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1. Module 2.2:
The Modern Atomic Theory
and Quantum Mechanics
Veronica Calindas, R.C.
Adamson University
1
This lecture is based on textbooks authored by Chang, Brown & Holme, and Redmore

2. Modern Atomic Theory
(from Dalton’s Hypotheses)
1. All matter is composed of atoms. The atom is the
smallest body that retains the unique identity of the
element.
2. Atoms of one element cannot be converted into
atoms of another element in a chemical reaction.
Elements can only be converted into other elements
in nuclear reactions.

3. Modern Atomic Theory
(from Dalton’s Hypotheses)
3. All atoms of an element have the same number
of protons and electrons, which determines the
chemical behavior of the element. Isotopes of an
element differ in the number of neutrons, and thus in
mass number. A sample of the element is treated as
though its atoms have an average mass.
4. Compounds are formed by the chemical
combination of two or more elements in specific
ratios.

4. The Atom and its Subatomic
Particles

5. Properties of Subatomic Particles
Properties of the Three Key Subatomic Particles
Charge Mass
Relative
1+
0
1-
Absolute (C)*
+1.60218 x 10-19
0
-1.60218 x 10-19
Relative (amu)†
1.00727
1.00866
0.00054858
Absolute (g)
1.67262 x 10-24
1.67493 x 10-24
9.10939 x 10-28
Location
in the Atom
Nucleus
Outside
Nucleus
Nucleus
Name (Symbol)
Electron (e-)
Neutron (n0)
Proton (p+)
Table 2.2
* The coulomb (C) is the SI unit of charge.
† The atomic mass unit (amu) equals 1.66054 x 10-24 g.

6. Atomic Number, Mass Number
and Isotopes
Atomic Number (Z) = number of protons present in the nucleus
of each atom of an element.
Mass Number (A) = total number of neutrons and protons
present in the nucleus of an atom of an element.

7. Atomic Number, Mass Number
and Isotopes

8. Atomic Number, Mass Number
and Isotopes
 In some cases, atoms that have the same atomic
number but different mass numbers exist. These are
called isotopes.

9. Sample Problem:
(1) Give the number of protons, neutrons
and electrons in each of these species:
a) 82Pb b) 29Cu
c) 80Hg d) 80Hg
ANSWERS: a) 82, 125, 82 b)29, 34, 29 c) 80, 119, 80, d) 80, 120, 80
207 63
199 200

10. Molecules and Ions
 Molecules – an aggregate of at least two
atoms in a definite arrangement held
together by chemical forces (chemical bonds)
-may contain atoms of the same element or
atoms of two or more elements.
• Ions – an atom or a group of atoms that has
either a net positive or net negative charge.
- only e- are either lost or gained during
chemical changes

11. Molecules
 Monoatomic molecules – those that exist as single
atoms
e.g. Group 8A Noble Gases
 Diatomic molecules – those that contains only two
atoms.
e.g. N2, O2, and most of Group 7A Halogens
 Polyatomic molecules – those that contain more
than two atoms

12. Ions
 Cation (X+) – an ion with positive net charge due to
loss of electron
 Anion (X-) – an ion with negative net charge due to
gaining of electron
Na
11 protons
11 electrons
Na+ 11 protons
10 electrons
Cl
17 protons
17 electrons Cl- 17 protons
18 electrons

13. Ions
 Monoatomic ions– an ion that contains only one
atom
e.g. Na+, Mg2+, Fe3+, S2-, N3-
 Polyatomic ions – an ion containing more than one
atom
e.g. OH-, CN-, NH4+

14. Sample Problem:
(1) Give the number of protons, neutrons
and electrons in each of these species:
a) K+ b) Mg2+
c) Fe3+ d) Br-
e) Mn2+ f) C-4
ANSWERS: a) 11, 12, 10 b) 12, 12, 10 c) 26, 29, 23 d) 35, 45, 36 e) 25, 30,
23 f) 6, 6, 10

15. The Duality of Electron
 Erwin Schrödinger wrote a complicated
mathematical equation that incorporates both
particle behavior and wave behavior of an electron
with respect to its probable location in the space of
the system.
 Schrödinger’s equation for hydrogen atom gave birth
to a new era in physics and chemistry, this new field
is called quantum mechanics
Eψ = -h2
8π2μ {∂2ψ
∂x2
+ ∂2ψ
∂y2 +∂2ψ
∂z2
{
+V(x,y,z)ψ

16. The Schrödinger Equation
Wave function ( )
describes:
1. energy of e- with a
given
2. probability of finding
e- in a volume of space
Schrödinger’s equation can
only be solved exactly for the
hydrogen atom. Must
approximate its solution for
multi-electron systems.

17. The Four Quantum Numbers
 Derived from Schrödinger’s equation
for the hydrogen atom
 Quantum numbers are required to
describe the distribution of e- in
hydrogen and other atoms, and the
behavior of a specific e-.
17

18. The Four Quantum Numbers
1. Principal Quantum Number (n)
2. Azimuthal or Angular Momentum
Quantum Number (l )
3. Magnetic Quantum Number (ml )
4. Spin Quantum Number (ms)
18

19. Principal Quantum Number (n)
 Relates to the
average distance of
an e- from the
nucleus in a
particular orbital
 Determines the
energy of an orbital
 Values are whole
numbers only
19

20. The Schrödinger Equation
20
fn(n, l, ml, ms)
principal quantum number n
Where n = 1, 2, 3, 4, ….
n=1 n=2 n=3
distance of e- from the nucleus

21. Where 90% of the
e- density is found
for the 1s orbital
Principal Quantum Number (n)

22. Angular Momentum Quantum
Number (l)
 Determines the shape of
an orbital
 The value of l depends on
the value of n (from 0 to
n-1)
◦ 0  s  spherical
◦ 1  p  dumb-bell
◦ 2  d  clover leaf
◦ 3  f
 Subshell – one or more
atomic orbitals having
the same n and l values
22

23. The Schrödinger Equation
23
fn(n, l, ml, ms)
angular momentum quantum number l
for a given value of n, l = 0, 1, 2, 3, … n-1
Thus, if n = 1, then l = 0
n = 2, then l = 0 or 1
n = 3, then l = 0, 1, or 2
Shape of the “volume” of space that the e- occupies

24. Orbital ‘Shapes’ Based on l Values
l = 0 (s orbitals)
l = 1 (p orbitals)

25. Orbital ‘Shapes’ Based on l Values
l = 2 (d orbitals)

26. Orbital ‘Shapes’ Based on l Values
l = 3 (f orbitals)

27. Magnetic Quantum Number (ml)
 Describes the orientation of the orbital in
space
 Values depend on the l (values are denoted as
–l, 0, +l)
 For a subshell of quantum number l, there is
a total of 2l + 1 atomic orbitals within that
subshell. Atomic orbitals within the same
subshell have essentially the same energy.
27

28. The Schrödinger Equation
28
fn(n, l, ml, ms)
magnetic quantum number ml
for a given value of l
ml = -l, …., 0, …. +l
orientation of the orbital in space
if l = 1 (p orbital), then ml = -1, 0, or 1
if l = 2 (d orbital), then ml = -2, -1, 0, 1, or 2

29. Orbital ‘Orientation’ Based on ml
Values
ml = -1 ml = 0 ml = 1

30. Orbital ‘Orientation’ Based on ml
Values
ml = -2 ml = -1 ml = 0 ml = 1 ml = 2

31. Atomic Orbitals
31

32. Atomic Orbitals
32

33. Spin Quantum Number (ms)
33
 Emission spectra showed
that the lines can be split
by applying an external
magnetic field.
 According to
Electromagnetic Theory, a
spinning charge generates
a magnetic spin, which
causes the e- to behave
like a magnet.
 There are 2 possible values
for motion of e-: clockwise
(+ ½ ) or counter
clockwise (– ½ )

34. The Schrödinger Equation
34
fn(n, l, ml, ms)
spin quantum number ms where the only possible
values are either +½ or -½
ms = -½ms = +½

35. Sample Problem:
 List the values of n, l, and ml for
orbitals of the following subshells:
(1) 4d
(2) 6p
(3) 4s
(4) 5f
ANSWERS: (1) n=4, l=2, ml=7 ,(2) n=6, l=1, ml=3, (3) n=4, l=0,
ml=1, (4) n=5, l=3, ml=7

36. Sample Problem:
 What is the total number of orbitals
associated with the following principal
number?
(1) n = 3
(2) n = 5
(3) n = 2
(4) n = 4
ANSWERS: (1) 9; (2) 19; (3) 7; (4) 16

37. Electron Configuration
 Describes how the electrons are distributed
among the various atomic orbitals.
 A shorthand way of writing the quantum
numbers for a specific atom

38. Electron Configuration: Orbital
Diagram
Example: Hydrogen atom: n=1, l=0, ml=0
1s1
principal quantum
number n angular momentum
quantum number l
number of electrons
in the orbital or subshell
1s1
H
Then, the arrow-box configuration would yield:
Upward spin = +½
Downward spin = -½

39. Rules for Writing an Electron
Configuration
1) From the modern Atomic Theory, in a neutral
atom, the number of protons equal to the number
of electrons.
If Atomic number = number of protons and
Number of protons = number of electrons, then
Atomic number = number of electron
(for atoms with no charge)
Only 2 electrons can occupy any subshell.

40. Rules for Writing an Electron
Configuration
2) No two electrons in the same atom can have the
same four quantum numbers (Pauli exclusion
principle).
◦ If two electrons have the same n, l, and ml then they MUST
have different values for ms – meaning, they must have
opposite spins
Example:
1s2
He
1s21s2
(a) (b) (c)

41.  Paramagnetism – when the two electrons
have parallel spins
 Paramagnetic substances are attracted to magnets.
The Pauli Exclusion Principle
1s2
He
1s2

42.  Diamagnetism – when the two electrons in a
single orbital have opposite spins
 Diagmagnetic substances are slightly repelled by magnets.
He
1s2
REMEMBER: Any atom with an odd number of electrons must
be paramagnetic. On the other hand, atoms that have an even
number of electrons can either be paramagnetic or diamagnetic.
The Pauli Exclusion Principle

43. 3) The most stable arrangement of electrons in
subshells is the one with the greatest parallel spins
(Hund’s Rule of Multiplicity).
Example: Nitrogen (Z=7) is 1s2 2s2 2p3, therefore the
electron distribution as denoted by the arrow-box
configuration would be
Rules for Writing an Electron
Configuration
N
1s2 2s2 2px 2py 2pz

44. Example: Be (Z=4) is 1s2 2s2, therefore a diamagnetic
Rules for Writing an Electron
Configuration
Be
1s2 2s2
Example: Si (Z=14) is 1s2 2s2 2p6 3s2 3p2 and thus, a
paramagnetic
Si
1s2 2s2 2px 2py 2pz 3s2 3px 3py 3pz

45. 4) An electron occupies the lowest energy
orbital first before going to the next energy
level (Aufbau principle).
Rules for Writing an Electron
Configuration
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

46. H 1 electron
H 1s1
He 2 electrons
He 1s2
Li 3 electrons
Li 1s22s1
Be 4 electrons
Be 1s22s2
B 5 electrons
B 1s22s22p1
C 6 electrons
? ?
46

47. C 6 electrons
C 1s22s22p2
N 7 electrons
N 1s22s22p3
O 8 electrons
O 1s22s22p4
F 9 electrons
F 1s22s22p5
Ne 10 electrons
Ne 1s22s22p6
47

48. The Shielding Effect in Many-Electron
Atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
 The 1s lies at lower energy level than 2s and 2p in a many-electron
atom
• This means that the 2s and 2p
electrons are partly ‘shielded’ from the
nucleus’s attractive force by the much-
closer 1s electron.
•Because the stability of an electron is
determined by the strength of its
attraction to the nucleus, it follows
that it will require less energy to
remove an electron from 2p orbital
than it would to remove the electron in
2s.

49. Problem:
 Write the electronic configuration of
the following:
1. Ne (Z= 10)
2. Sc (Z= 21)
3. Ru (Z= 44)
4. Pb (Z= 82)
5. W (Z= 74)

50. Valence Electrons
 Electrons which occupies the
outermost orbitals of an electron or the
valence shell
 Responsible for the reactions that an
atom of an element can undergo
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53. 7.87/21/2013 53General Chemistry for Engineers

54. What is the electron configuration of Mg?
Mg 12 electrons
1s < 2s < 2p < 3s < 3p < 4s
1s22s22p63s2 2 + 2 + 6 + 2 = 12 electrons
Abbreviated as [Ne]3s2 [Ne] 1s22s22p6
What are the possible quantum numbers for the last (outermost)
electron in Cl?
Cl 17 electrons 1s < 2s < 2p < 3s < 3p < 4s
1s22s22p63s23p5 2 + 2 + 6 + 2 + 5 = 17 electrons
Last electron added to 3p orbital
n = 3 l = 1 ml = -1, 0, or +1 ms = ½ or -½
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56. Classification of Groups of Elements in the Periodic
Table Accd’g to Type of Outermost Subshell filled