Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 1 of 49

Philip DuttonUniversity of Windsor, Canada

N9B 3P4

Prentice-Hall © 2002

General ChemistryPrinciples and Modern Applications

Petrucci • Harwood • Herring

8th Edition

Chapter 9: Electrons in Atoms

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 2 of 49

Contents

9-1 Electromagnetic Radiation

9-2 Atomic Spectra

9-3 Quantum Theory

9-4 The Bohr Atom

9-5 Two Ideas Leading to a New Quantum Mechanics

9-6 Wave Mechanics

9-7 Quantum Numbers and Electron Orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 3 of 49

Contents

9-8 Quantum Numbers

9-9 Interpreting and Representing Orbitals of the Hydrogen Atom

9-9 Electron Spin

9-10 Multi-electron Atoms

9-11 Electron Configurations

9-12 Electron Configurations and the Periodic Table

Focus on Helium-Neon Lasers

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 4 of 49

9-1 Electromagnetic Radiation

• Electric and magnetic fields propagate as waves through empty space or through a medium.

• A wave transmits energy.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 5 of 49

EM Radiation

Low ν

High ν

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 6 of 49

Frequency, Wavelength and Velocity

• Frequency (ν) in Hertz—Hz or s-1.

• Wavelength (ë) in meters—m.

• cm µm nm D pm

(10-2 m) (10-6 m) (10-9 m) (10-10 m) (10-12 m)

• Velocity (c)—2.997925 H 108 m s-1.

c = ëν ë = c/ν ν= c/ë

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 7 of 49

Electromagnetic Spectrum

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 8 of 49

RedOrange

Yellow

Green

Blue

Indigo

Violet

Prentice-Hall ©2002 General Chemistry: Chapter 9 Slide 8

ROYGBIV

700 nm 450 nm

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 9 of 49

Constructive and Destructive Interference

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 10 of 49

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 11 of 49

Refraction of Light

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 12 of 49

9-2 Atomic Spectra

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 13 of 49

Atomic Spectra

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 14 of 49

9-3 Quantum Theory

Blackbody Radiation:

Max Planck, 1900:

Energy, like matter, is discontinuous.

º = hν

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 15 of 49

The Photoelectric Effect

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

• ν > νo threshold frequency

• e- % I

• ek % ν

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 16 of 49

The Photoelectric Effect

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 17 of 49

The Photoelectric Effect

• At the stopping voltage the kinetic energy of the ejected electron has been converted to potential.

mu2 = eVs12

• At frequencies greater than νo:

Vs = k (ν - νo)

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 18 of 49

The Photoelectric Effect

Eo = hνoEk = eVs νo = eVo

h

eVo, and therefore νo, are characteristic of the metal.

Conservation of energy requires that:

hν = mu2 + eVo2

1

mu2 = hν - eVoeVs =2

1

Ephoton = Ek + Ebinding

Ek = Ephoton - Ebinding

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 19 of 49

9-4 The Bohr Atom

E = -RH

n2

RH = 2.179 H 10-18 J

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 20 of 49

Energy-Level Diagram

ÄE = Ef – Ei = -RH

nf2

-RH

ni2

–

= RH ( ni2

1

nf2

–1

) = hν = hc/ë

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 21 of 49

Ionization Energy of Hydrogen

ÄE = RH ( ni2

1

nf2

–1

) = hν

As nf goes to infinity for hydrogen starting in the ground state:

hν = RH ( ni2

1) = RH

This also works for hydrogen-like species such as He+ and Li2+.

hν = -Z2 RH

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 22 of 49

Emission and Absorption Spectroscopy

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 23 of 49

9-5 Two Ideas Leading to a New Quantum Mechanics

• Wave-Particle Duality.– Einstein suggested particle-like properties of

light could explain the photoelectric effect.

– But diffraction patterns suggest photons are wave-like.

• deBroglie, 1924– Small particles of matter may at times display

wavelike properties.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 24 of 49

deBroglie and Matter Waves

E = mc2

hν = mc2

hν/c = mc = p

p = h/ë

ë = h/p = h/mu

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 25 of 49

X-Ray Diffraction

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 26 of 49

The Uncertainty Principle

Äx Äp �h4ð

• Werner Heisenberg

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 27 of 49

9-6 Wave Mechanics

2Ln

• Standing waves.– Nodes do not undergo displacement.

ë = , n = 1, 2, 3…

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 28 of 49

Wave Functions

• ø, psi, the wave function.– Should correspond to a

standing wave within the boundary of the system being described.

• Particle in a box.

=

Lxn π

sinL

2ø

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 29 of 49

Probability of Finding an Electron

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 30 of 49

Wave Functions for Hydrogen

• Schrödinger, 1927 Eø = H ø

– H (x,y,z) or H (r,è,ö)

ø(r,è,ö) = R(r) Y(è,ö)

R(r) is the radial wave function.

Y(è,ö) is the angular wave function.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 31 of 49

Principle Shells and Subshells

• Principle electronic shell, n = 1, 2, 3…

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

– l = 2, p

– l = 3, d

– l = 4, f

• Magnetic quantum number, ml= 0, 1, 2…(±l )

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 32 of 49

Orbital Energies

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 33 of 49

9-8 Interpreting and Representing the Orbitals of the Hydrogen Atom.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 34 of 49

s orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 35 of 49

p Orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 36 of 49

p Orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 37 of 49

d Orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 38 of 49

9-9 Electron Spin: A Fourth Quantum Number

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 39 of 49

9-10 Multi-electron Atoms

• Schrödinger equation was for only one e-.

• Electron-electron repulsion in multi-electron atoms.

• Hydrogen-like orbitals (by approximation).

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 40 of 49

Penetration and Shielding

Zeff is the effective nuclear charge.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 41 of 49

9-11 Electron Configurations

• 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.

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 42 of 49

Orbital Energies

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 43 of 49

Orbital Filling

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 44 of 49

Aufbau Process and Hunds Rule

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 45 of 49

Filling p Orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 46 of 49

Filling the d Orbitals

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 47 of 49

Electon Configurations of Some Groups of Elements

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 48 of 49

9-12 Electron Configurations and the Periodic Table

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 49 of 49

Focus on He-Ne Lasers

Prentice-Hall © 2002 General Chemistry: Chapter 9 Slide 50 of 49

Chapter 9 Questions