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6.5-6.9
6.5 Quantum Mechanics and Atomic Orbitals
Reading: sections 6.5-6.6
Erwin Schrödinger proposed an equation containing both wave and particle
terms. The solution of the equation is known as a wave function, Ψ (psi).
As you read this material, ask yourself the following
questions:
 What are wave functions and orbitals, how do orbitals differ from
orbits?
describes the behavior of a quantum mechanical object, like an electron
 What can we learn about an electron from a wave function?
 What properties of the electron do the principal quantum
number(n), the angular momentum quantum number(l) and the
magnetic quantum number determine(ml). What values can each of
these quantum numbers have, how are their values related?
Ψ2 is the probability density
Ψ2 gives the electron density for
the atom
 What are the shapes of the orbitals for different values of the
angular momentum quantum number (different subshells)? Sketch
these shapes. What labels do we give these subshells?
A region of high electron density = high probability of finding an electron
 How do the energy levels differ in many electron atoms?
Orbitals and quantum numbers
 What is the fourth quantum number (ms) and what values can it
have?
 When assigning energies to electrons, what are the implications of
the Pauli Exclusion principle?
Chem 101
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If we solve the Schrödinger equation we get wave functions and corresponding
energies.
These wave functions are called orbitals
For interest only: do not need to memorise
Wavefunctions:
Chem 101
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6.6 Representations of Orbitals
Probability function (Ψ2)
The s orbitals ( to memorize) (l=0)
• All s orbitals are spherical
• As n increases, the s orbitals get larger
• As n increases, the number of nodes increases
analogy: compare probability of dart landing here
vs. there
Chem 101
height of
graph
indicates
electron
density
node = probability of
finding an electron is 0
For an s orbital the
number of nodes is
given by n – 1
5
1
6.5-6.9
s orbitals
(ℓ = 0)
[4πr2Ψ(r)2]
The p orbitals: (l=1) to memorize
two lobes and a node at the nucleus
• p orbitals are dumbell-shaped
• 3 values of m ℓ 3 different orientations (x,y,z)
n = 1, ℓ = 0
pz
1s orbital
node
n = 2, ℓ = 0
px
py
2s orbital
pg 230-231 (a closer look)7
Chem 101
The d orbitals : to be aware of
To memorise
5 values of mℓ so 5 different orientations
3 d orbitals lie in a plane bisecting the x-, y-, and z-axes
2 d orbitals lie in a plane aligned along the x-, y-, and z-axes
4 of the d orbitals have 4 lobes each
1 d orbital has 2 lobes and a “donut”
To be aware of (ie: draw a d orbital)
f orbitals (Lanthanides and Actinides: for interest only)
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6.5-6.9
Electron Spin and the Pauli Exclusion Principle
.Stern and Gerlach designed an experiment to determine why line splitting occurs. A
beam of atoms was passed through a slit and into a magnetic field and the atoms were
detected:
6.7 Many electron atoms
Beam of
atoms
n+ ℓ = 5
n+ ℓ = 4
n+ ℓ = 4
Beam
collector
plate
n+ ℓ =3
Slit
n+ ℓ =3
n+ ℓ =2
Magnet
n+ ℓ =1
1 electron system (H,or He+ etc..)
Multi- electron system (all atoms but H)
Chem 101
electron spin is
quantized
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6.8 Electron configuration
6.9 Electron Configurations and the Periodic Table
The periodic table can be used as a guide for electron configurations.
the period number is the value of n
d-block
s-block
transition metals
alkali and
alkaline
earth
metals
main
group
elements
f-block
Chem 101
p-block
lanthanides and actinides
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6.9 Electron Configurations and the Periodic Table
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