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C H A P T E R
The Periodic Table of the Elements
O U T L I N E
2.1 Atomic Structure 41
2.2 The Shell Model of the Atom 48
2.3 Electron Assignments 54
2.4 The Periodic Table of the Elements 58
2.5 Periodic Trends 64
Important Terms 70
Study Questions 71
Problems 72
2.1 ATOMIC STRUCTURE
As we saw in Chapter 1, chemists have over the years identified the 98 naturally occurring
elements that make up all of the molecules and materials that we find on our planet. Each of
these elements is defined by its distinctive chemical and physical properties, which set it apart
from all the other elements. Each element was named as it was discovered. Some of the names
of the elements were derived from their observed properties or their method of discovery. For
example, the element hydrogen was discovered by Henry Cavendish in 1766. He noted that it
generated water when reacted with oxygen and named it from the Greek words for water
(hydros) and generator (genes). Helium was named from the Greek word for sun (Helios) as
it was originally discovered in 1895 through studies of the solar emission spectrum. Other
elements were named for their discoverers or their place of discovery. Europium, discovered
by a French chemist Euge`ne-Anatole Demarcay in 1896, was named for the European conti-
nent where it was discovered while americium was named for America, the continent where
it was discovered. Similar histories can be found for all of the elements. Only one element has
been named for a chemist while he was still alive. This element is Seaborgium, named for
Dr. Glenn Seaborg who led the discovery of a number of short-lived elements that were
artificially generated using nuclear reactions at the University of California, Berkeley. We will
discuss these elements and their radioactivity in Chapter 14.
In an attempt to determine the scientific basis for the observed differences in the properties
of the elements, chemists looked to the internal structure of the atom that makes up each of the
General Chemistry for Engineers 41 # 2018 Elsevier Inc. All rights reserved. https://doi.org/10.1016/B978-0-12-810425-5.00002-
elements. It was determined that atoms are made up of three types of particles: electrons, pro-
tons, and neutrons. The atomic nucleus consists of positively charged protons and uncharged
neutrons held tightly together in a small volume at the center of the atom as shown in Fig. 2.1.
The negatively charged electrons “orbit” this nucleus forming the electron cloud surround-
ing the nucleus. Since the proton and neutron have the highest mass of the three particles (see
Table 2.1), the nucleus makes up most of the mass of the atom while the electrons in their
orbits make up most of the volume of the atom.
The number of protons in the nucleus of the atom is the atomic number of the element and
is commonly designated by the symbol Z. For a neutral atom, the number of electrons equals
the number of protons. The atomic number is specific to each element as it also determines the
number of electrons, which determines the properties of the element. The sum of the number
of protons and neutrons in the nucleus is called the mass number of the element since these
two heaviest particles determine the approximate mass of the atom. The mass number is
commonly designated by the symbol A.
- Z ¼ number of protons ¼ number of electrons
- A ¼ number of protons + number of neutrons
- A–Z ¼ number of neutrons
Nucleus
Neutron
Proton Electron
FIG. 2.1 Structure of the atom.
TABLE 2.1 Properties of the Subatomic Particles
Particle Symbol Charge Mass (g) Mass Relative to Neutron Proton p +1 1.6726 10 ^24 0. Neutron n 0 1.6749 10 ^24 1. Electron e^ 1 9.1094 10 ^28 0.
42 2. THE PERIODIC TABLE OF THE ELEMENTS
Most of the symbols of the elements are derived directly from their common name using
the first letter (capitalized) often coupled with a second letter. Twelve of the elements use
only the first letter of the element name. These are Boron, Carbon, Fluorine, Hydrogen,
Iodine, Nitrogen, Oxygen, Phosphorous, Sulfur, Uranium, Vanadium, and Yttrium. Forty
four of the elements use the first and second letters of their name. Still others use the first
and third letters, etc. The symbols for a few of the elements can be quite different from their
current names. This generally occurred for elements discovered very early and originally
given Latin names, which described the element’s properties. Later, these elements were
given names equivalent to the English translation of the original Latin names. The seem-
ingly strange atomic symbol was then derived from the original Latin name of the element.
A list of the elements whose atomic symbols were derived from names different from their
current names is given in Table 2.3. All the names in this list were Latin except for wolfram
(tungsten), which is German.
TABLE 2.2 Atomic Symbols of the Elements—cont’d
Name Symbol Name Symbol Name Symbol Californium Cf Lutetium Lu Silver Ag Carbon C Magnesium Mg Sodium Na Cerium Ce Manganese Mn Strontium Sr Chlorine Cl Meitnerium Mt Sulfur S Chromium Cr Mendelevium Md Tantalum Ta Cobalt Co Mercury Hg Technetium Tc Copernicium Cn Molybdenum Mo Tellurium Te Copper Cu Neodymium Nd Terbium Tb Curium Cm Neon Ne Thallium Tl Darmstadtium Ds Neptunium Np Thorium Th Dubnium Db Nickel Ni Thulium Tm Dysprosium Dy Niobium Nb Tin Sn Einsteinium Es Nitrogen N Titanium Ti Erbium Er Nobelium No Tungsten W Europium Eu Osmium Os Uranium U Fermium Fm Oxygen O Vanadium V Flerovium Fl Palladium Pd Xenon Xe Fluorine F Phosphorous P Ytterbium Yb Francium Fr Platinum Pt Yttrium Y Gadolinium Gd Plutonium Pu Zinc Zn Gallium Ga Polonium Po Zirconium Zr
44 2. THE PERIODIC TABLE OF THE ELEMENTS
Atoms with the same number of protons and electrons, but with different numbers of neu-
trons, are called isotopes. Since they have the same number of protons and electrons, they are
the same element and have the same chemistry. But because they have different numbers of
neutrons, they have different masses. For example, hydrogen has one proton and one electron
with an atomic number of 1 and a mass number of 1. If we add a neutron to the proton in the
hydrogen nucleus, the atomic number is still 1. However, the mass number will now be 2 and
this isotope will have a mass about twice that of the hydrogen atom. Hydrogen is the only
element whose isotopes have different names. The isotope of hydrogen with a mass number
of 2 is called deuterium. Another isotope of hydrogen has a mass number of 3 and is called tri-
tium. Both deuterium and tritium have the same chemistry as hydrogen, but deuterium weighs
twice as much and tritium weighs three times as much as hydrogen. So, an isotope is an atomic
form of an element that has a different mass, but retains the same basic chemistry. Note that
although the chemistry is the same, the change in mass can affect the rates at which the element
will react. This is known as a kinetic isotope effect, which we will discuss in detail in Chapter 9.
Most elements occur naturally as a mixture of isotopes all with different masses. Normally,
one isotope will be the most abundant and will make up most of the naturally observed form
of the element. The mass number (A) in the atomic symbol is used to distinguish between the
different isotopes of an element. Chemists usually will represent a specific isotope of an
element by using only AX, as the difference between A and Z are the number of neutrons,
which defines the isotope, and the element itself defines the atomic number (Z). For example,
the stable isotopes of carbon are represented as 12 C and 13 C. Both of these isotopes have an
atomic number of 6, as carbon has 6 protons in all of its isotopes. The atomic symbols for
hydrogen, deuterium, and tritium are 1 H, 2 H, and 3 H. The mass number is usually left off
the atomic symbol for the most abundant isotope unless other isotopes need to be identified.
For example, H is always assumed to be 1 H.
The atomic mass of an element, also called atomic weight, is different from the mass num-
ber and represents an average of all the naturally occurring isotopes. The atomic mass is
TABLE 2.3 Atomic Symbols of Elements Derived From Names Other Than Their Current Name
Current Name Symbol Original Name Antimony Sb Stibium Copper Cu Cuprum Gold Au Aurum Iron Fe Ferrum Lead Pb Plumbus Mercury Hg Hydrargyrum Potassium K Kalium Silver Ag Argentium Sodium Na Natrium Tin Sn Stannum Tungsten W Wolfram
2.1 ATOMIC STRUCTURE 45
The xenon sample is introduced into the mass spectrometer as a gas stream where it passes
through a high energy electron beam. The high energy electrons collide with the xenon atoms caus-
ing an electron to be stripped from its orbit around the xenon nucleus resulting in xenon atoms with
54 protons and 53 electrons, giving them a positive charge. An atom with an unequal number of
protons and electrons is called an ion and the process of creating the ion from the uncharged atom
is called ionization (step 1). The stream of positively charged ions is then passed through a series of
negatively charged plates, causing the positively charged ions to become accelerated (step 2). The
rapidly moving xenon ions then pass through a magnetic field that is perpendicular to the flow of
the ions. The magnetic field causes the stream of xenon ions to curve and be deflected from their
original path (step 3). The extent of this deflection depends on the mass of the ions. The lighter
isotopes are deflected more severely than the heavier isotopes separating them according to their
masses. The extent of deflection of the isotopes is also dependent on the strength of the magnetic
field. As the strength of the magnetic field is slowly changed, the isotopic streams of differing
masses are each focused in turn on the surface of a detector (step 4). Since the ions are positive, they
pick up electrons from the detector and the amount of ions hitting the detector is measured as an
electric current. The strength of the magnetic field at the time each isotope is detected determines its
mass and the magnitude of the electric current determines its natural abundance.
A plot of the relative abundances of the isotopes versus their mass is called a mass spectrum. The
mass spectrum of xenon is shown in Fig. 2.3 and the results are summarized in Table 2.4.
The mass spectrum shows that xenon has nine naturally occurring isotopes; 124 Xe, 126 Xe, 128 Xe,
129 Xe, 130 Xe, 131 Xe, 132 Xe, 134 Xe, and 136 Xe. Since all the xenon isotopes have 54 protons, the number
of neutrons for each isotope is equal to:
Mass number 54 ¼ 70, 72,74,75, 76,77, 78,80, and 82:
Except for 12 C, which is defined as having a mass of 12.0 amu, isotopic masses are not integer values.
But, they are always very close to the mass number. The actual mass of the nine xenon isotopes as
measured by the mass spectrometer in Table 2.4 are from 0.09 to 0.1 amu less than their mass
Relative abundance (%)
Mass
FIG. 2.3 The mass spectrum of xenon.
2.1 ATOMIC STRUCTURE 47
numbers. This is due in part to the mass of the electrons, which is not included in the mass number.
It is also due to the contribution of binding energy between the neutrons and protons, which will be
discussed in Chapter 14.
Since the atomic mass of xenon is equal to the sum of the masses of each isotope multiplied by the
fraction of its natural abundances, the atomic mass for xenon is;
ð 123 : 91 Þ ð 0 : 001 Þ + 125ð : 90 Þ ð 0 : 001 Þ + 127ð : 90 Þ ð 0 : 019 Þ + 128ð : 91 Þ ð 0 : 264 Þ + 129ð : 90 Þ ð 0 : 041 Þ
+ 130ð : 91 Þ ð 0 : 212 Þ + 131ð : 90 Þ ð 0 : 269 Þ + 133ð : 91 Þ ð 0 : 104 Þ + 135ð : 91 Þ ð 0 : 089 Þ ¼ 131 :29amu (2)
2.2 THE SHELL MODEL OF THE ATOM
In order to further explain the properties of the elements, scientists struggled to determine
the exact structure of the electron cloud surrounding the nucleus of an atom. Why was it that
the attractive forces between the negatively charged electrons and the positively charged pro-
tons did not result in the electrons falling into the nucleus? Niels Bohr addressed this question
by proposing that the electrons orbit the nucleus in circular orbits of fixed energy. These orbits
exist at stable distances from the nucleus and the electrons must remain in these orbits to pre-
vent them from collapsing into the nucleus. The electrons cannot exist between orbits. There
are a series of these stable orbits of different energies and at different distances from the nu-
cleus. The orbit closest to the nucleus is of lowest energy, while the one farthest from the nu-
cleus is of highest energy. This arrangement results in the energy of the electrons being
restricted to certain allowed values. This restriction of electrons to a limited number of pos-
sible energy values is known as being quantized. The allowed orbits are each designated by a
positive integer n called the principal quantum number. The value of n is equal to 1 for the
orbit closest to the nucleus and increases with distance from the nucleus as shown in Fig. 2.4.
TABLE 2.4 Relative Abundances of the Xenon Isotopes as Determined From the Mass Spectrum
Mass Number Isotopic Mass (amu) Number of Neutrons Abundance (%) 124 123.91 70 0. 126 125.90 72 0. 128 127.90 74 1. 129 128.91 75 26. 130 129.90 76 4. 131 130.91 77 21. 132 131.90 78 26. 134 133.91 80 10. 136 135.91 82 8.
48 2. THE PERIODIC TABLE OF THE ELEMENTS
infrared at 1875, 1282, and 1094 nm. They are called the Paschen series also after their discoverer
Friedrich Paschen.
It should be noted that these three series of lines differ not only by the wavelength range in which
they occur, but also by the number of lines in each series and the separation between them. The
Lyman Series appears at shorter wavelengths and is composed of five lines. These five lines are very
close together, being separated by an average distance of 7 nm. The Balmer Series, in the visible
wavelength range, is composed of four lines with an average separation of 82 nm. The Paschen series
appears at longer wavelengths and is composed of only three lines separated by much larger
distances with an average distance of 390 nm.
The atomic number of hydrogen is 1. It has one electron in the lowest energy level (n ¼ 1). Bohr
attempted to explain the occurrence of the hydrogen line emission spectrum by suggesting that the
energy added to the hydrogen atoms when exposed to the electric current caused the hydrogen
electron to “jump” to higher orbits as shown in Fig. 2.6. It then would return to its original orbit
by releasing the excess energy in the form of light. Since the allowed orbits available to the electron
are quantized, the energy released is also quantized and appears as narrow lines at specific wave-
lengths in the line emission spectrum. The wavelength of each line is dependent on the difference in
energy between the two electronic orbits. An electron falling from the n ¼ 2 orbit to the n ¼ 1 orbit
would release light of wavelength λ 1 in Fig. 2.6, while an electron falling from n ¼ 3 orbit to the n ¼ 1
orbit would release light of wavelength λ 2. Since n ¼ 3 is of higher energy than n ¼ 2, the light emit-
ted from the n ¼ 3 to n ¼ 1 transition would be of shorter wavelength than that from the n ¼ 2 to n ¼ 1
transition (λ 1 > λ 2 in Fig. 2.6).
The energy released when the electron falls back to a lower orbit is related to the wavelength of
light observed by;
E ¼ hc=λ ¼ hν (3)
where h is Plank’s constant (6.626 10 ^34 J • s), c is the speed of light (2.998 108 m/s), λ is the light
emission wavelength in nm, and ν is the emission frequency. (So, when someone asks you “What’s
new” you can answer by saying “c over lambda.”) The emission line observed at the shortest
wavelength (highest energy) in the hydrogen line emission spectrum arises from electrons falling
from the highest orbit (n ¼ 6) back to the lowest orbit (n ¼ 1). This line of highest energy appears
at 94 nm in the Lyman Series. The lines occurring at longer wavelengths (lower energy) occur from
electrons falling between orbits closer together in energy.
n = 3
l 1 l 2
n = 2
n = 1
Energy
FIG. 2.6 The transition of an electron from a
lower orbit to a higher orbit due to the absorption of energy followed by the electron returning to the lower orbit with the release of the excess energy in the form of light of a specific wavelength (λ).
50 2. THE PERIODIC TABLE OF THE ELEMENTS
The Lyman series appears in the ultraviolet (highest energy) because all five lines arise from
electrons in the higher orbits (n ¼ 2, 3, 4, 5, and 6) falling back to their original n ¼ 1 orbit as shown
in Fig. 2.7. The Balmer series has four lines (four electronic transitions) caused by electrons in
orbits n ¼ 3, 4, 5, and 6 falling to the n ¼ 2 orbit. The three lines in the Paschen series are from
electrons in orbits n ¼ 4, 5, and 6 falling to the n ¼ 3 orbit. Both the Balmer and Paschen series
require a second transition for the hydrogen atoms to return to the lowest energy and most stable
state. This lowest possible energy state is known as the ground state of the atom. Higher energy
states arising from the absorption of energy and the transition of electrons to higher orbits are
known as excited states.
The energy difference between the two orbits in an electronic transition (n 2 to n 1 ) responsible for
each emission line in the spectrum can be calculated from the wavelength of the emission line as;
ΔE ¼ E f Ei ¼ hc=λ (4)
where Ei is the energy of the initial state and Ef is the energy of the final state. The wavelength of light
emitted from an electronic transition (n f to ni) can be calculated from;
1 =λ ¼ R 1 =n f 2 1 =ni^2 ^ (5)
Balmer developed this relationship to help explain the source of the visible lines in the Balmer series.
The constant R is known as the Rydberg constant (1.0974 107 m^1 ) and the equation is known as the
Balmer equation. For the red line in the Balmer series, the wavelength of the transition ni ¼ 3 to nf ¼ 2
is;
1 1 : 0974 107 ^ 1 = 22 1 = 32 ^ ¼ 6 : 56 10 ^7 m ¼ 656nm: (6)
Lyman series
n = 1
n = 2
n = 3
n = 4 n = 5 n = 6
94 nm 95 nm 97 nm 103 nm 122 nm Balmer series
Paschen series
410 nm
1094 nm
1282 nm
1875 nm
434 nm
656 nm486 nm
FIG. 2.7 Electronic transitions re-
sponsible for the hydrogen line emission spectrum. Modified from Szdori, Wikimedia Commons.
2.2 THE SHELL MODEL OF THE ATOM 51
Each orbital can contain a maximum of two electrons. Since negatively charged electrons
will repel each other, in order for the orbital to accept two electrons they must be of opposite
spin. The electron spin is also assigned a quantum number called the spin quantum number
(s). The spin quantum number has the values of +½ or ½. The complete description of the
energy level of any electron within an atom requires all four quantum numbers (n, l, m, and s)
and no two electrons in the same atom can have the same four quantum numbers. This rule is
called the Pauli Exclusion Principle. The properties of the four quantum numbers are sum-
marized in Table 2.6.
The first two quantum numbers (n and l) also determine the maximum number of electrons
in each electron shell. The K shell (n ¼ 1) can have only one subshell (s with l ¼ 0) with one
orbital (2l + 1) and a maximum of two electrons [2(2l + 1)]. So, the maximum number of elec-
trons in the K shell is equal to two. The L shell (n ¼ 2) can have two subshells (s with l ¼ 0 and p
with l ¼ 1) with a total of four orbitals (1 + 3) and eight electrons (2 + 6).
s orbital
d orbitals
p orbitals
z y
x
x
x x
x x
y y y y^ y
z z z
z z
z y x
z y x
z y x
d (^) xy d (^) xz d (^) yz dx (^2) − y 2 dz 2
px p (^) y p (^) z
FIG. 2.8 Shapes of the s, p, and d atomic orbitals.
TABLE 2.6 The Properties of the Four Quantum Numbers That Describe the Energy Level of an Electron
Name Symbol Value Property Relationships Principal quantum number
n 1, 2, 3,⋯ Energy level n ¼ number of subshells in shell
Azimuthal quantum number
l n 1 0, 1, 2, 3
Orbital shape l ¼ number of nodal planes, 2 l + 1 ¼ number of orbitals in subshell 2(2l + 1) ¼ number of electrons in subshell Magnetic quantum number
m +l… 0 ….l Orbital spatial orientation Spin quantum number s +½, ½ Electron spin
2.2 THE SHELL MODEL OF THE ATOM 53
EXAMPLE 2.1: DETERMINING THE MAXIMUM NUMBER OF ELECTRONS IN AN ELECTRON SHELL
What is the maximum number of electrons in the M and N electron shells?
1. Determine the number of subshells.
M shell: n ¼ 3, subshells ¼ 3 (s, p, d)
N shell: n ¼ 4, subshells ¼ 4 (s, p, d, f)
2. Determine the number of orbitals per subshell.
Number of orbitals ¼ 2 l + 1: s ¼ 2(0) + 1, p ¼ 2(1) + 1, d ¼ 2(2) + 1, f ¼ 2(3) + 1
M shell: 2l + 1 ¼ 1 + 3 + 5 ¼ 9
N shell: 2l + 1 ¼ 1 + 3 + 5 + 7 ¼ 16
3. Multiply the total number of orbitals by two to obtain the number of electrons.
M shell: 2(9) ¼ 18
N shell: 2(16) ¼ 32
2.3 ELECTRON ASSIGNMENTS
The electrons of any element are assigned to the shells, subshells, and orbitals in the order
of increasing energy. Each electron will occupy the orbital of lowest energy available. They
will enter an orbital of higher energy only when the orbitals of lower energy are all filled. This
procedure for assigning electrons to shells, subshells, and orbitals in the order of increasing
energy is known as the Aufbau principle (aufbau is the German word for “building up”). The
Aufbau principle is guided by:
1. The Pauli Exclusion Principle: no more than two electrons can occupy any one orbital.
2. Hund’s Rule: within a subshell, electrons will occupy the orbitals individually (with
parallel spins) before filling them in pairs (with opposite spins).
The energy of any orbital is predicted by both the n and l quantum numbers, which determine
the energies of the electronic shell and subshell. In general, the electrons fill all the subshells in
a shell in the order of increasing energy s < p < d < f before beginning to fill the next higher
shell. This method of assigning electrons to subshells according to the increasing principal
quantum number holds strictly for elements of atomic number 1–18. The trend is more com-
plex for elements with atomic numbers higher than 18.
An element with an atomic number of 1 (hydrogen) has only one electron in the single or-
bital of the s subshell of the n ¼ 1 shell. The element with an atomic number of 2 (helium) has
two electrons in the single orbital of the s subshell of the n ¼ 1 shell each with opposite spin.
Since the n ¼ 1 shell has only one orbital and can only have two electrons, the element with
atomic number 3 (lithium) has two electrons in the 1s subshell and one electron in the 2s
subshell. This assignment of electrons to the electronic shells, subshells, and orbitals is called
the electronic configuration of the atom and is most often represented in a symbolic notation
known as subshell notation. This form lists the principal quantum number of the electron
shell, followed by the subshell type, and the number of electrons in each subshell as shown
in Fig. 2.9. Each subshell in the atom containing electrons is listed in this manner beginning
with the 1s. The electronic configurations in subshell notation for the elements with atomic
54 2. THE PERIODIC TABLE OF THE ELEMENTS
However, the value of n + l for the 3d subshell is equal to 5. So, the 4s subshell is actually of
lower energy than the 3d subshell because it has a lower n + l value. This is why electrons are
placed in the 4s subshell before the 3d subshell.
The Aufbau principle is then modified to account for the electron assignments of the ele-
ments with atomic numbers above 18 as follows:
1. Electron subshells are filled in the order of increasing n + l.
2. Where two subshells have the same n + l, the subshell with the lowest n is filled first.
3. No more than two electrons can occupy any one orbital.
4. Electrons will fill all orbitals in a subshell individually (with parallel spins) before filling
them in pairs (with opposite spins).
So, the resulting order of energies for the electronic subshells according to the increasing n + l
values is;
1 s < 2 s < 2 p < 3 s < 3 p < 4 s < 3 d < 4 p < 5 s < 4 d < 5 p < 6 s < 4 f < 5 d < 6 p < 7 s < 5 f < 6 d < 7 p < 8 s
Table 2.8 details the calculation of n + l values for all available subshells and determines the
electron filling order of each subshell. Fig. 2.10 summarizes the electron filling order in
TABLE 2.8 Electron Filling Order According to the n + l Rule
Subshell n l n + l Filing Order 1 s 1 0 1 1 2 s 2 0 2 2 2 p 2 1 3 3 3 s 3 0 3 4 3 p 3 1 4 5 3 d 3 2 5 7 4 s 4 0 4 6 4 p 4 1 5 8 4 d 4 2 6 10 4 f 4 3 7 13 5 s 5 0 5 9 5 p 5 1 6 11 5 d 5 2 7 14 5 f 5 3 8 17 6 s 6 0 6 12 6 p 6 1 7 15 6 d 6 2 8 18 7 s 7 0 7 16 7 p 7 1 8 19 8 s 8 0 8 20
56 2. THE PERIODIC TABLE OF THE ELEMENTS
diagram form. Subshells above the 6d, 7p, and 8s are not known to exist in the ground state of
any known element.
Although the subshell notation is a simple way to represent the electronic configuration
of an atom, it holds no information regarding the electronic orbitals or electron spin.
A more detailed way of describing the electronic configuration is by an orbital diagram
where the orbitals are designated by boxes and the electrons are shown by arrows inside
the boxes. Electron spin is represented by the direction of the arrow in each box. An upward
pointing arrow represents a spin of +½ and a downward pointing arrow represents a spin of
½. Elements with atomic numbers 1–10 would be represented in orbital diagrams shown in
Fig. 2.11.
1 1 s
n
n + l =
2 s 3 s 4 s 5 s 6 s 7 s 8 s
7 p
6 d
5 f
4 f 5 d
4 d
3 d
6 p
5 p
4 p
3 p
2 2 p 3
Electron shell
l = (^) 0 1 2 3
FIG. 2.10 Diagrammatic representa-
tion of the electron filling order according to the n + l rule.
Atomic number Orbitals 1 s 1 2 3 4 5 6 7 8 9
2 s 2 p
FIG. 2.11 Orbital diagrams for the elements with atomic numbers 1–10.
2.3 ELECTRON ASSIGNMENTS 57
mass between 40 (calcium) and 48 (titanium) and Mendeleyev left a vacant space for it in his
table. Later in 1879, the element scandium was discovered with an atomic mass of 45 and
properties that were consistent with giving it the position in the previously unassigned spot
in the table. The discovery of scandium was one of a series of elemental discoveries which
validated the periodic law, thus leading to Mendeleev being given primary credit for the
development of the Periodic Table of the Elements. However, some inconsistencies remained
with Mendeleev’s version of the periodic table.
In 1913, Henry Moseley, a British physicist, was able to determine the atomic numbers of
all the known elements using X-ray emission spectroscopy. He then proceeded to rearrange
the elements in Mendeleev’s periodic table according to increasing atomic numbers. This
arrangement seemed to clear up the contradictions and inconsistencies in Mendeleev’s
arrangement by atomic masses. Since atomic number defines the number of protons in the
nucleus and therefore the number of electrons in the neutral atom, this arrangement was more
directly related to electronic structure and more clearly predicted properties of the elements.
Moseley restated the periodic law originally proposed by Mendeleev and Meyer as a function
of the atomic number of the elements. Moseley’s periodic law as stated below is now consid-
ered the current Periodic Law.
- The physical and chemical properties of the elements recur periodically in a systematic and
predictable way when the elements are arranged in order of increasing atomic number.
An understanding of this periodicity of the chemical properties of the elements allowed
chemists to predict how elements would combine and how they would behave when reacting
with other elements. The development of the Periodic Table of the Elements can thus be
compared to the discovery of the “Rosetta Stone,” which provided the key to the translation
of ancient languages into modern text and for the first time allowed scholars to be able to
understand the meaning of ancient documents. Similarly, the periodic table effectively
organizes the elements into classes according to their electronic configurations, providing
the key to understanding and predicting the chemical behavior of the elements. In order
to effectively use the periodic table to predict chemical properties and behavior of the
elements, it is important to first know how its structure relates to electronic configurations.
The general layout of the modern periodic table is shown in Fig. 1.12. It arranges the ele-
ments in vertical columns called groups. There are 18 groups in the periodic table numbered
1 – 18. Elements in the same group generally share the same chemical properties with clear
trends associated with increasing atomic number going down a group. Some groups are
known by family names to indicate the similar properties that they share. Group 1 is called
the alkali metals (lithium, sodium, potassium, rubidium, cesium, and francium). Group 2 is
known as the alkaline earth metals (beryllium, magnesium, calcium, strontium, barium, and
radium). Group 17 is the halogens (fluorine, chlorine, bromine, iodine, and astatine) and
group 18 is the noble gases (helium, neon, argon, krypton, xenon, and radon). Elements in
groups 3–12 are known collectively as the transition metals.
The elements are also arranged in seven horizontal rows called periods because the
periodic properties of the elements increase systematically with increasing atomic number
going across a row. There are seven periods in the periodic table numbered 1–7. The number
of each period corresponds to the principal quantum number of the outermost electron shell
containing electrons for all elements in the period. So, the elements in period 1 contain
2.4 THE PERIODIC TABLE OF THE ELEMENTS 59
electrons only in the n ¼ 1 shell, while the elements in period 2 contain electrons in the n ¼ 1
and n ¼ 2 shells, and elements in period 3 contain electrons in the n ¼ 1, 2, and 3 shells, and so
on. Since the periodic table is arranged according to atomic number, increasing the atomic
number by one corresponds to adding one electron to the electronic configuration of the pre-
vious element in the period.
Some areas of the periodic table are called blocks shown in Fig. 2.13. The blocks indicate the
filling sequence of the electron shells and each block is named according to the subshell in
which the outermost electrons reside for elements in that block. The s-block includes elements
in group 1 (alkali metals) and group 2 (alkaline earth metals). It also includes helium (atomic
number 2). All of these elements have outermost electrons in the s-subshell in the shell
corresponding to the number of the period. The p-block includes groups 13–18 and contains
the metalloids, post-transition metals, nonmetals, and the noble gases. The elements in this
block have their outermost electrons in p orbitals. Elements in groups 3–12 make up the d-
block which contains all of the transition metals. The f-block has no group numbers, but in-
cludes the lanthanide series excluding lanthanum and the actinide series excluding actinium.
The lanthanide and actinide series are often shown offset below the rest of the periodic table
for simplicity, as in Fig. 2.12. However, lanthanum and actinium are actually in group 3 and
part of the d-block elements. The rest of the lanthanide and actinide series belong between
groups 2 and 3 in periods 6 and 7.
The blocks appear in the periodic table according to the electron filling sequence following
Madelung’s rule described in Section 2.3. The d-block appears in periods 4–7 before the
p-block since the d subshell fills before the p subshell after the n ¼ 3 shell. Similarly, the f-block
Group 1 (^1) H Li^3 (^11) Na (^19) K Rb^37 (^55) Cs (^87) Fr
He^2 (^10) Ne (^18) Ar (^36) Kr (^54) Xe (^86) Rn 118
(^5) B (^13) Al (^31) Ca (^49) ln (^81) TI 113
C^6 (^14) Si Ge^32 (^50) Sn (^82) Pb 114
Be^4 Mg^12 (^20) Ca (^38) Sr (^56) Ba (^88) Ra
(^22) Ti (^40) Zr
(^21) Sc (^39) Y (^72) Hf
(^57) La (^89) Ac
Alkali metals Lanthanide metals Metalloids Non metals Noble gases
Actinide metals Post-transition metals
Alkaline earth metals Transition metals
(^58) Ce (^90) Th
(^59) Pr (^91) Pa Nd^60 (^92) U
Pm^61 (^93) Np
Sm^62 Pu^94
(^63) Eu Am^95
(^64) Gd Cm^96
(^65) Tb Bk^97
(^66) Dy (^98) Cf
(^67) Ho (^99) Es
(^68) Er (^100) Fm Tm^69 (^101) Md
(^70) Yb (^102) No
(^71) Lu (^103) Lr
(^23) V (^41) Nb Ta^73 (^104) Rf (^105) Db
(^24) Cr Mo^42 (^74) W (^106) Sg
Mn^25 (^43) Tc (^75) Re (^107) Bh
Fe^26 Ru^44 Os^76 (^108) Hs
Co^27 Rh^45 (^77) lr (^109) Mt
(^28) Ni (^46) Rd (^78) Pt (^110) Ds
Cu^29 Ag^47 Au^79 (^111) Rg
(^30) Zn (^48) Cd (^80) Hg (^112) Cn FI Lv
N^7 (^15) P (^33) As (^51) Sb (^83) Bi 115
O^89 F (^16) S CI Se^34 Te^52 (^84) Po 116
17 (^35) Br (^53) I (^85) At 117
Period^4 5 6 7
FIG. 2.12 The Periodic Table of the Elements. The atomic number of each element is displayed above the element’s
symbol. Modified from Sandbh, Wikimedia Commons.
60 2. THE PERIODIC TABLE OF THE ELEMENTS
