Chapter 7 – Atomic Structure and Periodicity
Introduction
You may recall that one of the ideas of Dalton’s Atomic Theory was that all elements are
composed of indivisible particles called atoms. For about 50 years past the time of John
Dalton (1766-1844) this idea remained. However, around 1900 J. J. Thomson discovered
the presence of electrons - small, light quantities of negative charge. This chapter focuses
on the electron and the arrangement of electrons in atoms.
The Wave-like Nature of the Electron
Every object has a wave-like nature to it. For most common objects, however, the
macroscopic quantities are enormous compared to the wave behavior; hence, we do not
normally associate wave characteristics with common objects. The electron, however, is
sufficiently small (it has very little mass) and so the wave characteristics are much more
pronounced. Here, we will examine the basics of waves.
Basics of Waves
The picture below shows a typical representation of a wave, and is copied from page 245
in your text. The wavelength () is the distance between adjacent points on a wave. It is
usually measured in meters, or some metric derivation thereof (such as nm). The frequency () of a wave is how many crests pasts by a certain point per second. Frequency
is usually measured in Hertz (Hz). One Hz is a wave per second, 1/sec, or sec-1. There is
an inverse relationship between frequency and wavelength - when one goes up the other
goes down, and vice versa.
Speed of a Wave
The speed of a wave is given by the product of the frequency and wavelength. If the
wave is an electromagnetic wave, such as light, then the speed of the wave through a
vacuum is a constant of 3.00 X 108 m/s.
c = 
EXAMPLE:
What is the frequency of light that has a wavelength of 580. nm?
(1 nm = 1 nanometer = 1 X 10-9 m)
EXAMPLE:
What is the wavelength of radiation that has a frequency of
6.00 X 1017 Hz?
Energy of a Photon
The energy of an electromagnetic wave (sometimes called a “photon”) is given by the
product of Planck’s constant times the frequency.
E=h
EXAMPLE:
where h = Planck’s constant = 6.63 X 10-34 Jsec
How much energy is in a photon of frequency 6.00 X 1017 Hz?
DeBroglie Wavelength
As we said earlier, all objects have some wave characteristics. In electrons, the wave
characteristics are dominant because of the electron’s very small size. We can calculate
the DeBroglie wavelength for any object using:
 = h/mv
where h is Planck’s constant, m is the mass of the object, and v is the speed of the object.
DeBroglie reasoned that if an electron behaves like a wave, then any allowable principle
energy level must be such that an integer number of electron wavelengths can fit into an
imaginary circle representing the energy level. The diagram below shows the case where
4 wavelengths of the electron are shown. Thus, only certain energy levels are allowed.
EX:
Calculate the DeBroglie wavelength of a 1350 kg car traveling at 25.0 m/s.
EX:
Calculate the DeBroglie wavelength of an electron traveling at 25.0 m/s. The
mass of an electron is 9.11 X 10-31 kg.
Heisenberg Uncertainty
As a result of quantum mechanics, there is a fundamental limitation to just how precisely
we can know both the position and momentum of a particle at a given time. (Momentum
is just the product of mass times velocity: p = mv.) This statement is known as the
Heisenberg Uncertainty Principle. Mathematically, we have:
Δx • Δ(mv) ≥ h/4π
EX:
Calculate the uncertainty in position (Δx) for an electron with an uncertainty in
speed (Δv) of 0.100 m/s.
Electromagnetic Radiation
Different types of electromagnetic radiation are shown below. Notice that those types of
radiation that have relatively short wavelengths have relatively large frequencies, and vice
versa. The visible spectrum is that tiny sliver around a frequency of 1014 Hertz.
Models of the Atom
Our description of the atom has evolved over the years. Below is a brief description of
the four basic models that have existed through the years.
1) Thomson Model
This model is sometimes called the plum pudding model. The negative
electrons (the plums) are embedded a positive matrix (the pudding). This
early model does not acknowledge the existence of the nucleus.
2) The Rutherford Model
This model is a direct result of the discovery of the nucleus by Rutherford in 1911. In this model, stationary electrons surround a center of
positive charge.
3) The Bohr Model
In 1913 Niels Bohr proposed a model in which the electrons circled
the nucleus, like the planets orbit the sun. This model is sometimes
called the planetary model. This model also proposed a very insightful
idea: that the electrons could only occupy certain positions around
the nucleus, and the farther out electrons got, the greater the electron’s
energy. An electron could only move to a higher energy level if it
acquired a certain amount (a quantum) of energy.
4) The Quantum Mechanical Model
In 1926, Erwin Schrodinger wrote a mathematical equation to describe
the location and speed of an electron in an atom. This model is based
on probability. This model describes the location in terms of the region
in which one will find an electron 90% of the time.
Arrangement of Electrons in Atoms
There are four levels of organization to describe the location of an electron in any
particular atom.
1) Principal Energy Level - Describes in very general terms how far away from the
nucleus an electron can be found. It is given the symbol n.
2) Sublevel - There are four different sublevels called s, p, d, and f. The first principal
energy level has only one sublevel, called the “1s”. The second principal
energy level has two sublevels: a “2s” and a “2p”. The third principal
energy level has three sublevels: a “3s”, a “3p” and a “3d”. The fourth
and all subsequent principal energy levels have four sublevels. For n = 4,
there is the 4s, 4p, 4d and 4f. Theoretically, there exists a “5g” in the fifth
principal energy level, but we run out of electrons before we begin filling
it.
3) Orbitals - The s sublevel contains only one orbital, which is spherically shaped. The
p sublevel contains three orbitals, which are shaped like dumbells and are
oriented mutually perpendicular to each other (like the x, y and z axes).
There are five d orbitals, and seven f orbitals. These d and f orbitals are
fairly complex in shape.
4) Spin -
Each orbital can contain two electrons, one with spin up and the other with
spin down. Two electrons with the same spin will never occupy the same
orbital.
The table below summarizes our results so far:
Principal Energy
Level
Number of
Sublevels
Types of
Sublevels
Maximum number of
Electrons (2n2)
n=1
1
1s
2
n=2
2
2s, 2p
8
n=3
3
3s, 3p, 3d
18
n=4
4
4s, 4p, 4d, 4f
32
Rules for Placing Electrons
1) Aufbau Principle - Electrons enter orbitals of lowest energy first.
2) Pauli Exclusion Principle - An orbital can only contain two electrons, of opposite spin.
Another way of stating this principle is to say that no two electrons within an atom
can have the same four quantum numbers.
3) Hund’s Rule - Within a sublevel, electrons enter singly before pairing up.
We will use these rules to place electrons in atoms in some examples
that will follow.
Energy Level Diagram for Sublevels
Below is a diagram which arranges sublevels in order of increasing energy. Each
number/letter combination represents an orbital.
1s
2s
3s
4s
5s
6s
7s
8s
2p
3p
4p
5p
6p
7p
3d
4d
5d
6d
4f
5f
EXAMPLES: Fill in the orbital diagram, and give the electron configuration
of the following elements:
1) H
1s
2) He
1s
2s
3) Li
1s
2s
4) Be
1s
2s
5) C
1s
2s
6) N
2p
1s
2s
7) F
2p
1s
2p
8) Ca
4s
4p
4d
3s
3p
3d
2s
2p
4f
1s
9) V
4s
4p
4d
3s
3p
3d
2s
2p
4f
1s
EXAMPLE: Write the electron configuration for Astatine (#85)
Exceptional Electron Configurations
Some of the elements have electron configurations that deviate from the norm. The
driving force for this deviation is the extra stability offered by filled and half-filled
sublevels. The most well-known exceptions are chromium and copper. The 3d sublevel
steals an electron from the 4s for added stability. Draw the configurations for copper and
chromium below:
EXPECTED CONFIGURATIONS
Cr
Cu
ACTUAL CONFIGURATIONS
Cr
Cu
Configurations of Ions
Atoms gain or lose electrons to form ions. To write the configuration of an anion, just
add an appropriate number of electrons to the configuration. When forming a cation,
remove electrons in the configuration. For transition metals, electrons will be lost from
the ns sublevel before losing electrons from the (n-1)d sublevel. The following examples
will demonstrate these procedures.
EXAMPLES: Write the electron configurations of the following ions:
O-2
Al+3
Co+3
Paramagnetism and Diamagnetism in Elements
If an element has unpaired electrons in its electron configuration, that element will be
paramagnetic and will be bent by a magnetic field. An element that has no unpaired
electrons is diamagnetic, and will not be bent in a magnetic field.
Example: Write the electron configuration, and determine if the following
elements are paramagnetic or diamagnetic.
Mg
S
Quantum Numbers
Each electron in every atom is assigned a set of four quantum numbers. According to the
Pauli exclusion principle, no two electrons can have the exact quantum numbers. The
rules are stated below.
1) Principal Quantum Number (n) - Just the value of the principal energy level.
2) Angular Momentum Quantum Number (l) - This number is determined from the
type of sublevel. The numbers are
0, 1, 2, and 3 for s, p, d, and f sublevels, respectively.
3) The Magnetic Quantum Number (ml) - This number runs from -l to +l.
4) The Spin Quantum Number (ms) - This is +1/2 for the first electron in an orbital, and
-1/2 for the second electron in an orbital.
EXAMPLES: Write the quantum numbers for each electron
1s1
1s2
4d3
4d6
2p1
2p4
EXAMPLES: Determine the electron for the following sets of quantum numbers.
3, 2, 0, -1/2
2, 1, 1, +1/2
3, 4, 0, +1/2
The Hydrogen Atom
Emission spectra are those wavelengths of light emitted by an excited electron as it falls
to lower sublevels. Absorption spectra are those dark lines where an electron has
absorbed energy to become excited. Bohr showed that the energy of an electron in a
hydrogen atom is given by:
En = -RH(1/n2)
where RH is the Rydberg constant for hydrogen, and is given by 2.18 X 10-18 J. The
number n is the principal quantum number and can, of course, only have integer values.
The difference in energies from an electron as it moves from ni to nf is given by:
E = RH(1/ni2 – 1/nf2)
EXAMPLE:
What is the wavelength of a photon emitted during a transition from n = 5
to n = 2 for hydrogen?
The Lyman series is the set of bands of electromagnetic radiation falling to n =1. The
Lyman series emits radiation in the ultraviolet range. The Balmer series is the set of
bands of electrons falling to n =2; emission in the visible and ultraviolet occurs. The
Paschen and Brackett series has the electrons falling to n = 3 and n = 4, respectively, and
emission occurs in the infrared range.
EXAMPLE:
Calculate the wavelength for the first two lines of the Paschen series.
Hydrogen-Like Ions
Hydrogen-like ions are those ions that have just one electron, like He+, or Al+12. In this
case,
En = -RH(Z2/n2)
Where Z represents the nuclear charge.
EX:
Calculate the wavelength of light emitted when an electron makes an n = 6 to n =
2 transition in a B+4 ion.
Periodic Trends in Atomic Properties
Introduction
In 1869 the Russian chemist Dmitri Mendeleev proposed a tabulation of the elements
based on the regular, periodic recurrence of their properties, and ordered them on the
basis of increasing atomic mass. The modern periodic table is very similar, but is based
on increasing atomic number.
Some Elementary Definitions
Representative Elements-
Group 1A through 7A; are characterized by having
incompletely filled s or p sublevels.
Noble Gases-
Group 8A (or Group 0); these elements have completely filled p sublevels (except for He).
Transition Metals-
Groups characterized by filling d sublevels (note:
according to your text, Zn, Cd and Hg are neither
transition metals nor representative elements)
Lanthanides/Actinides-
Groups characterized by filling f sublevels
valence electrons-
the outer atoms of an electron (same as group
number for representative elements); similarities
in the number of valence electrons are what give
elements in the same group similar properties.
isoelectronic-
species (atoms/ions) that have the same electron
configuration, such as Ne, Na+ and O-2
Periodic Variation in Physical Properties
Electrostatic Attraction
A classical equation in physics, which is used to calculate the force of attraction (or
repulsion) between two stationary charges is:
F = k Q1 Q2
r2
where Q1 and Q2 are charges with a distance of separation of “r”. The variable k is just
an experimentally-determine constant. What’s important to notice is the effect of the
size of the charges (Q1 and Q2) and the distance of separation (r) on the force, F. As you
can deduce, larger charges with smaller distances of separation results in larger values for
the force.
Effective Nuclear Charge
The effective nuclear charge (Zeff) is a measure of the net charge an electron “feels”
toward the nucleus. For example, an electron in a hydrogen atom “feels” a pull of one
proton, so Zeff = 1. But an electron in a helium atom feels the pull of 2 protons, but also
feels a slight repulsion of the other electron. An equation that is sometimes used is:
Zeff = Z - 
(where  is the number of shielding e-)
EX: Calculate Zeff for the following atoms:
(a) H
(b) He
(c) Li
(d) Mg
(e) Cl
Atomic Radius
The atomic radius decreases as you move up and to the right on the periodic table. There
are two reasons for this:
1) As you move up a group, you are adding electrons to smaller principal
energy levels, which are, on average, closer to the nucleus.
2) As you move left to right across a group, you are increasing the Zeff felt by
each electron. This is because the atomic number is increasing by 1, but
the shielding is remaining virtually constant as you move one element to the
right on the periodic table.
EX:
Arrange the following in order of increasing atomic radius: P, Si, N
Ionic Radius
In general, the anions are larger than the cations because the anions have gained electrons,
while the cations have lost them. Focusing in on isoelectronic species, those which have
the greatest number of protons will be smallest.
EX: For each of the following pair, circle which one is larger:
a) N-3 or F-
b) Mg+2 or Ca+2
c) Fe+2 or Fe+3
Ionization Energy
The ionization energy of a specie is the energy required to remove an electron from the
specie in its gaseous state:
X(g) + energy  X+(g) + eX+(g) + energy  X+2(g) + eX+2(g) + energy  X+3(g) + e-
first ionization energy
second ionization energy
third ionization energy
Two trends in ionization energy can be seen. First of all, the first ionization energy is
smaller than the second ionization energy, which is in turn smaller than the third
ionization energy. This trend is due to the fact that it gets harder and harder to pull
electrons off a positive specie. Second of all, there is a big jump in ionization energies in
all elements which gives some clue of their electron structure. For example, magnesium
shows an especially large jump in ionization energy between the second and third
ionization energies. This very large jump is because the first two ionization energies are
pulling off 3s electrons, while the third ionization energy is pulling of a 2p electron. See
page 328 for a table of ionization energies.
Another trend which emerges is that the first ionization energy increases as you move up
and to the right on the periodic table. As atoms get smaller and Zeff gets larger, it gets
harder to remove electrons.
Element First IE (kJ/mol)
H
1312
He
2371
Li
520
Be
900
B
800
C
1086
N
1402
O
1314
F
1681
Ne
2080
Na
496
Mg
738
Al
577
Si
786
P
1012
S
999
Cl
1255
Ar
1520
Second IE (kJ/mol) Third IE (kJ/mol)
--------5247
----7297
11810
1757
14840
2430
3659
2352
4619
2857
4577
3391
5301
3375
6045
3963
6276
4565
6912
1450
7732
1816
2744
1577
3229
1896
2910
2260
3380
2297
3850
2665
3947
EX:
Which atom should have a smaller first ionization energy, oxygen or
sulfur?
EX:
Which atom should have a larger first ionization energy, Li or Na?
EX:
Which atom should have a higher second ionization energy, lithium or
beryllium?
EX:
EX:
Boron and silicon have similar first ionization energies (in something called the
diagonal rule – atoms down and to the right or up and to the left are similar in
many respects). Explain why.
Which element listed below could have the following pattern for the first six
ionization energies?
(a)
(b)
(c)
(d)
EX:
Ca
Si
S
Cl
Which alkali metal is most reactive and why?
Electron Affinity
Electron affinity is defined to be the energy change associated when an atom in the
gaseous state accepts an electron.
X(g) + e-  X-(g)
ΔH = electron affinity
A negative electron affinity means that energy is released when an electron is added to an
atom. A large negative electron affinity means that the atom “wants” to gain an electron;
the negative ion is very stable.
The electron affinity tends to increase in the large, negative sense as you move up and to
the right on the periodic table. The electron affinity of the noble gases, however, is large
and positive, meaning that the noble gases really do not want to form negative ions.
EX:
Order the following elements in order of increasing electron affinity (in order of
increasing negative values): N, O, F, P.
EX:
Which halogen is most reactive and why?
Variation in Chemical Properties of the Representative Elements
(from Ch. 18)
Hydrogen (1s1)
There is no position totally suitable for hydrogen. It is shown in Group 1A, but it really
belongs in a group by itself. It can form the hydrogen ion (H+) or the hydride ion (H-1) in
compounds like NaH and CaH2. Ionic hydrides react with water to produce hydrogen gas
and the corresponding metal hydroxides:
2NaH(s) + 2H2O(l)  2NaOH(aq) + H2(g)
CaH2(s) + 2H2O(l)  Ca(OH)2(s) + 2H2(g)
Group 1A Elements (ns1)
This group (known as the alkali metals) have low ionization energies and tend to lose
their one valence electron. They react with water to produce hydrogen gas and the
corresponding metal hydroxide:
2Na(s) + 2H2O(l)  2NaOH(aq) + H2(g)
When exposed to air, they react with oxygen. Lithium forms lithium oxide (Li2O) but the
other alkali metals form oxides and peroxides (containing the O2-2 ion). Potassium,
rubidium, and cesium also form superoxides (containing the O2- ion).
Group 2A (ns2)
The alkali earth metals, as they are called, are less reactive than the alkali metals. Many
of the Be compounds are molecular, rather than ionic in nature. The reactivities in this
group vary. Be does not react with water, while Mg will react slowly with hot water or
steam. Ca, Sr and Ba will react with water:
Ba(s) + 2H2O(l)  Ba(OH)2(aq) + H2(g)
Group 3A (ns2np1)
The first member of this group, boron, is a metalloid; the rest are metals. Aluminum
reacts with the oxygen in the air to form a thin protective layer of aluminum oxide
(Al2O3) preventing further reaction. Aluminum only forms ions of +3, and it will readily
react with acids, releasing hydrogen gas. Many of the Group 3A elements will form
molecular compounds, such as AlH3.
Group 4A (ns2np2)
The first member of this group, carbon, is a nonmetal, and the next two members (Si and
Ge) are metalloids. These elements do not form ionic compounds. The next elements of
this group, tin and lead, do not react with water, but do react with acids to liberate
hydrogen gas (and form the Sn+2 and Pb+2 ions in solution). These elements can usually
be found in the +2 or +4 oxidation state.
Group 5A (ns2np3)
There is a great variation in this group. N and P are nonmetals, As and Sb are metalloids,
and Bi is a metal. Nitrogen forms a variety of oxides (NO, N2O, NO2, N2O4, and N2O5)
of which only N2O5 is a solid; all others are gases. Phosphorus exists as P4 and can form
two oxides (P4O6 and P4O10). The important oxyacids HNO3 and H3PO4 are formed
when the following oxides react with water:
N2O5(s) + H2O(l)  2HNO3(aq)
P4O10(s) + 6H2O(l)  4H3PO4(aq)
Group 6A (ns2np4)
The first three members of this group (O, S, and Se) are nonmetals, and the last two (Te
and Po) are metalloids. Sulfur is a yellow solid and comes in eight-membered rings of S8.
The elements in this group form a large number of molecular compounds. Sulfuric acid
is formed when sulfur trioxide reacts with water:
SO3(s) + H2O(l)  H2SO4(aq)
Group 7A (ns2np5)
The halogens are diatomic elements. Because of their great reactivity, they are never
found in the elemental form in nature. Fluorine is so reactive, it will attack water to form
hydrofluoric acid and oxygen: 2F2(g) + 2H2O(l)  4HF(aq) + O2(g). The halogens all
react with H2 to form hydrogen halides (halides are F-, Cl-, Br-, etc…...).
Group 8A (ns2np6)
The noble gases were once thought to be completely unreactive. It is now known that
some xenon and krypton compounds can be formed under special circumstances. The
noble gases have very high ionization energies, and they have no tendency to accept
electrons.
Properties of Oxides
A common way of comparing elements is comparing similar compounds, in this case
oxides. The most common oxides across period 3 are: Na2O, MgO, Al2O3, SiO2, P4O10,
SO3, and Cl2O7.
The first two oxides of Na2O and MgO are called basic oxides. Na2O reacts with water to
form sodium hydroxide: Na2O(s) + H2O(l)  2NaOH(aq). Magnesium oxide is not
soluble in water, but it will react with acids in a manner similar to an acid-base reaction:
MgO(s) + 2HCl(aq)  MgCl2(aq) + H2O(l).
Aluminum oxide is also very water insoluble. It can react with acids, however:
Al2O3(s) + 6HCl(aq)  2AlCl3(aq) + 3H2O(l). But aluminum oxide can also react with
bases: Al2O3(s) + 2NaOH(aq) + 3H2O(l)  2NaAl(OH)4. Therefore, Al2O3 is
classified as an amphoteric oxide because it has properties of both acids and bases.
Silicon dioxide is water insoluble, but can react with strong bases: SiO2(s) + 2NaOH(aq)
 Na2SiO3(aq) + H2O(l). For this reason, you should never store concentrated sodium
hydroxide solutions in glass, which is predominantly SiO2.
The remaining oxides (P4O10, SO3, and Cl2O7) in Period 3 are acidic. They react with
water to form phosphoric acid, sulfuric acid, and perchloric acid, respectively. Note that
the nonmetal retains