is discontinuous.

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Electronic

Structure

of Atoms


Long wavelength -->

small frequency

low energy

Short wavelength -->

high frequency

high energy


Electronic

Structure

of Atoms


Light with a short (large ) has a large E.

Light with large (small ) has a small E.

E = h •

Quantization of Energy

Electronic

Structure

of Atoms


The Photoelectric Effect

• Heinrich Hertz, 1888

– Light striking the surface of certain metals causes ejection of electrons.

– > o

threshold frequency

I Albert Einstein 1905

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Electronic

Structure

of Atoms



• Einstein used Planck’s

assumption to explain the

photoelectric effect.

• He concluded that energy is

proportional to frequency:

E = h

where h is Planck’s

constant, 6.626 10−34 J-s.

Electronic

Structure

of Atoms



• Therefore, if one knows the

wavelength of light, one

can calculate the energy in

one photon, or packet, of

that light:

c =

E = h

Electronic

Structure

of Atoms


Sample Exercise 6.3 Energy of a Photon

Calculate the energy of one photon of yellow light with a wavelength of 589 nm.

We can use Equation 6.1 to convert the

wavelength to frequency:

We can then use Equation 6.3 to calculate

energy:

Solve: The frequency, v, is calculated from the

given wavelength.:

:

Use the frequency and Planck’s constant

to calculate the energy of the photon.

Comment: If one photon of radiant energy

supplies 3.37 × 10–19 J, then one mole

of these photons will supply

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Electronic

Structure

of Atoms



Another mystery in

the early 20th

century involved the

emission spectra

observed from

energy emitted by

atoms and

molecules.

Electronic

Structure

of Atoms


9-2 Atomic Spectra

(a) (b) (c) (d) (e)

Electronic

Structure

of Atoms


Atomic Spectra

Helium

Hydrogen

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Electronic

Structure

of Atoms



• For atoms and

molecules one does

not observe a

continuous spectrum,

as one gets from a

white light source.

• Only a line spectrum of

discrete wavelengths

is observed.

Electronic

Structure

of Atoms



• Niels Bohr adopted Planck’s

assumption and explained

these phenomena in this

way:

1. Electrons in an atom can only

occupy certain orbits

(corresponding to certain

energies).

Electronic

Structure

of Atoms






way:

2. Electrons in permitted orbits

have specific, “allowed”

energies; these energies will

not be radiated from the atom.

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Electronic

Structure

of Atoms






way:

3. Energy is only absorbed or

emitted in such a way as to

move an electron from one

“allowed” energy state to

another; the energy is defined

by

E = h

Electronic

Structure

of Atoms


8-4 The Bohr Atom

E = -RH

n2

RH = 2.179 10-18 J

Electronic

Structure

of Atoms


Energy-Level Diagram

ΔE = Ef – Ei = -RH

nf2

-RH

ni2

–

= RH ( ni

2

1

nf2

– 1 ) = h = hc/λ

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Electronic

Structure

of Atoms



The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

E = RH ( ) 1

ni2

1

nf2

-

where RH is the Rydberg

constant, 2.18 10−18 J, and ni

and nf are the initial and final

energy levels of the electron.

Electronic

Structure

of Atoms


Sample Exercise 6.4 Electronic Transitions in the Hydrogen Atom

Using Figure 6.14, predict which of the following electronic

transitions produces the spectral line having the longest

wavelength: n = 2 to n = 1, n = 3 to n = 2, or n = 4 to n = 3.

Solution

The longest wavelength will be associated with the lowest

frequency.

According to Planck’s equation, E = hv, the lowest frequency

is associated with the lowest energy.

In Figure 6.14 the shortest vertical line represents the smallest

energy change. Thus, the n = 4 to n = 3 transition produces the

longest wavelength (lowest frequency) line.

Electronic

Structure

of Atoms


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Electronic

Structure

of Atoms


Emission and Absorption Spectroscopy

Electronic

Structure

of Atoms


Quantum Mechanical View of Electron

• Bohr’s Model only worked for a one-

electron atom.

• Scientists began to view the electron as

a wave.

Electronic

Structure

of Atoms


Two Ideas Leading to a New

Quantum Mechanics

• Wave-Particle Duality

– Einstein suggested particle-like

properties of light could explain the

photoelectric effect.

– Diffraction patterns suggest photons

are wave-like.

• deBroglie, 1924

– Small particles of matter may at

times display wavelike properties. Louis de Broglie

Nobel Prize 1918

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Electronic

Structure

of Atoms


The Wave Nature of Matter

• Louis de Broglie posited that if light can

have material properties, matter should

exhibit wave properties.

• He demonstrated that the relationship

between mass and wavelength was

= h

mv

Electronic

Structure

of Atoms


The Uncertainty Principle

• Heisenberg showed that the more precisely

the momentum of a particle is known, the less

precisely is its position known:

• In many cases, our uncertainty of the

whereabouts of an electron is greater than the

size of the atom itself!

(x) (mv) h

4

Electronic

Structure

of Atoms


Quantum Mechanics

• Erwin Schrödinger

developed a

mathematical treatment

into which both the

wave and particle nature

of matter could be

incorporated.

• It is known as quantum

mechanics.

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Electronic

Structure

of Atoms


Quantum Mechanics

• The wave equation is

designated with a lower

case Greek psi ().

• The square of the wave

equation, 2, gives a

probability density map of

where an electron has a

certain statistical likelihood

of being at any given instant

in time.

Electronic

Structure

of Atoms


Wave Functions

• ψ, psi, the wave function.

– Should correspond to a

standing wave within the

boundary of the system

being described.

• Particle in a box.

L

xnsin

L

2ψ

Slide 28 of 50 General Chemistry: Chapter 8 Prentice-Hall © 2007

Electronic

Structure

of Atoms


Probability of Finding an Electron

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Electronic

Structure

of Atoms


Wave Functions for Hydrogen

• Schrödinger, 1927 Eψ = H ψ

– H (x,y,z) or H (r,θ,φ)

ψ(r,θ,φ) = R(r) Y(θ,φ)

R(r) is the radial wave function.

Y(θ,φ) is the angular wave function.

Electronic

Structure

of Atoms


Quantum Numbers

• Solving the wave equation gives a set of

wave functions, or orbitals, and their

corresponding energies.

• Each orbital describes a spatial

distribution of electron density.

• An orbital is described by a set of three

quantum numbers.

Electronic

Structure

of Atoms


Principle Shells and Subshells • Principle electronic shell, n = 1, 2, 3…

• Angular momentum quantum number, l = 0, 1, 2…(n-1)

l = 0, s

l = 1, p

l = 2, d

l = 3, f

• Magnetic quantum number, ml= - l …-2, -1, 0,

1, 2…+l

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Electronic

Structure

of Atoms


Principal Quantum Number (n)

• The principal quantum number, n,

describes the energy level on which the

orbital resides.

• The values of n are integers ≥ 1.

Electronic

Structure

of Atoms


Angular Momentum Quantum

Number (l)

• This quantum number defines the

shape of the orbital.

• Allowed values of l are integers ranging

from 0 to n − 1.

• We use letter designations to

communicate the different values of l

and, therefore, the shapes and types of

orbitals.

Electronic

Structure

of Atoms


Angular Momentum Quantum

Number (l)

Value of l 0 1 2 3

Type of orbital s p d f

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Electronic

Structure

of Atoms


Magnetic Quantum Number (ml)

• The magnetic quantum number describes the three-dimensional orientation of the orbital.

• Allowed values of ml are integers ranging from -l to l:

−l ≤ ml ≤ l.

• Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

Electronic

Structure

of Atoms


Magnetic Quantum Number (ml)

• Orbitals with the same value of n form a shell.

• Different orbital types within a shell are

subshells.

Electronic

Structure

of Atoms


s Orbitals

• The value of l for s

orbitals is 0.

• They are spherical in

shape.

• The radius of the

sphere increases with

the value of n.

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Electronic

Structure

of Atoms


s Orbitals

Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

Electronic

Structure

of Atoms


p Orbitals

• The value of l for p orbitals is 1.

• They have two lobes with a node between

them.

Electronic

Structure

of Atoms


d Orbitals

• The value of l for a

d orbital is 2.

• Four of the five d

orbitals have 4

lobes; the other

resembles a p

orbital with a

doughnut around

the center.

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Electronic

Structure

of Atoms


Energies of Orbitals

• For a one-electron

hydrogen atom,

orbitals on the same

energy level have

the same energy.

• That is, they are

degenerate.

Electronic

Structure

of Atoms


Energies of Orbitals

• As the number of electrons increases, though, so does the repulsion between them.

• Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.

Electronic

Structure

of Atoms


Spin Quantum Number, ms

• In the 1920s, it was

discovered that two

electrons in the same

orbital do not have

exactly the same energy.

• The “spin” of an electron

describes its magnetic

field, which affects its

energy.

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Electronic

Structure

of Atoms


Spin Quantum Number, ms

• This led to a fourth

quantum number, the

spin quantum number,

ms.

• The spin quantum

number has only 2

allowed values: +1/2

and −1/2.

Electronic

Structure

of Atoms


Pauli Exclusion Principle

• No two electrons in the

same atom can have

exactly the same energy.

• Therefore, no two

electrons in the same

atom can have identical

sets of quantum

numbers.

Electronic

Structure

of Atoms


Electron Configurations

• This shows the

distribution of all

electrons in an atom.

• Each component

consists of

– A number denoting the

energy level,

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Electronic

Structure

of Atoms



• This shows the

distribution of all

electrons in an atom

• Each component

consists of


energy level,

– A letter denoting the type

of orbital,

Electronic

Structure

of Atoms



• This shows the

distribution of all

electrons in an atom.

• Each component

consists of


energy level,

– A letter denoting the type

of orbital,

– A superscript denoting

the number of electrons

in those orbitals.

Electronic

Structure

of Atoms


Orbital Diagrams

• Each box in the

diagram represents

one orbital.

• Half-arrows represent

the electrons.

• The direction of the

arrow represents the

relative spin of the

electron.

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Electronic

Structure

of Atoms


Hund’s Rule

“For degenerate

orbitals, the lowest

energy is attained

when the number of

electrons with the

same spin is

maximized.”

Electronic

Structure

of Atoms



• Aufbau process.

– Build up and minimize energy.

• Pauli exclusion principle.

– No two electrons can have all four

quantum numbers alike.

• Hund’s rule.

– Degenerate orbitals are occupied singly

first.

Electronic

Structure

of Atoms


Orbital Filling

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Electronic

Structure

of Atoms


Aufbau Process and Hunds Rule

Electronic

Structure

of Atoms


Filling p Orbitals

Electronic

Structure

of Atoms


Periodic Table

• We fill orbitals in

increasing order of

energy.

• Different blocks on the

periodic table (shaded

in different colors in

this chart) correspond

to different types of

orbitals.

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Electronic

Structure

of Atoms


Some Anomalies

Some

irregularities

occur when there

are enough

electrons to half-

fill s and d

orbitals on a

given row.

Electronic

Structure

of Atoms


Some Anomalies

For instance, the

electron

configuration for

chromium is

[Ar] 4s1 3d5

rather than the

expected

[Ar] 4s2 3d4.

Electronic

Structure

of Atoms


Some Anomalies

For instance, the

electron

configuration for

copper is

[Ar] 4s1 3d10

rather than the

expected

[Ar] 4s2 3d9.

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Electronic

Structure

of Atoms


Some Anomalies

• This occurs

because the 4s

and 3d orbitals

are very close in

energy.

• These anomalies

occur in f-block

atoms, as well.

Electronic

Structure

of Atoms


Filling the d Orbitals

Electronic

Structure

of Atoms


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Electronic

Structure

of Atoms


Electron Configurations and the Periodic Table

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