Quantum Mechanical Model of the Atom

Contributed by:

Jonathan James Fri, Jan 14, 2022 06:41 PM UTC

The highlights are:
1. Problems with Rutherford Model
2. The Bohr Model
3. Schrodinger's Theory
4. The Quantum Numbers

1. MODELS OF THE ATOM
Beginning with Rutherford

2. Section 7.5
PROBLEMS WITH RUTHERFORD’S
The Quantum Mechanical Model of the Atom
 It didn’t explain WHY metals and metal
compounds give off characteristic colors
when they are flame tested
 It didn’t explain why metals glow when
heated – first red, orange yellow and
then white
 It didn’t explain the CHEMICAL
properties of elements
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3. Section 7.5
The Quantum Mechanical Model of the Atom
BOHR’S THEORY
Electrons are located at
specific energy levels
surrounding the
nucleus
Each rung on the ladder
represents an energy
level
The higher the energy
Bohr thought the electrons moved in fixed
level – the farther it is
from the nucleus ORBITS around the nucleus – we know
this is
not true today
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4. Section 7.5
The Quantum Mechanical Model of the Atom
BOHR MODEL
 First model of the electron structure
 Gives levels where an electron is most likely to be
found
 Incorrect today, but a key in understanding the atom
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5. Section 7.4
The Bohr Model
• Bohr’s model gave hydrogen atom energy levels
consistent with the hydrogen emission spectrum.
• Ground state – lowest possible energy state (n = 1)
• Bohr’s model is incorrect. This model only works for
hydrogen.
• Electrons do not move around the nucleus in
circular orbits.
Electronic Transitions in
Electronic Transitions the Bohr Model for the
in the Bohr Model for Hydrogen Atom
the Hydrogen Atom
b) An Orbit-Transition
a) An Energy-Level Diagram, Which
Diagram for Electronic Accounts for the Return to TOC
5

6. Section 7.5
The Quantum Mechanical Model of the Atom
SCHRÖDINGER'S THEORY
 He agreed that electrons
have a specific amount of
energy
 He believed that the The electrons move
distance between rungs
on the ladder were not in regions of
consistent – they get
closer together as you probability around
move higher up
 Quantum – the amount of
the nucleus called
energy needed to move
from one energy level to
another ORBITALS
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7. Section 7.5
The Quantum Mechanical Model of the Atom
Quantum theory, also called wave mechanics,
describes the arrangement and space
occupied by electrons. Orbitals refers to the
three-dimensional regions in space where there is a
high probability of finding an electron around an
atom.
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8. Section 7.5
The Quantum Mechanical Model of the Atom
CHARACTERISTICS OF
Extremely small mass
Located outside the nucleus
Moving at extremely high speeds in
a sphere
Have specific energy levels
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9. Section 7.5
The Quantum Mechanical Model of the Atom
ENERGY OF
ELECTRONS
When atoms are heated, bright lines
appear called line spectra
Electrons in atoms arranged in discrete
levels.
An electron absorbs energy to “jump” to a
higher energy level.
When an electron falls to a lower energy
level, energy is emitted.
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10. Section 7.5
The Quantum Mechanical Model of the Atom
LOSS AND GAIN OF
G L
a o
I s
n s
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11. Section 7.5
The Quantum Mechanical Model of the Atom
LEARNING CHECK
Answer with
1) Energy absorbed 2) Energy emitted
3) No change in energy
A. What energy change takes place when
an electron in a hydrogen atom moves
from the first (n=1) to the second shell
(n=2)?
B. What energy change takes place when
the electron moves from the third shell to
the second shell?
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12. Section 7.5
The Quantum Mechanical Model of the Atom
SOLUTION
A. 1) Energy absorbed
B. 2) Energy emitted
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13. Section 7.5
The Quantum Mechanical Model of the Atom
• We do not know the detailed pathway of an electron.
• The electrons move in regions of probability around the
nucleus called ORBITALS
RELATIVE ORBITAL SIZE
 Difficult to define precisely.
 Orbital is a wave function.
 Picture an orbital as a three-dimensional
electron density map.
 Hydrogen 1s orbital:
 Radius of the sphere that encloses 90% of
the total electron probability. 13
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14. Section 7.5
THEQuantum Mechanical
ELECTRONS MOVE Model
INofREGIONS
the Atom OF
PROBABILITY AROUND THE NUCLEUS
CALLED ORBITALS
DEFINING THESE ORBITALS:
Quantum Numbers are used to define:
 The energy of the electron
 The electron’s relative distance from the nucleus
 The size and shape of the ORBITAL
 The pairings of the electrons
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15. Section 7.5
The Quantum Mechanical Model of the Atom
QUANTUM NUMBERS
Principle Quantum Number (n) – define the
energy of the electron
n=1 is closest to the nucleus – low energy
n=2 is farther than n=1, slightly more
energy
n=3 is farther than n=1 and n=2, still
increasing in energy
n=4 …..
Remember – The difference in energy
between energy levels decreases as “n”
increases
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16. Section 7.5
The Quantum Mechanical Model of the Atom
Within each principle energy level (n) – there are
sublevel(s).
The larger the value of ‘n’, the more sublevels you
can have.
Sublevels – named by their shape
s – sphere p – pear
d- dumbbell f - fundamental
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17. Section 7.5
The Quantum Mechanical Model of the Atom
TWO REPRESENTATIONS FOR AN S ORBITAL
Figure 3.16, pg. 77
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Investigating Chemistry, 2nd Edition

18. Section 7.5
The Quantum Mechanical Model of the Atom
REPRESENTATIONS FOR P ORBITALS
EACH ORBITAL CAN HOLD UP TO 2 ELECTRONS,
REGARDLESS OF SHAPE. THIS SET OF THREE
ORBITALS HOLDS 6 ELECTRONS.
Figure 3.17, pg. 77
Investigating Chemistry, 2nd Edition
© 2009 W.H. Freeman & Company
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19. Section 7.5
The Quantum Mechanical Model of the Atom
THERE IS A SET OF FIVE DIFFERENT D ORBITALS.
THERE IS A SET OF SEVEN F ORBITALS.
EACH ORBITAL REGARDLESS OF ITS SHAPE HOLDS
2 ELECTRONS.
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20. Section 7.7
Orbital Shapes and Energies
1s Orbital
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20

21. Section 7.7
Orbital Shapes and Energies
Two Representations
of the Hydrogen 1s,
2s, and 3s Orbitals
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21

22. Section 7.7
Orbital Shapes and Energies
2px Orbital
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22

23. Section 7.7
Orbital Shapes and Energies
2py Orbital
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23

24. Section 7.7
Orbital Shapes and Energies
2pz Orbital
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24

25. Section 7.7
Orbital Shapes and Energies
The Boundary Surface Representations of All Three 2p Orbitals
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25

26. Section 7.7
Orbital Shapes and Energies
3dx -y Orbital
2 2
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26

27. Section 7.7
Orbital Shapes and Energies
3dxy Orbital
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27

28. Section 7.7
Orbital Shapes and Energies
3dxz Orbital
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28

29. Section 7.7
Orbital Shapes and Energies
3dyz Orbital
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29

30. Section 7.7
Orbital Shapes and Energies
3d z 2 Orbital
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30

31. Section 7.7
Orbital Shapes and Energies
The Boundary Surfaces of All of the 3d Orbitals
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31

32. Section 7.7
Orbital Shapes and Energies
Representation of the 4f Orbitals in Terms of Their Boundary
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32

33. Section 7.5
The Quantum Mechanical Model of the Atom
Principle Energy Level Sublevel
n= 1 s
n=2 s and p
n=3 s and p and d
n=4 s, p, d, and f
NOTICE: The value of ‘n’ tells you how many
sublevels are present in that energy level
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34. Section 7.6
Quantum Numbers
• Principal quantum number (n) – size and energy
of the orbital.
• Angular momentum quantum number (l) – shape
of atomic orbitals (sometimes called a subshell).
• Magnetic quantum number (ml) – orientation of
the orbital in space relative to the other orbitals
in the atom.
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34

35. QUANTUM NUMBERS FOR THE FIRST FOUR LEVELS
OF ORBITALS IN THE HYDROGEN ATOM
35

36. Section 7.6
Quantum Numbers
Exercise
For principal quantum level n = 3,
determine the number of allowed subshells
(different values of l), and give the
designation of each. (hint refer to previous
chart)
# of allowed subshells = 3
l = 0, 3s
l = 1, 3p
l = 2, 3d
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36

37. Section 7.6
Quantum Numbers
Exercise
For l = 2, determine the magnetic quantum
numbers (ml) and the number of orbitals.
(note refer to previous chart)
magnetic quantum numbers = –2, – 1, 0, 1, 2
number of orbitals = 5
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37

38. Section 7.7
Orbital Shapes and Energies
Locating these on the Periodic Table
Principle Energy Level (n) – is the period in the periodic
table
The Sublevels are located in specific regions – Color these
together
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39. Section 7.7
Orbital Shapes and Energies
• The periodic table is structured so that elements with the same type of valence electron configuration are
arranged in columns.
•The left-most columns include the alkali metals and the alkaline earth metals. In these elements the valence s
orbitals are being filled
• On the right hand side, the right-most block of six elements are those in which the valence p
orbitals are being filled
• In the middle is a block of ten columns that contain transition metals. These are elements in which d orbitals are
being filled
• Below this group are two rows with 14 columns. These are commonly referred to the f-block metals. In these
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columns the f orbitals are being filled 39

40. Section 7.7
Orbital Shapes and Energies
• The periodic table is structured so that elements with the same type of valence electron configuration are
arranged in columns.
Important facts to remember:
•2, 6, 10 and 14 are the number of electrons that can fill the s, p, d and f subshells (the l=0,1,2,3
azimuthal quantum number)
•The 1s subshell is the first s subshell, the 2p is the first p subshell
•3d is the first d subshell, and the 4f is the first f subshell Return to TOC
40

41. Section 7.7
Orbital Shapes and Energies
Naming the sublevels
2s 2p
3s 3p 3d
4s 4p 4d 4f
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42. Section 7.7
Orbital Shapes and Energies
Orbitals are regions of probability – each orbital can hold a
maximum of 2 e-
The ‘s’ sublevel has 1 orbital
The ‘p’ sublevel has 3 orbitals
The ‘d’ sublevel has 5 orbitals
The ‘f’ sublevel has 7 orbitals
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43. Section 7.7
Orbital Shapes and Energies
Do you have to memorize this?
NO
Look at the sublevel regions that you colored in on your
periodic table.
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44. Section 7.7
Orbital Shapes and Energies
Count how many electrons are in the ‘s’ sublevel
2
This means that since there are two electrons, and each
orbital can hold two electrons, that there is only ONE
orbital.
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45. Section 7.7
Orbital Shapes and Energies
Count how many electrons are in the ‘p’ sublevel
6
This means that since there are six electrons, and each
orbital can hold two electrons, that there are THREE
orbitals.
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46. Section 7.7
Orbital Shapes and Energies
Count how many electrons are in the ‘d’ sublevel
10
This means that since there are ten electrons, and each
orbital can hold two electrons, that there are FIVE
orbitals.
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47. Count how many electrons are in the ‘f’ sublevel
14
This means that since there are fourteen electrons,
and each orbital can hold two electrons, that
there are SEVEN orbitals.

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