One Point Quiz

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One Point Quiz

• One quiz per table, list everyones name
• Agree on an answer
• You have two minutes

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Descriptive Chemistry

• Besides assigned readings on orbital shapes and
  electron probability, there are readings on
  descriptive chemistry.
• This week
• Group III (Boron family)
• Group IV (Carbon family)

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Orbital Shapes

• Edward A. Mottel
• Department of Chemistry
• Rose-Hulman Institute of Technology

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Orbitals

• The region around a nucleus in which an electron
  has a probability of being located is called an
  orbital.
• Orbitals can vary in
• distance from the nucleus (radial function)
• direction (angular function)

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Wave Function
The shape of the orbital and the energy of the
electron is related to the wave function (y).
The electron is mathematically described by the
wave function,
The wave function is composed of radial and
angular functions (in three dimensions).
the Schrödinger Equation is used to calculate the
energy of that electron.
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Spherical Coordinates
r distance of electron from nucleus
q angle of declination (angle from z-axis)
f angle of rotation (angle from x-axis
in xy plane)
coordinates (r,q,f)
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Orbital Shapes

• The shape of the orbital is determined by the
  wave function.
• The shape of the orbital can be determined from
  the nodes of the wave function.
• ao Bohr radius (0.529 Å)
• Z nuclear charge

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Orbital Wave Functions
Radial
Angular
Wave Function
Nodes
Nodes
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Orbitals WithNo Angular Dependence
1s
isotropic orbitals
2s
s orbitals have a spherical shape
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Orbital Wave Functions
Radial Nodes
Angular Nodes
Wave Function
no radial nodes
q 90
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Orbital Wave Functions
Radial Nodes
Angular Nodes
Wave Function
no radial nodes
q 0 or f 90
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Orbital Wave Functions
Radial Nodes
Angular Nodes
Wave Function
no radial nodes
q 0 or f 0
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Orbitals WithAngular Dependence
Anisotropic orbitals
p orbitals have a propeller shape
the angular probability function is not the same
in all directions
How can you distinguish px from py or pz?
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Higher Energy Orbitals

• Higher energy levels correspond to higher wave
  functions including 3s, 3px, 3py, 3pz and d
  orbitals.

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d Orbitals
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Orbital Sets

• s orbitals are spherical in shape and therefore
  spherically symmetric.

• Other orbitals are anisotropic, however when they
  are combined as a set the result is "spherically
  symmetric" (i.e., isotropic).

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Orbital Sets
p orbitals are individually anisotropic, but as a
set are isotropic.
px
py
pz
no angular dependence º spherically symmetric º
isotropic
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Orbital Sets
d orbitals are individually anisotropic, but as a
dxy, dxz, dyz, dx2-y2, dz2 set are isotropic.
electrons in spherically symmetric orbitals are
slightly more stable
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Quantum Numbers

• Each electron in the orbital of the atom can be
  described by an unique combination of values
  known as quantum numbers.

• There are four different quantum numbers

n , l , ml , ms
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Principal Quantum Number
range n 1, 2, 3, ,
n1
n2
Larger values of n refer to higher
energy orbitals (further from the nucleus)
n3
n4
n5
n6
n7
The principal quantum number is related to the
rows of the periodic table.
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Angular Quantum Number
range l 0, , n-1
l 0
l 1
l 2
l 3
s orbital
p orbital
d orbital
f orbital
(no angular dependence)
Is it possible to have a 3p orbital?
Is it possible to have a 2f orbital?
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Magnetic Quantum Number
ml -l , , 0, , l
p-1
p0
p1
In a magnetic field aligned along the z-axis, an
electron in the 2pz orbital will behave
differently than an electron in the 2px or 2py
orbitals.
Differentiates between orbitals with the same n
and l quantum numbers
What would be the names of these orbitals?
How many f-orbitals are there in an f-orbital set?
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Spin Quantum Number
ms -1/2, 1/2
Each orbital can contain up to two electrons
one aligned with an external field
one aligned against an external field
Which electron has lower energy?
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Quantum Numbersand the Periodic Table
p
s
d
f
Identify the regions of the periodic table
that correspond to the s, p, d and f orbitals
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Four Quantum Numbers

• Each electron in an atom can be described
  uniquely by the four quantum numbers.

• Three rules involving quantum numbers
• Pauli Exclusion Principle
• Aufbau Principle
• Hund's Rule

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Pauli Exclusion Principle

• Only one electron in an atom may have the same
  four quantum numbers.

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Aufbau Principle

• In the ground state, electrons fill in the lowest
  available energy state (orbital) first

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Hund's Rule

• If more than one electron occupies a degenerate
  set of orbitals (orbitals of the same energy),
  then the electrons will fill in such a way as to
  maximize the number of orbitals filled.

• It is more stable for the spin of the electrons
  to be aligned in the same direction.

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Laboratory

• Special extra lab period today periods 7-9

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Problem Set

• Electron Filling PS due Thursday
• Four Ions PS to be done (but not submitted) by
  Exam 2