Quantum Mechanical Model of the Atom ppt

1. MODELS OF THE ATOM
Beginning with Bohr

2. Section 7.5
The Quantum Mechanical Model of the Atom
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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
level – the farther it is
from the nucleus
Bohr thought the electrons moved in
fixed ORBITS around the nucleus –
we know this is not true today

3. Section 7.5
The Quantum Mechanical Model of the Atom
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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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4. Section 7.4
The Bohr Model
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4
• 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 the
Bohr Model for the
Hydrogen Atom
a) An Energy-Level
Diagram for Electronic
Transitions
Electronic Transitions
in the Bohr Model for
the Hydrogen Atom
b) An Orbit-
Transition Diagram,
Which Accounts for
the Experimental
Spectrum

5. Section 7.5
The Quantum Mechanical Model of the Atom
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SCHRÖDINGER'S THEORY
 He agreed that electrons
have a specific amount of
energy
 He believed that the
distance between rungs on
the ladder were not
consistent – they get closer
together as you move
higher up
 Quantum – the amount of
energy needed to move
from one energy level to
another
The electrons
move in regions of
probability
around the
nucleus called
ORBITALS

6. Section 7.5
The Quantum Mechanical Model of the Atom
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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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7. Section 7.5
The Quantum Mechanical Model of the Atom
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CHARACTERISTICS OF ELECTRONS
 Extremely small mass
 Located outside the nucleus
 Moving at extremely high speeds in a
sphere
 Have specific energy levels
7

8. Section 7.5
The Quantum Mechanical Model of the Atom
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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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9. Section 7.5
The Quantum Mechanical Model of the Atom
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LOSS AND GAIN OF ENERGY
9
G
a
I
n
L
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s
s

10. Section 7.5
The Quantum Mechanical Model of the Atom
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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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11. Section 7.5
The Quantum Mechanical Model of the Atom
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SOLUTION
A. 1) Energy absorbed
B. 2) Energy emitted
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12. Section 7.5
The Quantum Mechanical Model of the Atom
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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. 12
• We do not know the detailed pathway of an electron.
• The electrons move in regions of probability around the
nucleus called ORBITALS

13. Section 7.5
The Quantum Mechanical Model of the Atom
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THE ELECTRONS MOVE IN REGIONS 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

14. Section 7.5
The Quantum Mechanical Model of the Atom
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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

15. Section 7.5
The Quantum Mechanical Model of the Atom
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SUBLEVELS
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

16. Section 7.5
The Quantum Mechanical Model of the Atom
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TWO REPRESENTATIONS FOR AN S ORBITAL
Figure 3.16, pg. 77
Investigating Chemistry, 2nd Edition
© 2009 W.H. Freeman & Company

17. Section 7.5
The Quantum Mechanical Model of the Atom
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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

18. Section 7.5
The Quantum Mechanical Model of the Atom
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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.

19. Section 7.7
Orbital Shapes and Energies
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19
Two Representations
of the Hydrogen 1s,
2s, and 3s Orbitals

20. Section 7.7
Orbital Shapes and Energies
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20
The Boundary Surface Representations of All Three 2p Orbitals

21. Section 7.7
Orbital Shapes and Energies
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21
The Boundary Surfaces of All of the 3d Orbitals

22. Section 7.7
Orbital Shapes and Energies
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22
Representation of the 4f Orbitals in Terms of Their Boundary
Surfaces

23. Section 7.7
Orbital Shapes and Energies
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• As shown in Table, the s subshell has one lobe, the p
subshell has three lobes, the d subshell has five lobes,
and the f subshell has seven lobes. Each of these lobes
is labeled differently and is named depending on which
plane the lobe is resting in. If the lobe lies along the x
plane, then it is labeled with an x, as in 2px. If the lobe
lies along the xy plane, then it is labeled with a xy such
as dxy. Electrons are found within the lobes. The plane
(or planes) that the orbitals do not fill are called nodes.
These are regions in which there is a 0 probability
density of finding electrons.
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24. Section 7.7
Orbital Shapes and Energies
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24

25. Section 7.5
The Quantum Mechanical Model of the Atom
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SUBLEVELS
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

26. Section 7.6
Quantum Numbers
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26
• 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.

27. QUANTUM NUMBERS FOR THE FIRST FOUR LEVELS OF ORBITALS IN
THE HYDROGEN ATOM
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28. Section 7.6
Quantum Numbers
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28
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

29. Section 7.6
Quantum Numbers
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29
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

30. Section 7.7
Orbital Shapes and Energies
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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

31. Section 7.7
Orbital Shapes and Energies
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31
• 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 columns the f orbitals are being filled

32. Section 7.7
Orbital Shapes and Energies
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32
• 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

33. Section 7.7
Orbital Shapes and Energies
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Naming the sublevels
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f

34. Section 7.7
Orbital Shapes and Energies
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Orbitals
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

35. Section 7.7
Orbital Shapes and Energies
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Orbitals
Do you have to memorize this?
NO
Look at the sublevel regions that you colored in on your
periodic table.

36. Section 7.7
Orbital Shapes and Energies
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Orbitals
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.

37. Section 7.7
Orbital Shapes and Energies
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Orbitals
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.

38. Section 7.7
Orbital Shapes and Energies
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Orbitals
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.

39. ORBITALS
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.