Quantum Theory and the Electronic Structure of Atoms

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Quantum Theory and the Electronic Structure of
Atoms
Chapter 7
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• Learning outcomes for Chapter 7
• Explain the relationship between Plank's quantum
  theory and the energy absorbed or emitted when
  electrons change energy levels.
• Define and explain the relationship between
  shells, subshells, and orbitals.
• Sketch and name each of the s, p, and d
  orbitals.
• Write the electronic configuration of atoms and
  ions.
• Use the rules for assigning electrons to atomic
  orbitals.
• Describe how the periodic table is built up
  using orbital theory.
• Determine the relative size of atoms and ions

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Properties of Waves
Wavelength (l) is the distance between identical
points on successive waves.
Amplitude is the vertical distance from the
midline of a wave to the peak or trough.
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Properties of Waves
Frequency (n) number of waves that pass through a
particular point in 1 second (Hz 1 cycle/s).
speed (u) l x n
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Visible light consists of electromagnetic
waves. They have a electrical field component AND
a magnetic field component
Speed of light (c) in vacuum 3.00 x 108 m/s
All electromagnetic radiation l x n c
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l x n c
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Quantum theory
Energy (light) is emitted or absorbed in discrete
units (quantum).
E h x n Plancks constant (h) h 6.63 x 10-34
Js
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Energy (light) is emitted or absorbed in discrete
units (quantum).
E h x n Plancks constant (h) h 6.63 x 10-34
Js
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Photoelectric Effect Einstein (1905)

• Demands that light has both
• wave nature
• particle nature

Photon is a particle of light
Reality is merely an illusion, albeit a very
persistent one. A. Einstein
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De Broglie (1924) reasoned that e- is both
particle and wave.
u velocity of e-
m mass of e-
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l h/mu
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E h x n
E h x c / l
E 6.63 x 10-34 (Js) x 3.00 x 10 8 (m/s) /
0.154 x 10-9 (m)
E 1.29 x 10 -15 J
7.2
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Heisenberg Uncertainty Principle
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Bohrs Model of the Atom (1913)

• e- can only have specific (quantized) energy
  values
• light is emitted as e- moves from one energy
  level to a lower energy level

n (principal quantum number) 1,2,3,
RH (Rydberg constant) 2.18 x 10-18J
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Ephoton 2.18 x 10-18 J x (1/25 - 1/9)
Ephoton h x c / l
l 1280 nm
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Schrodinger Wave Equation

• In 1926 Schrodinger wrote an equation that
  described both the particle and wave nature of
  the e-
• Wave function (Y) describes
• . energy of e-
• . probability of finding e-

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4 quantum numbers to describe distribution of e
in orbitals n, l, ml, ms
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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
principal quantum number n
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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
l angular momentum quantum number Refers to
SHAPE of orbital
for a given value of n, l 0, 1, 2, 3, n-1
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7.6
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7.6
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4 quantum numbers to describe distribution of e
in orbitals n, l, ml, ms
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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
magnetic quantum number ml
for a given value of l ml -l, ., 0, . l
if l 1 (p orbital), ml -1, 0, or 1 if l 2
(d orbital), ml -2, -1, 0, 1, or 2
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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
spin quantum number ms
ms ½ or -½
ms -½
ms ½
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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
electron in atom is described by its unique set
of quantum numbers wave function Y.
Pauli exclusion principle no two electrons in an
atom can have the same four quantum numbers.
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List the set of quantum numbers for Ar
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List the set of quantum numbers for Ar
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Schrodinger Wave Equation
Y fn(n, l, ml, ms)
Shell electrons with the same value of n
Subshell electrons with the same values of n
and l
Orbital electrons with the same values of n, l,
and ml
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Energy of orbitals in a multi-electron atom
Energy depends on n and l
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Fill up electrons in lowest energy orbitals
(Aufbau principle)
Li 3 electrons
Be 4 electrons
B 5 electrons
C 6 electrons
Li 1s22s1
Be 1s22s2
B 1s22s22p1
H 1 electron
He 2 electrons
H 1s1
He 1s2
7.9
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C 6 electrons
N 7 electrons
O 8 electrons
F 9 electrons
Ne 10 electrons
C 1s22s22p2
N 1s22s22p3
O 1s22s22p4
F 1s22s22p5
Ne 1s22s22p6
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Order of orbitals (filling) in multi-electron atom
1s lt 2s lt 2p lt 3s lt 3p lt 4s lt 3d lt 4p lt 5s lt 4d lt
5p lt 6s
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Order of orbitals (filling) in multi-electron atom
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Outermost subshell being filled with electrons
7.8
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Electron configuration is how the electrons are
distributed among the various atomic orbitals in
an atom.
1s1
Orbital diagram
H
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Mg 12 electrons
1s lt 2s lt 2p lt 3s lt 3p lt 4s
1s22s22p63s2
2 2 6 2 12 electrons
Abbreviated as Ne3s2
Ne 1s22s22p6

• 1s22s22p63s3
• 1s22s22p83s2
• 1s22s42p63s2
• 1s22s22p63s2
• 1s22s22p6

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Cl 17 electrons
1s22s22p63s23p5
Last electron added to 3p orbital
n 3
l 1
ml -1, 0, or 1
ms ½ or -½

• n1, l1, ml0, ms1/2
• n1, l2, ml0, ms1/2
• n2, l1, ml0, ms1/2
• n3, l1, ml1, ms1/2
• n3, l1, ml-1, ms1/2

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Paramagnetic
Diamagnetic
unpaired electrons
all electrons paired
Attracted to magnet
Not attracted to magnet