Download 6.5-6.9 1 6.5 Quantum Mechanics and Atomic Orbitals

6.5-6.9
Reading: sections 6.5-6.6
As you read this material, ask yourself the following
questions:
 What are wave functions and orbitals, how do orbitals differ from
orbits?
 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?
 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?
 How do the energy levels differ in many electron atoms?
 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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6.5 Quantum Mechanics and Atomic Orbitals
Erwin Schrödinger proposed an equation containing both wave and particle
terms. The solution of the equation is known as a wave function, Ψ (psi).
describes the behavior of a quantum mechanical object, like an electron
Ψ2 is the probability density
Ψ2 gives the electron density for
the atom
A region of high electron density = high probability of finding an electron
Orbitals and quantum numbers
If we solve the Schrödinger equation we get wave functions and corresponding
energies.
These wave functions are called orbitals
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6.5-6.9
For interest only: do not need to memorise
Wavefunctions:
Chem 101
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6.5-6.9
Probability function (Ψ2)
analogy: compare probability of dart landing here
vs. there
Chem 101
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6.6 Representations of Orbitals
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
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
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s orbitals
(ℓ = 0)
[4πr2Ψ(r)2]
n = 1, ℓ = 0
1s orbital
node
n = 2, ℓ = 0
2s orbital
pg 230-231 (a closer look)7
Chem 101
The p orbitals: (l=1) to memorize
• p orbitals are dumbell-shaped two lobes and a node at the nucleus
• 3 values of mℓ 3 different orientations (x,y,z)
pz
px
py
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The d orbitals : to be aware of
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 memorise
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To be aware of (ie: draw a d orbital)
f orbitals (Lanthanides and Actinides: for interest only)
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6.7 Many electron atoms
n+ ℓ = 5
n+ ℓ = 4
n+ ℓ = 4
n+ ℓ =3
n+ ℓ =3
n+ ℓ =2
n+ ℓ =1
1 electron system (H,or He+ etc..)
Multi- electron system (all atoms but H)
Chem 101
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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:
Beam of
atoms
Beam
collector
plate
Slit
Magnet
electron spin is
quantized
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6.5-6.9
6.8 Electron configuration
Chem 101
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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
p-block
main
group
elements
f-block
lanthanides and actinides
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6.9 Electron Configurations and the Periodic Table
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