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Quantum Chemistry
Chapter 6
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Electromagnetic Radiation
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Electromagnetic Waves
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Electromagnetic Radiation
c
= frequency of the wave
c = speed of light
= wavelength
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Electromagnetic Spectrum
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Electromagnetic Spectrum
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Visible Spectrum
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Energy, Wavelength & Frequency
• The energy of a photon is given by –
hcE = h =
h = 6.626×10-34 J.s, Plank’s constant
c = 3.00×108 m/s
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Sample Problem
What is the energy of a photon of infraredlight that has a wavelength of 850. nm?
34 8
9
19
6.626 10 Js 3.00 10 m/ shcE =
1 m850 nm
10 nm
E 2.34 10 J
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Hydrogen Spectra
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Emission Spectrum
• When hydrogen atoms are excited, they emit radiation.
• The wavelengths of this radiation can be calculated from -
.f in n
2 12 2
1 1 11 0968 10 nm
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Hydrogen Spectra
.f in n
2 12 2
1 1 11 0968 10 nm
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Emission Spectra
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Bohr Model
• Bohr postulated that the energy an electron has when it occupies an orbit around the nucleus in a hydrogen atom
is:
18
n 2
2.1786 10 JE
n
n = 1, 2, 3, 4, ……..
• Ground state is the lowest energy level, n = 1.
• Excited state is a higher energy level.
Bohr model of the hydrogen
atom
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• If an electron moves from a lower energy level to a higher energy level, it absorbs energy.
• If an electron moves from a higher energy level to a lower energy level, it emits energy.
• The change in energy is –
E = Ef - Ei
Bohr Model
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Bohr Model
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Bohr Model
• For the hydrogen electron –
182 2f i
2 12 2f i
1 1E 2.1786 10 J
n n
and
1 1 11.097 10 nm
n n
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Electronic Transitions
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Sample Problem
Calculate the wavelength of light emitted by the transition of a hydrogen electron from n=4 to n=1.
-2 12 2
f i
-2 12 2
1 1 11.097 10 nm
n n
1 1 11.097 10 nm
1 4
97.23 nm
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Wave - Particle Duality
• Very small, light weight particles, such as electrons can behave like waves.
• de Broglie’s equation allows us to calculate the wavelength of an electron.
h
mv
h = Planck’s constantm = massv = velocity
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De Broglie Wavelength
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Sample Problem
What is the wavelength of an electron traveling 5.31×106 m/s?
34
31 6
10
h
mv
6.626 10 J s
9.11 10 kg 5.31 10 m/ s
1.37 10 m
0.137 nm
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The Wave Equation
• If an electron can behave like a wave, it should be possible to write an equation that describes its behavior.
• Schrödinger equation allows us to calculate the energy available to the electrons in an atom.
• Ψ is a wave function that describes the position and paths of the electron in its energy level.
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The Wave Equation
• Ψ*Ψ, the square of the wave function, is the probability of finding the electron in some region of space.
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Quantum Numbers
• There are four quantum numbers used to describe the electron in the hydrogen atom
• n, principle quantum number, describes the size and energy of the orbital
n = 1, 2, 3, 4, ………(only integers)
• l – angular momentum quantum number, describes the shape of the orbital.
l = 0 to n-1 (only integers)
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Quantum Numbers
• ml – magnetic quantum number, describes the spatial orientation of the orbital.
ml = -l to 0 to +l (only integers)• ms – spin quantum number,
describes the direction and spin of the electron.
ms = +1/2 or -1/2 (only two values)
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Quantum Numbers
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Quantum Numbers
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Quantum Numbers
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Pauli Exclusion Principle
Pauli Exclusion Principle
• No two electrons can have the same four quantum numbers.
• Spins of electrons in an orbital must be opposite.
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Quantum Numbers
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Orbital Shapes: s orbital
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s Orbitals
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Orbital Shapes: s orbital
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p Orbitals
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Orbital Shapes: 2px orbitals
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Orbital Shapes: 2py orbital
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Orbital Shapes: 2pz orbital
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d Orbitals
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Orbital Shapes: 3dx2-y2 orbital
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Orbital Shapes: 3dz2 orbital
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Orbital Shapes: 3dxy orbital
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Orbital Shapes: 3dyz orbital
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Orbital Shapes: 3dxz orbital
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f Orbitals
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Orbital Energies
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Electron spin
Spin up Spin down
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Electron shielding
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Orbital Energy Levels in Multi-electron Atoms
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Electron Configurations
• Aufbau principle gives the order of the orbitals
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Sample Problem
Write the electron configuration for Ca using the Aufbau principle.
1s22s22p63s23p64s2
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Hund’s Rule
• Hund’s rule - maximize the number of unpaired electrons in orbitals.• Orbital diagram for C (z = 6) would be: () () ( ) ( ) ( )
1s 2s 2p
not () () ( ) ( ) ( ) 1s 2s 2p
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Electron configuration
Three possible electron configurations for carbon
electron configurations
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Periodic Table
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Electron Configurations
• Representative Elements are s orbital and p orbital fillers.
• Transition metals fill the d orbitals.
• Lanthanides are 4f fillers.
• Actinides are 5f fillers
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Periodic Table Blocks
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Sample Problem
Write the electron configuration for Br & Fe using the periodic table.
Br: [Ar]4s23d104p5
Fe: [Ar]4s23d6
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Homework
26, 34, 38, 46, 52, 64, 76, 82, 92, 98, 106,