Download Quantum Mechanics and the Heisenberg Uncertainty Principle

Chapter 5
Periodicity and Atomic Structure
QUANTUM MECHANICS AND THE
HEISENBERG UNCERTAINTY PRINCIPLE
In 1926 Erwin Schrödinger proposed the quantum
mechanical model of the atom which focuses on the
wavelike properties of the electron.
In 1927 Werner Heisenberg stated that it is impossible to know
precisely where an electron is and what path it follows—a
statement called the Heisenberg uncertainty principle.
QUANTUM MECHANICS AND THE
HEISENBERG UNCERTAINTY PRINCIPLE

Heisenberg Uncertainty Principle – both the position
(Δx) and the momentum (Δmv) of an electron cannot be known
beyond a certain level of precision
1.
(Δx) (Δmv) > h
4π
2.
Cannot know both the position and the momentum
of an electron with a high degree of certainty
3.
If the momentum is known with a high degree of
certainty
i.
Δmv is small
ii.
Δ x (position of the electron) is large
4.
If the exact position of the electron is known
i.
Δmv is large
ii.
Δ x (position of the electron) is small
WAVE FUNCTIONS AND QUANTUM NUMBERS
Wave
equation
solve
Wave function
or orbital (Y)
Probability of finding
electron in a region
of space (Y 2)
A wave function is characterized by three parameters called
quantum numbers, n, l, ml.
WAVE FUNCTIONS AND QUANTUM
NUMBERS
Principal Quantum Number
( n)
• Describes the size and
energy level of the orbital
• Commonly called shell
• Positive integer (n = 1, 2,
3, 4, …)
• As the value of n
increases:
• The energy increases
• The average distance
of the e- from the
nucleus increases
WAVE FUNCTIONS AND QUANTUM NUMBERS
Angular-Momentum Quantum Number (l)
• Defines the three-dimensional shape of the orbital
• Commonly called subshell
• There are n different shapes for orbitals
• If n = 1 then l = 0
• If n = 2 then l = 0 or 1
• If n = 3 then l = 0, 1, or 2
• etc.
• Commonly referred to by letter (subshell notation)
• l=0
s (sharp)
• l=1
p (principal)
• l=2
d (diffuse)
• l=3
f (fundamental)
• etc.
WAVE FUNCTIONS AND QUANTUM NUMBERS
Magnetic Quantum Number (ml )
• Defines the spatial orientation of the orbital
• There are 2l + 1 values of ml and they can have any
integral value from -l to +l
• If l = 0 then ml = 0
• If l = 1 then ml = -1, 0, or 1
• If l = 2 then ml = -2, -1, 0, 1, or 2
• etc.
WAVE FUNCTIONS AND QUANTUM NUMBERS
WAVE FUNCTIONS AND QUANTUM
NUMBERS
 Identify
the possible values for each of the
three quantum numbers for a 4p orbital.

Give orbital notations for electrons in orbitals
with the following quantum numbers:
a)

n = 2, l = 1, ml = 1
b) n = 4, l = 0, ml =0
Give the possible combinations of quantum
numbers for the following orbitals:

A 3s orbital
b) A 4f orbital
THE SHAPES OF ORBITALS
Node: A surface of zero
probability for finding the
electron.
THE SHAPES OF ORBITALS
ELECTRON SPIN AND THE PAULI EXCLUSION
PRINCIPLE
Electrons have spin which gives rise to a tiny magnetic field and to a spin
quantum number (ms).
Pauli Exclusion Principle: No two electrons in an atom can have the same four
quantum numbers.
ORBITAL ENERGY LEVELS IN MULTIELECTRON
ATOMS
ELECTRON CONFIGURATIONS OF
MULTIELECTRON ATOMS
Effective Nuclear Charge (Zeff): The nuclear charge actually
felt by an electron.
Zeff = Zactual - Electron shielding
ELECTRON CONFIGURATIONS OF
MULTIELECTRON ATOMS
Electron Configuration: A description of which orbitals are occupied by
electrons.
1s2 2s2 2p6 ….
Degenerate Orbitals: Orbitals that have the same energy level. For
example, the three p orbitals in a given subshell.
2px 2py 2pz
Ground-State Electron Configuration: The lowest-energy
configuration.
1s2 2s2 2p6 ….
Orbital Filling Diagram: using arrow(s) to represent occupied in an
orbital
ELECTRON CONFIGURATIONS OF
MULTIELECTRON ATOMS
Aufbau Principle (“building up”): A guide for determining the filling
order of orbitals.
Rules of the aufbau principle:
1. Lower-energy orbitals fill before higher-energy orbitals.
2. An orbital can only hold two electrons, which must have opposite
spins (Pauli exclusion principle).
3. If two or more degenerate orbitals are available, follow Hund’s rule.
Hund’s Rule: If two or more orbitals with the same energy are available,
one electron goes into each until all are half-full. The electrons in the halffilled orbitals all have the same spin.
ELECTRON CONFIGURATIONS OF
MULTIELECTRON ATOMS
Electron
Configuration
1s1
1 electron
s orbital (l = 0)
n=1
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ELECTRON CONFIGURATIONS OF
MULTIELECTRON ATOMS
Electron
Configuration
1s1
He:
1s2
2 electrons
s orbital (l = 0)
n=1
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ELECTRON CONFIGURATIONS OF
MULTIELECTRON ATOMS
Electron
Configuration
1s1
He:
1s2
Lowest energy to highest energy
Li:
1s2 2s1
1 electrons
s orbital (l = 0)
n=2
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ELECTRON CONFIGURATIONS AND THE
PERIODIC TABLE
Valence Shell: Outermost shell or the highest energy .
Na: 3s1
Cl: 3s2 3p5
Br: 4s2 4p5
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Li: 2s1
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ELECTRON CONFIGURATIONS AND THE
PERIODIC TABLE

O (Z = 8)
 Ti (Z = 22)
 Sr (Z = 38)
 Sn (Z = 50)

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Inc.
Give expected ground-state electron
configurations for the following atoms, draw –
orbital filling diagrams and determine the
valence shell
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ELECTRON CONFIGURATIONS AND PERIODIC
PROPERTIES: ATOMIC RADII
radius
row
radius
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Inc.
column
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ELECTRON CONFIGURATIONS AND PERIODIC
PROPERTIES: ATOMIC RADII
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Inc.
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EXAMPLES

Arrange the elements P, S and O in order of
increasing atomic radius