This chapter discusses the quantum mechanical model of the atom. It covers early theories of electromagnetic radiation and the photoelectric effect that led to the development of quantum theory. The chapter then describes the Bohr model of the atom and its limitations. It introduces wave mechanics and the Schrodinger equation for describing electron orbitals. The chapter covers electron configurations, orbital shapes, and how quantum numbers are used to interpret and represent atomic orbitals. It also discusses how electron configurations relate to the periodic table.

1. General Chemistry
Principles and Modern Applications
Petrucci • Harwood • Herring
8th Edition
Chapter 9: Electrons in Atoms
Philip Dutton
University of Windsor, Canada
Prentice-Hall © 2002
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2. 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
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3. 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
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4. 9-1 Electromagnetic Radiation
• Electric and magnetic fields
propagate as waves through
empty space or through a
medium.
• A wave transmits energy.
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5. EM Radiation
Low ν
High ν
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6. Frequency, Wavelength and Velocity
• Frequency (ν) in Hertz—Hz or s-1.
• Wavelength (λ) in meters—m.
• cm µm nm  pm
(10-2 m) (10-6 m) (10-9 m) (10-10 m) (10-12 m)
• Velocity (c)—2.997925  108 m s-1.
c = λν λ = c/ν ν= c/λ
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7. Electromagnetic Spectrum
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8. ROYGBIV
Red
Orange
Yellow
700 nm Green 450 nm
Blue
Indigo
Violet
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9. Constructive and Destructive Interference
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11. Refraction of Light
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12. 9-2 Atomic Spectra
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13. Atomic Spectra
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14. 9-3 Quantum Theory
Blackbody Radiation:
Max Planck, 1900:
Energy, like matter, is discontinuous.
є = hν
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15. The Photoelectric Effect
• Light striking the surface of certain metals
causes ejection of electrons.
∀ν > νo threshold frequency
• e-  I
• ek  ν
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16. The Photoelectric Effect
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17. The Photoelectric Effect
• At the stopping voltage the kinetic energy of the
ejected electron has been converted to potential.
1
mu2 = eVs
2
• At frequencies greater than νo:
Vs = k (ν - νo)
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18. The Photoelectric Effect
eVo
Ek = eVs Eo = hνo νo =
h
eVo, and therefore νo, are characteristic of the metal.
Conservation of energy requires that:
1
Ephoton = Ek + Ebinding hν = mu2 + eVo
2
1
Ek = Ephoton - Ebinding eVs = mu2 = hν - eVo
2
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19. 9-4 The Bohr Atom
-RH
E= 2
n
RH = 2.179  10-18 J
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20. Energy-Level Diagram
-RH -RH
ΔE = Ef – Ei = – 2
nf 2
ni
1 1
= RH ( 2 – 2 ) = hν = hc/λ
ni nf
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21. Ionization Energy of Hydrogen
1 1
ΔE = RH ( 2 – 2 ) = hν
ni nf
As nf goes to infinity for hydrogen starting in the ground state:
1
hν = RH ( 2 ) = RH
ni
This also works for hydrogen-like species such as He+ and Li2+.
hν = -Z2 RH
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22. Emission and Absorption Spectroscopy
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23. 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.
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24. deBroglie and Matter Waves
E = mc2
hν = mc2
hν/c = mc = p
p = h/λ
λ = h/p = h/mu
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25. X-Ray Diffraction
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26. The Uncertainty Principle
• Werner Heisenberg
h
Δx Δp ≥
4π
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27. 9-6 Wave Mechanics
• Standing waves.
– Nodes do not undergo displacement.
2L
λ = , n = 1, 2, 3…
n
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28. 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.
2  nπ x 
ψ = sin  
L  L 
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29. Probability of Finding an Electron
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30. 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.
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31. 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 • Magnetic quantum number,
l = 2, d ml= - l …-2, -1, 0, 1, 2…+l
l = 3, f
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32. Orbital Energies
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33. 9-8 Interpreting and Representing the
Orbitals of the Hydrogen Atom.
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34. s orbitals
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35. p Orbitals
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36. p Orbitals
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37. d Orbitals
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38. 9-9 Electron Spin: A Fourth Quantum
Number
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39. 9-10 Multi-electron Atoms
• Schrödinger equation was for only one e-.
• Electron-electron repulsion in multi-
electron atoms.
• Hydrogen-like orbitals (by approximation).
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40. Penetration and Shielding
Zeff is the effective nuclear charge.
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41. 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.
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42. Orbital Energies
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43. Orbital Filling
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44. Aufbau Process and Hunds Rule
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45. Filling p Orbitals
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46. Filling the d Orbitals
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47. Electon Configurations of Some Groups of
Elements
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48. 9-12 Electron Configurations and the Periodic Table
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49. Focus on He-Ne Lasers
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50. Chapter 9 Questions
1, 2, 3, 4, 12, 15,
17, 19, 22, 25, 34,
35, 41, 67, 69, 71,
83, 85, 93, 98
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