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Atomic Physics -4
§ 1.1 Historical perspective
1895
1896
The discovery of X-rays
Discovery of radioactivity
Röntgen
Becquerel
4
+
U →234
Th
90
2 He
238
92
1897
1900
1905
1911
1912
1913
1919
1920
The discovery of electron
The discovery of the black body radiation formula
The development of the theory of special relativity
Rutherford’s atomic model
Discovery of isotopes
Bohr’s theory of the hydrogen atom
Induced nuclear transmutation
The radii of a few heavy nuclei
~ 10-14 m = 10 F << 10-10 m
J.J. Thomson
Max Planck
Albert Einstein
Rutherford
J.J. Thomson
Niels Bohr
J.J. Thomson
Chadwick
1928 Alpha decay
Gamow, Gurney and Condon
1932 Discovery of neutron
Chadwick
1932 n-p hypothesis
Heisenberg
1932 Discovery of positron
Anderson
1934 Beta decay
Enrico Fermi
1935 Roles of mesons in nuclear forces
Yukawa
1936 Discovery of μ meson
Anderson and Neddermeyer
1946 Discovery of π meson
Powell
1956 Non-conservation of parity in beta decay
Lee, Yang and 吳健雄教授
Atomic Physics
The physics of the electronic, extra-nuclear structure of
Nuclear Physics
The physics of the atomic nucleus, believed to be constituted
of neutrons and protons
Elementary Particle Physics
The physics of quarks and gluons, believed to be the
constituents of protons and neutrons, and of leptons
and gauge bosons and…
who knows what else!
Quarks, gluons, leptons, and gauge bosons are believed to
have no substructure.
atoms
Characteristics of types of
radiation
Radioactivity
(Spontaneous emission of radiation)
Type
Alpha
particle
Beta
particle
Positron
Gamma ray
Symbol
Charge
Mass (amu)
2+
4.002 60
0 e
-1
1-
0.000 548 6
0 e
+1
1+
0.000 548 6
0
0
He
β or
β or
γ
Types of Radiation
The three most common types
of radiation are alpha (α),
beta (β), and gamma (γ).
The Discovery of Atomic Structure
Radioactivity
The Discovery of Atomic Structure
Radioactivity
A high deflection towards the positive plate corresponds
to radiation which is negatively charged and of low
mass. This is called β-radiation (consists of electrons).
No deflection corresponds to neutral radiation. This is
called γ-radiation.
Small deflection towards the negatively charged plate
corresponds to high mass, positively charged radiation.
This is called α-radiation (He nuclei).
Two isotopes of Helium
or Na-23
or Na-24
Isotope: one of two or more atoms having the same
number of protons but different numbers
of neutrons
Atomic Number




Atoms are composed of identical protons, neutrons, and
electrons
 How then are atoms of one element different from
another element?
Elements are different because they contain different
numbers of PROTONS
The “atomic number” of an element is the number of
protons in the nucleus
# protons in an atom = # electrons
Atomic Number
Atomic number (Z) of an element is the number
of protons in the nucleus of each atom of that
element.
Element
# of protons
Atomic # (Z)
Carbon
6
6
Phosphorus
15
15
Gold
79
79
Mass Number
Mass number is the number of protons and
neutrons in the nucleus of an isotope:
Mass # = p+ + n0
p+
n0
e- Mass #
8
10
8
18
Arsenic - 75
33
42
33
75
Phosphorus - 31
15
16
15
31
Nuclide
Oxygen - 18
Complete Symbols

Contain the symbol of the element, the mass
number and the atomic number.
Superscript →
Mass
number
Subscript →
Atomic
number
X
A
X
Z
Complete Symbols
Symbol
A = Mass number(equal to the no. of proton + no. of
neutron)
Z = Atomic number (equal to the no. of protons,
therefore, equal to the no. of electrons)
Contain the symbol of the element, the mass number and the atomic
number.
1
H
1
A=1
Z=1
p=1
e=1
n=0
16
O
8
A = 16
Z=8
p=8
e=8
n=8
Symbols

Find each of these:
a) number of protons
b) number of
neutrons
c) number of
electrons
d) Atomic number
e) Mass Number
80
35
Br
Symbols

If an element has an atomic
number of 34 and a mass
number of 78, what is the:
a) number of protons
b) number of neutrons
c) number of electrons
d) complete symbol
Symbols
 If an element has 91
protons and 140 neutrons
what is the
a) Atomic number
b) Mass number
c) number of electrons
d) complete symbol
Symbols
 If an element has 78
electrons and 117 neutrons
what is the
a) Atomic number
b) Mass number
c) number of protons
d) complete symbol
Practice – Complete the table
27
13
Al
Practice – Complete the table
13
6C
96
42 Mo
27
13 Al
133
55 Cs
Tro: Chemistry: A Molecular Approach, 2/e
No change occurs inside a nucleus in chemistry
Atoms can lose or gain electrons
Na − e−  Na+
positive ion = cation
Mg − 2e−  Mg2+
Cl + e−  Cl−
O + 2e−  O2−
negative ion = anion
Practice – Complete the table
Al
3+
Practice – Complete the table
S
2−
2+
Mg
Al3 +
Br
Tro: Chemistry: A Molecular Approach, 2/e
−
Symbol
Number of Number of
Number of
Protons in Neutrons
Net charge
Electrons
Nucleus in Nucleus
87Rb+
16
18
36
2−
28
1+
Symbol
Number of Number of
Number of
Protons in Neutrons
Net charge
Electrons
Nucleus in Nucleus
87Rb+
37
50
36
1+
32S2−
16
18
18
2−
65Cu+
29
36
28
1+
Isotopes




Dalton was wrong about all elements of the
same type being identical
Atoms of the same element can have
different numbers of neutrons.
Thus, different mass numbers.
These are called isotopes.
Isotopes



Frederick Soddy (1877-1956) proposed the idea of
isotopes in 1912
Isotopes are atoms of the same element having
different masses, due to varying numbers of
neutrons.
Soddy won the Nobel Prize in Chemistry in 1921 for
his work with isotopes and radioactive materials.
Isotopes
Adding neutrons to a nucleus (or taking them away) does not affect the
nuclear charge (or number of electrons) so chemically the atom is not different
It does affect the nuclear properties (stability etc )
- specify an element by Z
- specify an isotope by A
a complete description requires both
Z is implied by the historical name
eg 14C A = 14 Z = 6 - carbon with 2 extra neutrons
Hydrogen
Deuterium
Tritium
p+e
p+n+e
p+n+n+e
1
1
1
1H
2H
3H
(in heavy water)
These are all isotopes of hydrogen but are not separate elements
they have the same chemical properties but different nuclear properties
(therefore things like nuclear burning in stars are different).
Naming Isotopes
 We
can also put the mass
number after the name of the
element:
carbon-12
carbon-14
uranium-235
Isotopes are atoms of the same element having
different masses, due to varying numbers of
neutrons.
Isotope
Protons Electrons
Neutrons
Hydrogen–1
(protium)
1
1
0
Hydrogen-2
(deuterium)
1
1
1
1
1
2
Hydrogen-3
(tritium)
Nucleus
Isotopes
Elements
occur in
nature as
mixtures of
isotopes.
Isotopes are
atoms of the
same element
that differ in
the number of
neutrons.
Atomic Weights


Weighted average of the masses of the constituent isotopes
Lower number on periodic chart

How do we know what the values of these numbers are?
Measuring Atomic Mass
--the Mass Spectrometer
The mass
spectrometer
can be used
to determine
the atomic
mass of
isotopes.
Mass Spectrometry
A mass spectrometer is a
device that separates positive
gaseous ions according to their
mass-to-charge ratios
A record of the separation of
ions is called a mass spectrum
Mass Spectrometer
If a stream of positive ions
having equal velocities is brought
into a magnetic field, the lightest
ions are deflected the most,
making a tighter circle
Mass Spectrum of Neon

The mass spectrum neon shows three isotopes with the isotope
at atomic mass = 20 accounting for more than 90% of neon.
Mass Spectrum of Germanium

The mass spectrum of germanium shows 5 peaks at relative
atomic masses of 70, 72,73,74, and 75
Atomic Mass
Actual masses of individual atoms are small and impractical
to work with.
It is more useful to compare the relative masses of atoms
using a reference isotope as a standard
The carbon-12 atom was assigned a mass of exactly 12
atomic mass units.
Atomic mass unit (amu) – one twelfth of the mass of
carbon-12 atom.
Atomic Mass Units




An atomic mass unit (amu) is equal to exactly 1/12 of the mass
of an atom of Carbon 12.
One atomic mass unit is equal to 1.66054 x 10-24 grams. Note
that this is slightly less than the mass of a proton or a neutron.
An atomic mass unit is sometimes called a Dalton (D).
1.00 g = 6.02214 x 1023 amu. This number is also known as
Avogadro’s Number and it defines the size of a quantity we call
a mole.
Atomic Mass



How heavy is an atom of oxygen?
 It depends, because there are different kinds of
oxygen atoms.
We are more concerned with the average atomic
mass.
This is based on the abundance (percentage) of
each variety of that element in nature.
 We don’t use grams for this mass because the
numbers would be too small.
Measuring Atomic Mass



Instead of grams, the unit we use is the Atomic
Mass Unit (amu)
It is defined as one-twelfth the mass of a
carbon-12 atom.
 Carbon-12 chosen because of its isotope
purity.
Each isotope has its own atomic mass, thus we
determine the average from percent
abundance.
To calculate the average:
 Multiply
the atomic mass of
each isotope by it’s
abundance (expressed as a
decimal), then add the
results.
Atomic Masses
Atomic mass is the average of all the
naturally occurring isotopes of that element.
Isotope
Symbol
Carbon-12
12C
Carbon-13
13C
Carbon-14
14C
Composition of
the nucleus
6 protons
6 neutrons
6 protons
7 neutrons
6 protons
8 neutrons
Carbon = 12.011
% in nature
98.89%
1.11%
<0.01%
Question
Knowns
and
Unknown
Solution
Answer
1H
1.6735 x 10−24 g
16O
2.6560 x 10−23 g
One atomic mass unit (amu) is defined as 1/12 of
the mass of a 12C atom.
12C
atom: 6 protons, 6 neutrons, 6 electrons.
1 amu = 1.6605 x 10−24 g
1H
1.6735 x 10−24 g
16O
2.6560 x 10−23 g
1 amu = 1.6605 x 10−24 g
1.6735 × 10
− 24
1 amu
g×
= 1.0078 amu
− 24
1.6605 × 10 g
1 amu
2.6560 × 10 g ×
15.995 amu
=
−24
1.6605 × 10 g
−23
Calculating the average relative
atomic mass

The average atomic mass that is shown in the periodic
table is really the weighted average of the atomic masses
of each of the elements isotopes. Germanium has 5
isotopes whose relative atomic masses are shown in the
table
Mass Number
70
72
73
74
75
% Abundance
20.55
27.37
7.67
36.74
7.67
Calculating the Average
Relative Atomic Mass

To calculate the average atomic mass multiply the atomic mass
of each isotope by its abundance (expressed as a decimal
fraction)
Mass Number
70
72
73
74
75
% Abundance
20.55
27.37
7.67
36.74
7.67
Average atomic mass
= (0.2055)(70) + (0.2737)(72) + (0.0767)(73) + (0.3674)(74)+ (0.0767)(75)
= 72.36
Note: atomic masses are ratios so they do not have real units although they are
sometimes called atomic mass units or amu
Lithium has two naturally occurring isotopes. Lithium-6 has an
atomic mass of 6.015 amu; lithium-7 has an atomic mass of 7.016
amu. The atomic mass of lithium is 6.941 amu. What is the
Percentage of naturally occurring lithium-7?
7.016x + 6.015(1-x) = 6.941
1.001x = 0.926
x=(.925)(100%) = 92.5%
A note on natural abundances of nuclides:
Elements with an even number of neutrons are more abundant than elements
with an odd number of neutrons. Elements with an even number of protons and
an even number of neutrons are more abundant than elements with an odd
number of protons and an even number of neutrons.
Moles




A mole is the amount of substance
that contains as many particles as
there atoms in exactly 12g of
carbon-12.
It’s a counting unit (like a dozen)
The number of particles in one
mole of a pure substance is
Avogadro’s number 6.022 x 1023
Molar mass – the mass of one mole
of a pure substance is its molar
mass.
Using a mass spectrometer, scientists determined that
the mass of one hydrogen atom (about 1 “atomic mass unit”) is 1.6605 x 1024 gram.
This means that there are 6.0223 x 1023 “amu” in
1.0000 g.
Or 6.0223 x 1023 hydrogen atoms in 1.0000 g.
We define 6.0223 x 1023 atoms of any element to be
“one mole” of that element.
It follows that:
one mole of He atoms (each 4 amu) = 4 grams He.
one mole of C atoms (each 12 amu) = 12 grams C.
Generalizing:
The atomic mass of any element = the number of grams in one mole of that
element.
That is, the larger, non-integral number for each element in the periodic table
is the element’s “grams per mole.”
Exceptions: elements whose atoms “pair up” to form molecules.
H2, O2, N2, F2, Cl2, Br2, I2
In this case, one mole = 6.0223 x 1023 molecules, not atoms.
So one mole of hydrogen is one mole of H2
molecules = 2 grams, not 1 gram.
How is the mole useful to chemists?
Take, for example, the compound iron sulfide, FeS.
The formula tells us that any amount of FeS contains equal
numbers of Fe and S atoms.
So suppose I have some iron and some sulfur and want to
make 100 g of FeS.
If I want equal numbers of Fe and S atoms, then I want
equal numbers of moles of Fe and S atoms.
Going to the Periodic Table, I see that 55.85 g Fe is one
mole, and 32.06g S is one mole. If I use these amounts I
will have 55.85 + 32.06 = 87.91 g FeS (Law of
Conservation of Matter.)
Scaling up, I can combine 63.53g Fe + 36.47g S to get 100g FeS.
By understanding the mole, I accomplished two things:
1. I did not waste any Fe or S.
2. I produced pure FeS, not a mixture of FeS and some leftover Fe or S.
Einstein – Energy/Mass Equivalence
In 1905, Albert Einstein published a 2nd major theory
called the Energy-Mass Equivalence in a paper
called, “Does the inertia of a body depend on its
energy content?”
Energy Unit Check
2
m
EB = ∆mc → Joule = kg × 2
s
W = Fx → Joule = Nm
m
Fnet = ma → N = kg × 2
s
2
m
m
E = W = kg × 2 × m = kg × 2
s
s
2
Mass Defect
The nucleus of the atom is held together by a STRONG NUCLEAR
FORCE.
The more stable the nucleus, the more energy needed to break it apart.
Energy need to break the nucleus into protons and neutrons is called the
Binding Energy
Einstein discovered that the mass of the separated particles is greater than
the mass of the intact stable nucleus to begin with.
This difference in mass (∆m) is called the mass defect.
Mass Defect - Explained
The extra mass turns into energy
holding the atom together.
Mass Defect – Example
A Ton of TNT
For some reason, the comparison unit for nuclear explosions which became most
popular was the "ton of TNT". A nominal energy release for a ton of TNT can be
extracted from general statements about nuclear weapons. One of those is "one
kilogram of mass converted to energy is equivalent to about 22 megatons of TNT".
From the Einstein equation, the conversion is
mc2 = (1kg)c2 = 9E16 Joules = 22 megatons TNT
mc2 = (0.001kg)c2 = 9E13 J = 22 kilotons
This is consistent with the oft-quoted statement that the 20 kiloton Hiroshima bomb
converted about 1 gram of mass to energy.
Paths of Radioactive Decay
Nucleosynthesis




After the creation of the universe, energy had
transformed into matter in accordance with
Einstein’s equation E = mc2.
The first types of matter to form were the smallest
fundamental particles: electrons, and quarks.
Quarks are particles that combine to form neutrons
and protons.
Nucleosynthesis is the fusing of fundamental and
subatomic particles to create atomic nuclei.
Fusion of Hydrogen and the Mass Defect
protons
4
2He
Positrons
4 11H
4
2He
+ 01 e
Binding energy of the 42He nucleus
• 2 neutrons + 2 protons:
2 x 1.67494E-24 + 2 x 1.67263E-24 = 6.69513E-24 g
• Subtract the actual mass of the nucleus:
6.69513E-24 – 6.64465E-24 = 5.048E-24 g
• This is the mass defect.
• E = (∆m)c2
• (5.048E-29 kg) x (2.998E8 m/s)2 = 4.537E-12 kg (m/s)2
• or 4.537E-12 J (Joules) = Binding energy for helium-4
For the reaction: H2(g) + ½ O2(g) → H2O(l)
the energy released is 4.7E-19 J per H2 molecule.
The mass of a stable nucleus is always less than
the mass of the individual particles that make up
the nucleus.
This is known as the mass defect (∆m). The
larger the mass defect the stronger the energy
that binds the nuclear particles together.
The binding energy (E) can be calculated by
substituting the mass defect into Einstein's
equation for the relationship between mass and
energy:
E = mc2 to become E = (∆m)c2
Periodic Table
Periodic Table – an arrangement of elements in which the
elements are separated into groups based on a set of
repeating properties.
Do You Understand Isotopes?
How many protons, neutrons, and electrons are in
14
6
C
11
6
C?
?
6 protons, 8 (14 - 6) neutrons, 6 electrons
How many protons, neutrons, and electrons are in
6 protons, 5 (11 - 6) neutrons, 6 electrons
Compton effect
Elastic scattering of massless photon with electron (initially at rest)  particle
nature of photon
§ 1.5 The nuclear constituents
Notation used to represent a given nuclide
Z: atomic number
A: atomic mass number
N: neutron number
A
Z
XN
A= Z +N
X: chemical symbol
M ≈ integer × M H
M:
the mass of a specific atom
MH: the mass of a hydrogen atom
Mendeleev’s Periodic Table


Dmitrii I. Mendeleev
arranged elements in the
periodic table by their
chemical and physical
properties.
He left open spaces in his
periodic table to account for
elements not yet discovered.
The Modern Periodic Table




The modern periodic table is also based on a
classification of elements in terms of their physical and
chemical properties.
The horizontal rows are called periods.
Columns contain elements of the same family or group.
Transition metals are the elements in group 3 through
12 in the periodic table.
Groups of Elements

Group 1 contains the alkali metals.

Group 2 contains the alkaline earth metals.

Group 17 contains the halogens.
Broad Categories of Elements

Metals are elements on the left-hand side of the table.



Metals are shiny solids that conduct heat and electricity well
and are malleable and ductile.
Nonmetals have properties opposite to those of the
metals and are on the right side of table
Metalloids are the elements between the metals and
nonmetals.
Continued


Main group elements or representative elements
are the elements in groups 1,2 and 13 through
18.
The noble gases are the elements in Group 18.
Kinds of Compounds





Molecular Compounds are composed of atoms held
together by covalent bonds.
Covalent bonds are shared pairs of electrons that
chemically bond atoms together.
Ionic Compounds are composed of positively and
negatively charged ions that are held together by
electrostatic attraction.
Ions with negative charge are called anions.
Ions with positive charge are called cations.
Periodic Table
Each element is identified by its symbol place in a square.
The atomic number of the element is shown centered above the
symbol. Elements are listed in order of increasing atomic number,
from left to right and from top to bottom.
Period - each horizontal row of the periodic table. Within a given
period, the properties of the elements vary as you move across it
from element to element.
Group – each vertical column of the periodic table. Elements within a
group have similar chemical and physical properties. Each group is
identified by a number and the letter A or B.
Noble Gas
Halogen
Group
Alkali Metal
Alkali Earth Metal
Period
A molecule is an aggregate of two or more atoms in a definite arrangement held together by
chemical bonds
H2
H2O
NH3
A diatomic molecule contains only two atoms
H2, N2, O2, Br2, HCl, CO
A polyatomic molecule contains more than two atoms
O3, H2O, NH3, CH4
CH4
An ion is an atom, or group of atoms, that has a net positive or negative charge.
cation – ion with a positive charge
If a neutral atom loses one or more electrons
it becomes a cation.
Na
11 protons
11 electrons
Na+
11 protons
10 electrons
Cl-
17 protons
18 electrons
anion – ion with a negative charge
If a neutral atom gains one or more electrons
it becomes an anion.
Cl
17 protons
17 electrons
A monatomic ion contains only one atom
Na+, Cl-, Ca2+, O2-, Al3+, N3-
A polyatomic ion contains more than one atom
OH-, CN-, NH4+, NO3-
Do You Understand Ions?
How many protons and electrons are in
27
3+ ?
13 Al
13 protons, 10 (13 – 3) electrons
How many protons and electrons are in
34 protons, 36 (34 + 2) electrons
78 Se 234
?
A molecular formula shows the exact number of
atoms of each element in the smallest unit of a
substance
An empirical formula shows the simplest
whole-number ratio of the atoms in a substance
molecular
empirical
H2O
H2O
C6H12O6
CH2O
O3
O
N2H4
NH2
Ionic compounds consist of a combination of cations and an anions
• the formula is always the same as the empirical formula
• the sum of the charges on the cation(s) and anion(s) in each
formula unit must equal zero
The ionic compound NaCl
Formula of Ionic Compounds
2 x +3 = +6
3 x -2 = -6
Al2O3
Al3+
O21 x +2 = +2
2 x -1 = -2
CaBr2
Ca2+
Br1 x +2 = +2
1 x -2 = -2
Na2CO3
Na+
CO32-
Some Polyatomic Ions
NH4+
ammonium
SO42-
sulfate
carbonate
2SO3
sulfite
HCO3
bicarbonate
NO3
nitrate
ClO3-
chlorate
NO2-
nitrite
Cr2O72-
dichromate
SCN-
thiocyanate
CrO42-
chromate
OH-
hydroxide
CO3
2-
Chemical Nomenclature

Ionic Compounds


often a metal + nonmetal
anion (nonmetal), add “ide” to element name
BaCl2
barium chloride
K2O
potassium oxide
Mg(OH)2
magnesium hydroxide
KNO3
potassium nitrate

Transition metal ionic compounds

indicate charge on metal with Roman numerals
FeCl2
2 Cl- -2 so Fe is +2
iron(II) chloride
FeCl3
3 Cl- -3 so Fe is +3
iron(III) chloride
Cr2S3
3 S-2 -6 so Cr is +3 (6/2)
chromium(III) sulfide

Molecular compounds
nonmetals or nonmetals + metalloids
 common names


H2O, NH3, CH4, C60
element further left in periodic table is 1st
 element closest to bottom of group is 1st
 if more than one compound can be formed
from the same elements, use prefixes to
indicate number of each kind of atom
 last element ends in ide

Molecular Compounds
HI
hydrogen iodide
NF3
nitrogen trifluoride
SO2
sulfur dioxide
N2Cl4
dinitrogen tetrachloride
NO2
nitrogen dioxide
N2O
dinitrogen monoxide
TOXIC!
Laughing Gas
An acid can be defined as a substance that yields
hydrogen ions (H+) when dissolved in water.
HCl
•Pure substance, hydrogen chloride
•Dissolved in water (H+ Cl-), hydrochloric acid
An oxoacid is an acid that contains hydrogen, oxygen, and
another element.
HNO3
nitric acid
H2CO3
carbonic acid
H2SO4
sulfuric acid
A base can be defined as a substance that yields
hydroxide ions (OH-) when dissolved in water.
NaOH
sodium hydroxide
KOH
potassium hydroxide
Ba(OH)2
barium hydroxide
Most common charges on ions. Note elements within a Group (column) typically have the
same charge. Are these charges consistent with the most stable electron configurations?
Continued



Molecular compounds are made of nonmetals
Ionic compounds are made of a metal and a
nonmetal.
Metal form cations and nonmetals form anions.
Naming Compounds





Binary Molecular Compounds
 Compounds consisting of two nonmetals
First element in the formula is named first.
Second element is named by changing the elemental
name ending to ide.
Use prefixes to identify quantity of atoms.
 Mono-1, di-2, tri-3, tetra-4, penta-5, hexa-6, hepta-7,
octa-8, nona-9, deca-10
Never use the prefix mono-
P2O5 = diphosphorus pentoxide
Compounds and Earth’s Early
Atmosphere

Carbon Dioxide

Water (dihydrogen monoxide)

Sulfur Dioxide

Sulfur Trioxide

Nitrogen Oxide

Nitrogen Dioxide
Naming…Binary molecular compounds
CO
CO2
NO
NO3
SO2
SO3
Practice
Name the following compounds or give
the correct chemical formula.
1.
2.
3.
4.
Tetraphosphorus decoxide
CCl4
P2N5
Sulfur trioxide
Binary Ionic Compounds

Binary ionic compounds consist of cations
(usually metals) and anions (usually
nonmetals).
Binary Ionic Compounds

The cation is named first using the elemental
name.



If the metal can form cations with different charges
then a Roman numeral is added to indicate the
charge of the cation.
The anion is named with the ide ending.
The formulas for ionic compounds must always
be neutral.
Practice
Write the name or chemical formula for the
following compounds.
1.
2.
3.
4.
NaCl
CrCl3
Zinc nitride
Copper(I) oxide
Polyatomic Ions







Acetate
C2H3O2Carbonate
CO32Perchlorate ClO4Nitrate
NO3Sulfate
SO42Chromate
CrO42Examples from Table 2.3 on page 64
Practice
Write the names or chemical formulas for the
following compounds.
1.
2.
3.
4.
Cr(ClO4)3
NH4NO3
Lithium bicarbonate
Calcium hypobromite
Nomenclature
Give the chemical names for the following ionic compounds:
a.
NiCO3
b.
NaCN
c.
LiHCO3
d.
Ca(ClO)2
Give the formula and charge of the oxoanion of each of the following
a.
Potassium tellurite
b. sodium arsenate
c.
Calcium selenite
d. potassium chlorate
Naming Binary Acids



Binary acids contain hydrogen and a halogen
atom.
The names of these acids are contain the
halogen base name with the prefix, “hydro,” and
suffix, “ic,” and the word acid.
Example HBr - hydrobromic acid
Oxy Anions & Related Acids
Anion
Anion Name
Acid
HClO
Acid Name

ClO-Hypochlorite
Hypochlorous acid

ClO2-
Chlorite
HClO2
Chlorous acid

ClO3-
Chlorate
HClO3
Chloric acid

ClO4-
Perchlorate
HClO4
Perchloric acid
Periodic Table
What distinguishes the atoms from one element from the
atoms of another?
The number of protons
What equation tells you how to calculate the number of
neutrons in an atom?
Mass number – atomic number = # of neutrons.
How do the isotopes of a given element differ from one
another?
Different mass number and different numbers of neutrons.
Periodic Table
What makes the periodic table such a useful tool?
It allows you to compare the properties of the elements
What does the number represent in the isotope platinum194? Write the symbol from this atom using superscripts
and subscripts.
It represents the mass number
194
78
Pt
Periodic Table
Name the elements that have properties similar to those of the
element calcium (Ca).
Beryllium (Be), magnesium (Mg), strontium (Sr), Barium (Ba),
radium (Ra)
194
Consider Pt how would changing the value of the
78
subscript change the chemical properties of the atom?
The subscript is the number of protons in atoms of the isotope.
Changing the number of protons would change the chemical identity
of the isotope to that of another element.
Displacement Law (by Russel, by Soddy and Fajans)
1. The emission of an α-particle reduces the atomic mass by 4
and the atomic number by 2.
2. The emission of a β-particle increases the atomic number by
1 and leaves the mass number unchanged.
α-rays
An α particle, or a helium nucleus, is composed of two protons and
two neutrons, totally four nucleons. It carries +2e charge and has
strong capability of ionization.
When α particles passing through materials high density of ions are
created in a cylindrical shape along the path. It is called the
“cylindrical ionization”.
High energy α particles lose their energy fast and can only travel
through a short distance.
Ex.
210
84
Po
(polonium) emits 5.3 MeV α-partilces
@ Alpha particles with 5.3 MeV is able to penetrate through 3.8 cm thickness of air.
@ A piece of paper of common thickness is able to stop those alpha particles.
@ They can not penetrate through human skin.
β-rays
Beta rays (electrons) interact with atoms. They lose energy by exciting or
ionizing atoms to higher energy states and free states while traveling
through materials.
Ion density created by electrons are far less than those from alpha
particles with the same energy.
Electrons can travel through a much longer distance than alpha
particles.
@ Electrons with 5.3 MeV is able to penetrate through 20 m thickness of air.
This is roughly 500 times of alpha particles.
@ Electrons with 5.3 MeV is able to penetrate through 10 mm in Al and 2 mm in Pb .
@ β-rays are much more dangerous than α-rays
.
γ-rays
Gamma rays are energetic photons. They interact with materials
through three different kinds of effect.
1. Photoelectric effect
Eγ < 0.4 MeV
2. Compton effect
0.4 MeV < Eγ < 5 MeV
3. Pair production effect
Eγ > 5 MeV
@ These effects have very small effective cross section (very small
probability of occurrence) thus huge traveling distance.
@ γ-rays are able to penetrate through ~ cm in Pb .
@ Watch out for γ-rays .
§ 1.2
The Rutherford scattering formula
1. In 1906 Rutherford observed that a beam of α-particles became
spread slightly on traversing a thin layer of material.
A layer of material insufficient to stop α-particles (e.g. gold 4μm thick) would scatter
particles an average of about 9 degrees.
α-
2. In 1909 Rutherford’s colleagues, Geiger and Marsden, observed that
one in a few thousand α-particles suffered a scattering of greater than
90º.
Rare, Large-angle Scatters!!
Massive cores were encountered.
Alpha particles hit atoms
with massive nucleus cores.
1. The averaged 9 degrees small angle scattering
is the result of many very small angle deflections
(multiple scattering).
Multiple scattering: The deflection of the path is the result of the
sum of many very small deflections in many atoms, all
uncorrelated.
2. The rare large angle scattering is the result of a single encounter
(single scattering) with an atom.
Single scattering: The deflection of the path of a particle crossing a layer of material is the
result of a significant deflection in one, and only one, encounter with an atom.
Size of Nuclei
Atomic radius of aluminum = 1.3 x 10-10 m
Nuclear radius aluminum = 3.6 x 10-15 m
Size Comparison
Ernest Rutherford
(1871- 1937)
The Rutherford scattering formula
Assumptions
1 The nuclear model
2 Target nucleus fixed
(no recoil)
3 Point-like charges
4 Coulomb force only
5 Elastic scattering
6 Classical mechanics
p = Zze / 4πε 0T
2
p distance of closest
approach for b = 0
The notation for quantities used in deriving Rutherford’s formula for the differential
scattering cross-section for the elastic scattering of one charged particle by a fixed
charged target particle.
m
v
T
ze
mass
velocity
kinetic energy
electric charge
Incident
particle
Ze
b
d
u
θ
r, φ
charge of target nucleus (at O)
impact parameter
distance of closest approach (at D)
velocity of incident particle at D
angle of scatter
polar coordinates with respect to
OD of point (X) on the trajectory of
particle.
Quantities in the figure
1. The orbit is hyperbolic and at D the incident particle is at its
distance of closest approach, d .
2. The orbit is clearly symmetric about the line OD.
3. If b was zero the incident particles would approach to a distance p . At this point the incident
kinetic energy is transformed into mechanical potential energy in the Coulomb field, therefore:
1 2
mv p = Zze 2 / 4πε 0
2
Step 1 To find the connection between b and θ.
In this system the angular momentum about O is conserved.
dϕ
mvb = mr
dt
2
(1)
hence
dt dϕ
=
2
vb
r
(2)
Consider the component of the linear momentum in the direction OD.
This changes from –mvsin(θ/2) to mvsin(θ/2).
The total momentum change along
the OD direction is
mv sin(θ / 2) − [− mv sin(θ / 2)] = 2mv sin(θ / 2)
(3)
At X the rate of change of this momentum is the component of the Coulomb repulsion in the
direction OD.
2mv sin
From equation (2)
θ
2
+∞
= ∫ ( Zze 2 / 4πε 0 r 2 ) cos ϕdt
−∞
dϕ
dt = r
vb
2
(4)
put this into equation (4)
then we have
θ
Zze 2 ϕ =(π −θ ) / 2
p mv
(π −θ ) / 2
[
]
2mv sin =
cos
sin
ϕ
ϕ
ϕ
d
=
− (π −θ ) / 2
2 4πε 0 vb ∫ϕ = − (π −θ ) / 2
2 b
Finally
θ
p
tan =
2 2b
(6)
(5)
Step 2 To derive a first cross-section.
θ
p
tan =
2 2b
This equation means that as b decreases θ increases.
To suffer an angle of scatter greater than
the impact parameter b must be less than
( p / 2) cot(Θ / 2)
Θ
Θ
To suffer an angle of scatter greater than
( p / 2) cot(Θ / 2)
the impact parameter b must be less than
This means the incident particle must strike a disk of this radius centered at O and perpendicular
to the velocity v.
The area, σ, presented by the nucleus for scattering through an
angle greater than
Θ
is the area of this disk.
That is
πp 2
Θ
σ (θ > Θ) =
cot
4
2
2
(7)
Equation (7) can also be written as
2
π  Zze 
2 Θ
 cot
σ (θ > Θ) = 
4  4πε 0T 
2
2
The area σis called a cross-section.
(8)
Step 3 To obtain the angular differential cross-section.
We need the cross-section per unit solid angle located at an angle θ.
The element of solid angle dΩ between θand θ+dθ is given by
dΩ = 2π sinθ dθ
therefore
dσ
1
dσ
=
dΩ 2π sin θ dθ
The dσ/dθwe need is
d
σ (θ > Θ)
dΘ
from equation (8).
Hence we obtain
2
dσ  Zze 
4 θ
 cosec
= 
dΩ  16πε0T 
2
2
(9)
This is the famous Rutherford formula for the differential cross-section in Coulomb
scattering.
dσ
dΩ
θ
2
dσ  Zze 
θ
 cosec 4
= 
dΩ  16πε0T 
2
2
(9)
§ 1.3 The properties of the Rutherford differential
cross-section
2
dσ  Zze 
4 θ
 cosec
= 
dΩ  16πε0T 
2
2
The cross-section
(1) decreases rapidly with increasing angle,θ,
(2) becomes infinite at θ= 0,
(3) is inversely proportional to the square of the
incident particles kinetic energy, T,
(4) is proportional to the square of the charge of
the incident particle and of the target nucleus.
(9)
2
dσ  Zze 2 
θ
 cosec 4
= 
dΩ  16πε0T 
2
(9)
In the figure we have the momentum transfer q .
q = 2 P sin(θ / 2)
(10)
1. Greater value of q means larger electric force.
Larger electric force (or field) means close collisions therefore less cross-section with larger
scattering angle θ.
2. At a fixed angle the required momentum transfer will increase as does T. Thus the crosssection must decrease with increasing T.
§ 1.4 Examination of the assumptions
1. Neglect of nuclear recoil:
this can be avoid by transforming to the center-of-mass of the collision. The formula is the same
but the effective T is now the total kinetic energy in that frame and the angle of scatter and
differential cross-section apply in that frame.
2. The classical approach to the orbit:
a simple quantum mechanical approach using the Born approximation gives the same answer.
3. The point-like charges:
data from heavy nuclei (Au, Ag, and Cu targets) are all consistent with Rutherford formula. Using
targets of several light nuclei (i.e. Al) deviations from the Rutherford formula were found.
The effect of nuclear interaction
at short distances!!
§ 1.4 Examination of the assumptions (continued)
4. Absence of other forces:
Short range nuclear forces and magnetic effect (because of spin) are present.
5. Elastic scattering:
The α-particles used by Rutherford were not sufficiently energetic to cause a significant number of
inelastic collisions. By inelastic collision it means that one or both of the particles involved in the
collision event become excited or disintegrate. After Rutherford, artificial sources of more
energetic α-particles became available and these certainly can cause inelastic collisions.
6. Relativistic effect:
If the incoming particles are energetic enough the relativistic effect is not to be overlooked.
Example:
The scattering data of α-particle with energy exceeding 25MeV (Tα> 25MeV) on 92U deviate
from what is predicted by the Rutherford formula.
The closest distance D in the head-on collision with Tα = 25MeV is
D = 10.6 F
When an α-particle comes near the 92U nucleus to within 10.6 F it barely touch the surface of the
nucleus.
Energetic electron scattering experiments are able to
probe internal structures of all nuclei.
From the previous discussion it might be thought that a nucleus is comprised of
electrons. This argument may well explain the β-radioactivity.
A protons and N
This is wrong!!
If we consider the nucleus of the helium atom. In this model there will be 4 protons and 2
electrons occupy a volume of half linear dimension of about 2 fermis.
Reason 1
From the uncertainty principle
∆p∆x ~ 
For an electron confined in a region of 2 fermis its momentum is roughly
∆p ~
 197.3 MeV/c ⋅ F
=
~ 49 MeV
∆x
4 F
∆p ~
 197.3 MeV/c ⋅ F
=
~ 49 MeV/c
∆x
4 F
E = m 0 + ∆p 2 = 0.5112 + 49 2 ≈ 49 MeV
2
Te = E − m 0 = 49 MeV - 0.511 MeV ≈ 49 MeV
where Te is electron’s kinetic energy
Electrons with kinetic energies of the order of 49 MeV should remain
bound only if there is a potential well at least that deep. Such a potential
well would have effects on the optical spectroscopy of helium which do
not exist.
There is no electron in the nucleus!!
Reason 2
Another reason that it is impossible for electrons
to stay in a nucleus.
When (A-Z) turns out to be an odd integer
the model prediction of nuclei’s total angular momentum
does not agree with observations.
Example
Consider the deuteron
2
1
H1
A = 2, and Z = 1
Model: There should be 2 protons and an electron.
two protons
1 1
+
2 2
1 1 1
1
3
 + +
→
or
2 2 2
2
2


But actually the deuteron spin is measured
one electron
1
2
Possible spins of deuteron
J =1
Nomenclature
Nuclide
A specific nuclear species, with a given proton number
Z and neutron number N
Isotopes Nuclides of same Z and different N
Isotones Nuclides of same N and different Z
Isobars Nuclides of same mass number A (A = Z + N)
Isomer Nuclide in an excited state with a measurable half-life
Nucleon Neutron or proton
Mesons Particles of mass between the electron mass (m0) and
the proton mass (MH). The best-known mesons are π
mesons (≈ 270 m0), which play an important role in
nuclear forces, and μ mesons (207 m0) which are
important in cosmic-ray phenomena.
Positron
Photon
Positively charged electron of mass m0
Quantum of electromagnetic radiation, commonly
apparent as light, x ray, or gamma ray
The Balmer Series of Hydrogen Lines

In 1885, Johann Jakob Balmer (1825 - 1898),
worked out a formula to calculate the positions
of the spectral lines of the visible hydrogen
spectrum
m2
λ = 364.56 2 2
m −2
(
)
Where m = an integer, 3, 4, 5, …

In 1888, Johannes Rydberg generalized Balmer’s
formula to calculate all the lines of the hydrogen
spectrum
1
1
1
= RH
− 2
2
n2 n1
λ
(
Where RH = 109677.58 cm-1
)
The Bohr Model - 1913

Niels Bohr (1885-1962)
The Bohr Model – Bohr’s Postulates
1.
2.
3.
4.
Spectral lines are produced by atoms one at a
time
A single electron is responsible for each line
The Rutherford nuclear atom is the correct
model
The quantum laws apply to jumps between
different states characterized by discrete
values of angular momentum and energy
The Bohr Model – Bohr’s Postulates
5.
The Angular momentum is given by
h
p =n
2π
( )
6.
n = an integer: 1, 2, 3, …
h = Planck’s constant
Two different states of the electron in the
atom are involved. These are called “allowed
stationary states”
The Bohr Model – Bohr’s Postulates
7.
The Planck-Einstein equation, E = hν holds
for emission and absorption. If an electron
makes a transition between two states with
energies E1 and E2, the frequency of the
spectral line is given by
hν = E1 – E2
ν = frequency of the spectral line
E = energy of the allowed stationary state
8. We cannot visualize or explain, classically
(i.e., according to Newton’s Laws), the
behavior of the active electron during a
transition in the atom from one stationary
state to another
Bohr’s calculated radii of
hydrogen energy levels
r = n2A0
r = 53
pm
r = 4(53) pm
= 212 pm
r = 9 (53) pm
= 477 pm
r = 16(53) pm
= 848 pm
r = 25(53) pm
= 1325 pm
r = 36(53) pm
= 1908 pm
r = 49(53) pm
= 2597 pm
Lyman Series
Balmer Series
Paschen Series
Brackett Series
Series
Series
Pfund
Humphrey’s
The Bohr Model
The energy absorbed or emitted from
the process of an electron transition
can be calculated by the equation:
=
∆E RH
(
1
1
− 2
2
n2 n1
)
where
RH = the Rydberg constant, 2.18 × 10−18 J,
and
n1 and n2 are the initial and final energy levels
of the electron.
Quantum Numbers




Solving the wave equation gives a set of wave
functions, or orbitals, and their corresponding
energies.
Each orbital describes a spatial distribution of
electron density.
An orbital is described by a set of three
quantum numbers.
Quantum numbers can be considered to be
“coordinates” (similar to x, y, and z coodrinates
for a graph) which are related to where an
electron will be found in an atom.
Looking at Quantum Numbers:
The Principal Quantum Number, n


The principal quantum number, n ,
describes the energy level on which the
orbital resides.
The values of n are integers ≥ 0.
n = 1, 2, 3, etc.
Looking at Quantum Numbers:
The Magnetic Quantum Number, m l



Describes the orientation of an orbital with respect to a
magnetic field
This translates as the three-dimensional orientation of
the orbital.
Values of m l are integers ranging from -l to l :
−l ≤ m l ≤ l.
Values of l
Values of ml
Orbital
Number of
designation
orbitals
0
0
s
1
1
-1, 0, +1
p
3
2
-2, -1, 0, +1, +2
d
5
3
-3, -2, -1, 0, +1, +2, +3
f
7
Quantum Numbers and Subshells


Orbitals with the same value of n form a shell
Different orbital types within a shell are called
subshells.
A Summary
of Atomic
Orbitals
from 1s to 3d
Empty subshells
Valence
subshells
Full
subshells
Approximate energy levels for neutral atoms.
From Ronald Rich, Periodic Correlations, 1965

Wolfgang Pauli (1900-1958)
 Pauli Exclusion Principle, 1925
“There can never be two or more
equivalent electrons in an atom for
which in strong fields the values of
all quantum numbers n, k 1, k 2, m 1
(or, equivalently, n, k 1, m 1, m 1) are
the same.”
Hund’s Rule
Friedrich Hund (1896 1997)
For degenerate orbitals,
the lowest energy is
attained when the
electrons occupy
separate orbitals with
their spins unpaired.
J. Mauritsson, P. Johnsson, E. Mansten, M. Swoboda, T. Ruchon, A. L’Huillier,
and K. J. Schafer, Coherent Electron Scattering Captured by an Attosecond
Quantum Stroboscope, PhysRevLett.,100.073003, 22 Feb. 2008
http://www.atto.fysik.lth.se/
Remember…

Scientists







Dalton
Thomson – Cathode Ray
Tube
Millikan – Oil dropper
Apparatus
Rutherford – Gold Foil
Alpha Scattering
Bohr
Planck
Einstein

Models




Thomson Model
Rutherford Model
Bohr Model
Quantum Mechanical
Sub-Atomic Particles



Protons – positive charge, found in the nucleus.
Neutrons – no charge, found in the nucleus.
Electrons – negatively charged, found around
the nucleus (electron cloud).
Atomic Structure

Isotopes – same elements but different number of
neutrons.


The mass number will INDIRECTLY give you the number
of neutrons.
Ions – charged particles.



The loss of electrons gives the atom a positive charge (+).
The gaining of electrons gives the atom a negative charge.
The charge goes in the top right hand corner in a chemical
symbol.
Wave Functions




Erwin Schrödinger: We can describe the
electron mathematically, using quantum
mechanics (wave mechanics).
Schrödinger developed a wave equation to
describe the hydrogen atom.
An acceptable solution to Schrödinger’s wave
equation is called a wave function.
A wave function represents an energy state of
the atom.
The Wave Nature of Light




Electromagnetic waves originate from the
movement of electric charges.
The movement produces fluctuations in electric and
magnetic fields.
Electromagnetic waves require no medium.
Electromagnetic radiation is characterized by its
wavelength , frequency , and amplitude .
An Electromagnetic Wave
The waves don’t “wiggle” as
they propagate …
… the amplitude of the “wiggle”
simply indicates field strength .
Wavelength and Frequency

Wavelength (λ) is the distance between any two
identical points in consecutive cycles.
• Frequency (v) of a wave is the number of cycles
of the wave that pass through a point in a unit of
time. Unit = waves/s or s–1 (hertz ).
Wavelength and Frequency
The relationship between wavelength and
frequency:
c = λv
where c is the speed of light (3.00 × 108 m/s)
The Electromagnetic Spectrum
UV, X rays are shorter
wavelength, higher
frequency radiation.
Communications involve
longer wavelength, lower
frequency radiation.
Visible light is only
a tiny portion of
the spectrum.
A Continuous Spectrum
White light from a
lamp contains all
wavelengths of
visible light.
When that light is passed
through a prism, the different
wavelengths are separated.
We see a spectrum of all rainbow
colors from red to violet – a
continuous spectrum.
A Line Spectrum
Light from an
electrical discharge
through a gaseous
element (e.g., neon
light, hydrogen lamp)
does not contain all
wavelengths.
The spectrum is
discontinuous ; there
are big gaps.
We see a pattern of lines,
multiple images of the
slit. This pattern is called
a line spectrum . (duh!)
Line Spectra of Some Elements
The line emission
spectrum of an
element is a
“fingerprint” for
that element, and
can be used to
identify the
element!
How might you tell
if an ore sample
contained mercury?
Cadmium?
Line spectra are a
problem; they can’t
be explained using
classical physics …
Planck …




… proposed that atoms could absorb or emit electromagnetic
energy only in discrete amounts .
The smallest amount of energy, a quantum , is given by:
E = hv
where Planck’s constant, h, has a value of 6.626 × 10–34 J·s.
Planck’s quantum hypothesis states that energy can be
absorbed or emitted only as a quantum or as whole multiples of a
quantum, thereby making variations of energy discontinuous.
Changes in energy can occur only in discrete amounts.
The Photoelectric Effect
Light striking a
photoemissive cathode causes
ejection of electrons.
Ejected electrons reach the
anode, and the result is …
… current flow through an
external circuit.
But not “any old” light will cause ejection of electrons …
The Photoelectric Effect
(cont’d)
Each photoemissive
material has a
characteristic threshold
frequency of light.
When light that is above
the threshold frequency
strikes the photoemissive
material, electrons are
ejected and current flows.
Light of low frequency
does not cause current
flow … at all.
As with line spectra, the
photoelectric effect cannot be
explained by classical physics.
The Photoelectric Effect


Albert Einstein won the 1921 Nobel Prize in Physics for
explaining the photoelectric effect.
He applied Planck’s quantum theory: electromagnetic energy
occurs in little “packets” he called photons .
Energy of a photon (E) = hv
• The photoelectric effect arises when photons of light striking
a surface transfer their energy to surface electrons.
• The energized electrons can overcome their attraction for the
nucleus and escape from the surface …
• … but an electron can escape only if the photon provides
enough energy.
The Photoelectric Effect
Explained
The electrons in a
photoemissive material
need a certain minimum
energy to be ejected.
Short wavelength (high
frequency, high energy)
photons have enough
energy per photon to
eject an electron.
A long wavelength—low
frequency—photon
doesn’t have enough
energy to eject an electron.
The Bohr Model of Hydrogen
When excited, the
electron is in a higher
energy level.
Excitation: The atom
absorbs energy that is
exactly equal to the
difference between two
energy levels.
Each circle represents an
allowed energy level for the
electron. The electron may be
thought of as orbiting at a fixed
distance from the nucleus.
Emission: The atom
gives off energy—as
a photon.
Upon emission, the
electron drops to a
lower energy level.
Line Spectra Arise Because …


Transition from n
= 3 to n = 2.

Transition from n
= 4 to n = 2.
… each electronic
energy level in an
atom is quantized.
Since the levels are
quantized, changes
between levels must
also be quantized.
A specific change
thus represents one
specific energy, one
specific frequency,
and therefore one
specific wavelength.
Bohr’s Equation …

… allows us to find the energy change (∆Elevel) that
accompanies the transition of an electron from one energy
level to another.
Initial energy level:
Final energy level:
–B
–B
E i = ——
n i2
E f = ——
n f2
• To find the energy difference, just subtract:
–B
–B
∆Elevel = —— – —— = B
n f2
n i2
1
1
ni
nf
—
– —
2
2
• Together, all the photons having this energy (∆Elevel) produce
one spectral line.
Energy Levels and Spectral Lines for Hydrogen
What is the (transition that produces
the) longest-wavelength line in the
Balmer series? In the Lyman series?
In the Paschen series?
De Broglie’s Equation




Louis de Broglie’s hypothesis stated that an object in
motion behaves as both particles and waves, just as light does.
A particle with mass m moving at a speed v will have a
wave nature consistent with a wavelength given by the
equation:
λ = h/mv
This wave nature is of importance only at the microscopic
level (tiny, tiny m).
De Broglie’s prediction of matter waves led to the
development of the electron microscope.
De Broglie’s Equation…


de Broglie just messed up the Bohr model of the
atom.
Bad: An electron can’t orbit at a “fixed distance” if
the electron is a wave.



An ocean wave doesn’t have an exact location—neither
can an electron wave.
Worse: We can’t even talk about “where the
electron is” if the electron is a wave.
Worst: The wavelength of a moving electron is
roughly the size of an atom! How do we describe an
electron that’s too big to be “in” the atom??
Wave Functions




Erwin Schrödinger: We can describe the
electron mathematically, using quantum
mechanics (wave mechanics).
Schrödinger developed a wave equation to
describe the hydrogen atom.
An acceptable solution to Schrödinger’s wave
equation is called a wave function.
A wave function represents an energy state of
the atom.
The Uncertainty
Principle
Werner Heisenberg: We can’t
know exactly where a moving
particle is AND exactly how
fast it is moving at the same
time.
The photon that will
enter the microscope,
so that we might
“see” the electron …
… has enough momentum
to deflect the electron.
The act of measurement
has interfered with the
electron’s motion.
The Uncertainty Principle



A wave function doesn’t tell us where the electron is .
The uncertainty principle tells us that we can’t know
where the electron is.
However, the square of a wave function gives the
probability of finding an electron at a given location
in an atom.
Analogy: We can’t tell where a single leaf from a tree
will fall. But (by viewing all the leaves under the tree)
we can describe where a leaf is most likely to fall.
Quantum Numbers and Atomic Orbitals



The wave functions for the hydrogen atom contain
three parameters called quantum numbers that
must have specific integral values.
A wave function with a given set of these three
quantum numbers is called an atomic orbital .
These orbitals allow us to visualize the region in
which the electron “spends its time.”
Quantum Numbers: n
When values are assigned to the three quantum numbers, a
specific atomic orbital has been defined.
The principal quantum number (n) :
• Is independent of the other two quantum numbers.
• Can only be a positive integer (n = 1, 2, 3, 4, …)
• The size of an orbital and its electron energy depend on the
value of n.
• Orbitals with the same value of n are said to be in the same
principal shell.
Quantum Numbers: l
The orbital angular momentum quantum number (l) :
 Determines the shape of the orbital.
 Can have positive integral values from 0, 1, 2, … (n – 1)
 Orbitals having the same values of n and of l are said to be in
the same subshell .
Value of l
0
1
2
3
Subshell
s
p
d
f
• Each orbital designation represents a different region of
space and a different shape.
Quantum Numbers: m l
The magnetic quantum number (m l) :
 Determines the orientation in space of the
orbitals of any given type in a subshell.
 Can be any integer from –l to +l
 The number of possible values for ml is (2l
+ 1), and this determines the number of
orbitals in a subshell.
Notice: one s orbital in each principal shell
three p orbitals in the second shell (and in higher ones)
five d orbitals in the third shell (and in higher ones)
Electron Spin: m s
• The electron spin quantum number (m s) explains some of
the finer features of atomic emission spectra.
• The number can have two values: +½ and –½.


The spin refers to a magnetic field
induced by the moving electric
charge of the electron as it spins.
The magnetic fields of two
electrons with opposite spins
cancel one another; there is no
net magnetic field for the pair.
The Periodic Table:
A Preview
 A “periodic table” is an
arrangement of elements in which
the elements are separated into
groups based on a set of repeating
properties
The periodic table allows you to
easily compare the properties of
one element to another
The Periodic Table:
A Preview
 Each horizontal row (there are 7 of
them) is called a period
Each vertical column is called a
group, or family
Elements in a group have similar
chemical and physical properties
Identified with a number and
either an “A” or “B”
More presented in Chapter 6
Concept Check
Which photons have the highest energy?
A) Cell phone operating at 1900 MHz
B) A laser pointer using 635 nm light
“Most Successful Theory of the 20th Century”
Matter
Dalton
Thomson
Rutherford
Bohr &
de Broglie
Einstein
Plank
Maxwell
Light
Newton
Heisenberg
Schrödinger
Wave
Mechanics
IV. Isotopes

e.g. Determine the number of protons and
neutrons in carbon-12, carbon-13, and carbon14.
V. Masses of Atoms




The mass of an atom is measured relative to the
mass of a standard.
The modern standard is carbon-12, which is
assigned a mass of exactly 12 atomic mass units
(amu).
e.g. On this scale, a hydrogen atom has a mass of
1.008 amu.
Note that 1 amu = 1.66054 x 10-24 g.
Can we “see” the atoms?
By Eyes
By Optical microscope
By Electron microscope
no
no
possible
Modern methods:
The field emission microscope
To visualize single atom or large molecules on the tip of fine metal points
SEM(Scanning Electron Microscopy)
To image the individual atoms in molecules and in crystals.
TEM (Transmission Electron Microscopy)
STM (Scanning Tunneling Microscopy)
TEM
STM image
Atom manipulation
By STM
Fe atoms on Cu(111)
Formation of Nuclides
1
1
H +
1
1
n →
1
0
2
1
1
0
H
H is a proton and n is a neutron
2 H →
2
1
4
2
He