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Chapter 2
The Elements
2.1
Categorizing atoms – a history
Although elements such as gold, silver, tin, copper, lead and mercury have
been known since antiquity, the first scientific discovery of an element occurred in 1649 when Hennig Brand discovered Phosphorus. During the next
200 years, a vast body of knowledge concerning the properties of elements and
their compounds was acquired by chemists. By 1869, a total of 63 elements
had been discovered. As the number of known elements grew, scientists began to recognize patterns in properties and began to develop classification
schemes.
2.1.1
Law of Triads
In 1817 Johann Dobereiner noticed that the atomic weight of strontium fell
midway between the weights of calcium and barium, elements possessing similar chemical properties. In 1829, after discovering the halogen triad composed of chlorine, bromine, and iodine and the alkali metal triad of lithium,
sodium and potassium he proposed that nature contained triads of elements
the middle element had properties that were an average of the other two
members when ordered by the atomic weight (the Law of Triads).
This new idea of triads became a popular area of study. Between 1829 and
1858 a number of scientists (Jean Baptiste Dumas, Leopold Gmelin, Ernst
Lenssen, Max von Pettenkofer, and J.P. Cooke) found that these types of
chemical relationships extended beyond the triad. During this time fluorine
was added to the halogen group; oxygen, sulfur,selenium and tellurium were
15
Chapter 2
grouped into a family while nitrogen, phosphorus, arsenic, antimony, and
bismuth were classified as another. Unfortunately, research in this area was
hampered by the fact that accurate values were not always available.
2.1.2
First Attempts At Designing a Periodic Table
If a periodic table is regarded as an ordering of the chemical elements demonstrating the periodicity of chemical and physical properties, credit for the first
periodic table (published in 1862) probably should be given to a French geologist, A.E.Beguyer de Chancourtois. De Chancourtois transcribed a list of
the elements positioned on a cylinder in terms of increasing atomic weight.
When the cylinder was constructed so that 16 mass units could be written
on the cylinder per turn, closely related elements were lined up vertically.
This led de Chancourtois to propose that ”the properties of the elements are
the properties of numbers.” De Chancourtois was first to recognize that elemental properties reoccur every seven elements, and using this chart, he was
able to predict the stoichiometry of several metallic oxides. Unfortunately,
his chart included some ions and compounds in addition to elements.
2.1.3
Law of Octaves
John Newlands, an English chemist, wrote a paper in 1863 which classified
the 56 established elements into 11 groups based on similar physical properties, noting that many pairs of similar elements existed which differed by
some multiple of eight in atomic weight. In 1864 Newlands published his
version of the periodic table and proposed the Law of Octaves (by analogy
with the seven intervals of the musical scale). This law stated that any given
element will exhibit analogous behavior to the eighth element following it in
the table. (see Figure 2.1)
2.1.4
Who Is The Father of the Periodic Table?
There has been some disagreement about who deserves credit for being the
”father” of the periodic table, the German Lothar Meyer or the Russian
Dmitri Mendeleev. Both chemists produced remarkably similar results at
the same time working independently of one another. Meyer’s 1864 textbook
included a rather abbreviated version of a periodic table used to classify the
elements. This consisted of about half of the known elements listed in order of
16
The Elements
Figure 2.1: The Law of Octaves arrangement of elements
Figure 2.2: The periodic ordering of elements according to Meyer
their atomic weight and demonstrated periodic valence changes as a function
of atomic weight. In 1868, Meyer constructed an extended table which he
gave to a colleague for evaluation. Unfortunately for Meyer, Mendeleev’s
table became available to the scientific community via publication (1869)
before Meyer’s appeared (1870) (see Figure 2.2 and Figure 2.3).
While writing a textbook on systematic inorganic chemistry, Principles
of Chemistry, which appeared in thirteen editions the last being in 1947,
Mendeleev organized his material in terms of the families of the known el17
!
!
!
The Elements Beryllium (Be), Magnesium (Mg), and Calcium (Ca) all formed oxides in the ratio of one atom p
oxygen atom: RO
Boron (B) and Aluminum (Al) formed R2O3
Carbon (C) and Silicon (Si) formed RO2
Recognizing the patterns of combining ratios or "valency", Mendeleev created a table organized by placing elements
with similar combining ratios in the same group. He arranged the elements within a group in order of their atomic
mass.
Chapter 2
In 1869, the Russia
chemist Mendeleev
noted that the
repeating patterns o
behavior could be
arranged in a
sequence of elemen
giving rise to the
"Periodic Table" of
the elements.
Figure 2.3: The periodic ordering of elements according to Mendeleev. The
spaces marked with blank lines represent elements that Mendeleev deduced
existed but were unknown at the time, so he left places for them in the table.
The symbols at the top of the columns (e.g. R2 O and RH4 ) are molecular
Special thanks to Dr. Paul Karol's "Intro to Modern Chemistry" for providing much of the information on this page.
formulas written in the style of the 19th century
ements which displayed similar properties. The first part of the text was
devoted to the well known chemistry of the halogens. Next, he chose to
cover the chemistry of the metallic elements in order of combining power –
alkali metals first (combining power of one), alkaline earths (two), etc. However, it was difficult to classify metals such as copper and mercury which had
multiple combining powers, sometimes one and other times two. While trying
to sort out this dilemma, Mendeleev noticed patterns in the properties and
atomic weights of halogens, alkali metals and alkaline metals. He observed
similarities between the series Cl-K-Ca , Br-Rb-Sr and I-Cs-Ba. In an effort
to extend this pattern to other elements, he created a card for each of the 63
known elements. Each card contained the element’s symbol, atomic weight
and its characteristic chemical and physical properties. When Mendeleev
arranged the cards on a table in order of ascending atomic weight grouping
elements of similar properties together in a manner not unlike the card arrangement in his favorite solitaire card game, patience, the periodic table was
http://periodic.lanl.gov/mendeleev.htm (1 of 2) [10/24/2001 5:41:07 PM]
18
The Elements
Figure 2.4: Mendeleev’s Tabelle II in semi-modern Form: To the modern
eye, the 1869/71 formulations lacks any Group 18 rare gases and there are
few f-block elements:
formed. From this table, Mendeleev developed his statement of the periodic
law and published his work ”On the Relationship of the Properties of the
Elements to their Atomic Weights” in 1869. The advantage of Mendeleev’s
table over previous attempts was that it exhibited similarities not only in
small units such as the triads, but showed similarities in an entire network
of vertical, horizontal, and diagonal relationships. In 1906, Mendeleev came
within one vote of being awarded the Nobel Prize for his work.
At the time that Mendeleev developed his periodic table the experimentally determined atomic masses were not always accurate, so he reordered
elements despite their accepted masses. For example, he changed the weight
of beryllium from 14 to 9. This placed beryllium into Group 2 above magnesium whose properties it more closely resembled than where it had been
located above nitrogen. In all Mendeleev found that 17 elements had to
be moved to new positions from those indicated strictly by atomic weight
for their properties to correlate with other elements. These changes indi19
Chapter 2
cated that there were errors in the accepted atomic weights of some elements
(atomic weights were calculated from combining weights, the weight of an
element that combines with a given weight of a standard.) However, even
after corrections were made by redetermining atomic weights, some elements
still needed to be placed out of order of their atomic weights. From the gaps
present in his table, Mendeleev predicted the existence and properties of unknown elements which he called eka-aluminum, eka-boron, and eka-silicon.
The elements gallium, scandium and germanium were found later to fit his
predictions quite well. He was, however, incorrect in suggesting that the element pairs of argon-potassium, cobalt-nickel and tellurium-iodine should be
interchanged in position due to inaccurate atomic weights. Although these
elements did need to be interchanged, it was because of a flaw in the reasoning
that periodicity is a function of atomic weight.
2.1.5
Discovery of the Noble Gases
In 1895 Lord Rayleigh reported the discovery of a new gaseous element named
argon which proved to be chemically inert. This element did not fit any of
the known periodic groups. In 1898, William Ramsey suggested that argon
be placed into the periodic table between chlorine and potassium in a family
with helium, despite the fact that argon’s atomic weight was greater than
that of potassium. This group was termed the ”zero” group due to the zero
valency of the elements. Ramsey accurately predicted the future discovery
and properties of neon.
2.2
Atomic Structure and the Periodic Table
Although Mendeleev’s table demonstrated the periodic nature of the elements, it remained for the discoveries of scientists of the 20th Century to
explain why the properties of the elements recur periodically.
In 1897 J.J. Thomson showed that cathode rays generated by applying a
large voltage across a low density gas – first discovered in 1821 – were negatively charged. He found that they could be obtained from the discharge
of any gas while using different materials for the electrodes allowing him to
surmise that the negatively charged particles, now called electrons are constituents of all atoms. By studying the amount of deflection of the electrons
produced by electric and magnetic fields, he determined the mass-to-charge
20
The Elements
ratio me /e. Later, Millikan (1909) was able to determine just the charge of
these electrons from his famous oil-drop experiment.
In 1897 Becquerel found that uranium gave off a radiation that could
blacken a photographic plate even when the plate was separated from the
source of radiation by thick paper. This radiation was separable by a magnet
into two electrically charged beams (α- and β-rays) and a neutral beam called
γ-rays. Rutherford, in 1903, showed that the α-rays were actually a stream
of helium ions, He+2 , and the β-rays were later determined to be a stream
of high-speed electrons. The α-rays were clear evidence that uranium atoms
had disintegrated to give off helium. No longer could atoms be considered
uncharged particles.
Geiger and Marsden sent the He+2 ions into thin metal foils and found
that all but a few of the ions passed straight though the foil. The ones
that did not tended to be scatted by large angles. Rutherford explained this
scattering, in 1911, on the basis of the nuclear model of the atom; most of
the mass of an atoms is concentrated in a positively charged center called
the nucleus, around which negatively charged electrons moved. Nuclei have
diameter of about 10−15 m, where as atomic diameters are about 10−10 m —
a hundred thousand times larger. Atoms are mostly empty space.
In 1919 Rutherford then discovered that hydrogen nuclei appear to form
when α particles collide with nitrogen atoms. Subsequently it was shown
that the same thing happened with other elements besides nitrogen. These
experiments clearly showed that atomic nuclei had structure and appeared
to contain hydrogen nuclei, or protons. In 1930 Bothe and Becker obtained
radiation that easily penetrated many layers of matter when they bombarded
beryllium atoms with α particles. In 1932 this radiation was shown to consist
of neutral particles with a mass approximately equal to the proton, and to
be generated by many other elements when bombarded with α particles.
So atoms have a nucleus that is made up of neutrons and protons, and surrounded by enough electrons to make the atom charge neutral. The atomic
number, Z, is the number of protons in the nucleus. The mass number is
the total number of protons and neutrons in the nucleus. Sodium (Na), for
example, has an atomic number of 11 and an atomic mass of 23 (11 protons
and 12 neutrons), and is notated as 23
11 Na. Due to the discovery, in 1913
by Thompson, that atoms of the same element could have several different
atomic masses (isotopes), it became apparent that mass number (or atomic
weight) was not the significant player in the periodic law as Mendeleev, Meyers and others had proposed, but rather, the properties of the elements varied
21
Chapter 2
periodically with atomic number.
The question of why the periodic law exists was answered as scientists
developed an understanding of the electronic structure of the elements beginning with Niels Bohr’s studies of the organization of electrons into shells.
2.3
Atomic Spectroscopy
Chemists began studying colored flames in the eighteenth century. When
sodium compounds are sprayed into a flame, the flame burns with a bright
yellow color. Potassium gives a violet flame and lithium and strontium give
a red flame. A flame test is a simple way to identify an element. Although
the red flames of lithium and strontium appear similar, the light from each
can be separated into distinctly different colors. The red Strontium flame
when resolved with a prism shows a cluster of red lines and blue lines, while
lithium shows a red line, a yellow line and two blue lines (see Figure 2.5).
Each element has a characteristic line spectrum consisting of a unique
set of frequencies. Lines appear in the ultraviolet and infrared, as well as in
the visible frequency range, and they form series in which the lines become
more closely spaced with decreasing wavelength, approaching a series limit at
which the line spacing converges to zero. These spectra can be used not only
to identify elements, but also to learn about the element’s internal structure,
in particular, the electrons.
The spectroscopists Balmer and Rydberg had been able to fit the frequencies of hydrogen, and of some of the simpler spectra, with very accurate
empirical formulas. Balmer’s formula for hydrogen was
"
!
1
1
−
Frequency = R
4 n2
where R is a constant and n is an integer, equal to 3,4, ... This Balmer
formula was similar to Rydberg’s formula, which worked for the alkali metals
and some other cases. Rydberg’s formula was
!
"
1
Frequency = R const −
(n − d)2
where n again is an integer, d is a constant, and R is, remarkably enough, the
same constant found in Balmer’s formula. This constant, called the Rydberg
22
The Elements
Figure 2.5: The emission spectra of some elements. The lines correspond to
visible light emitted by atoms.
23
Chapter 2
frequency, equal to ≈ 3.29x1015 Hz, pointed to a far-reaching relation between
the spectra of different chemical elements.
In both Balmer’s formula and Rydberg’s formula the frequency appears
as a difference of two quantities, and Ritz, in 1908, showed that this concept
was a general principle. It was possible to write
!
"
1
1
Frequency = R
− 2
(n = n" + 1, n" + 2, ...)
"2
n
n
where for Balmer and Rydberg’s formula n" = 2. In the ultraviolet Lyman
found the n" = 1 series, and Paschen found the n" = 3 series in the infrared.
It was clear that there were discrete sets of lines that were now becoming, at
least for hydrogen, well categorized.
The problem with this scheme was that it seemed to be in violent disagreement with the implications of Rutherford’s nuclear atom picture. If one
studies the motion of a charged particle, like the electron, moving according
to classical mechanics in an inverse-square field such as the nucleus must provide one finds that the electron will continually radiate energy, of a frequency
equal to its rotational frequency about the nucleus. By studying the dynamics of a particle moving according to an inverse-square attraction, we easily
find that the orbit becomes smaller and the frequency of rotation in the orbit
greater, as the energy decreases. If, then, an electron rotating in such an orbit radiates energy away, it will move into orbits of successively smaller radii
and successively higher frequency of rotation, and will continue to radiate
more and more energy, of higher and higher frequency, until it falls into the
nucleus. This catastrophe would have to happen to a classically constructed
atom consisting of a nucleus and electrons. It clearly cannot be happening
with atoms of our experience; they radiate fixed frequencies, sharp spectral
lines, and have permanent existence. What prevents the catastrophe?
In 1913 Niels Bohr produced a set of hypotheses which circumvented the
above objection and which enabled him to derive the Rydberg formula for
the spectrum of hydrogen. Bohr made three basic assumptions:
1. The electrons move in circular orbits about the center of mass of the
atom
2. The only allowed orbits are such that the angular momentum of the
atom about its center of mass is an integral multiple of h/2π.
24
The Elements
3. Radiation occurs only when an electron ”jumps” from one of the allowed orbits to one of lower energy. The difference in energy ∆E is
then radiated as a photon of frequency ν = ∆E/h.
In addition, Bohr pointed out that the hydrogen atom evidently contains
only one electron, a fact not so obvious then as it is now.
Following these assumptions it is possible to calculate the radius of each
allowed orbit,
4π&0 n2 !2
rn =
,
mZe2
and then calculate the energy, which is a sum of the kinetic energy of the nucleus and the electron plus the negative electrostatic potential energy. (This
is all done in exactly the same way that planetary orbits are calculated using
the center of mass concept.)
En =
−mr Z 2 e4
,
32π 2 &20 n2 !2
where mr is the reduced mass of the two particle system (electron and nucleus).
In the Bohr picture, therefore, the possible energies of a hydrogen atom
may be represented by an energy level diagram like that of Figure 2.6, which
shows the energy corresponding to the various values of n. Arrows on the
diagram indicate transitions from one level to another, leading to emission
of photons which produce the spectral lines.
The lowest level E1 is the level which is normally occupied by the electron,
and its energy is therefore equal in magnitude to the energy required to free
the electron from the proton. This energy, in electron volts, is numerically
equal to the ionization potential, in volts, of atomic hydrogen. The energy
levels merge into a continuum for positive values of E; these are energy levels
of the free electron, which are not restricted to discrete values.
The energy equation above describes the spectrum of any one-electron
system – for example, 2 H (or deuterium, D), 3 H (or tritium, T), singly ionized
helium, doubly ionized lithium. The lines of deuterium differ from the lines
of ordinary hydrogen only because of the difference in the reduced mass mr .
Furthermore, we should note that Bohr’s assumptions explained many other
observations as well. For example, it is clear from his theory (and Figure
2.6) why the frequencies of emission and absorption lines are observed to be
the same. We can also understand why not all emission lines are observed in
25
Chapter 2
Figure 2.6: Energy levels of the hydrogen atoms, according to Bohr, showing
transitions which give rise to the Lyman, Balmer ,and other series of spectral
lines.
absorption: in a cold gas, the atoms will all be found in their ground states,
and therefore only those frequencies can be absorbed which correspond to
transitions from the ground state up to some excited states.
The Bohr model was eventually found to have some significant limitations.
The largest one for the single electron hydrogen atom was the lack of fine
structure that was seen in the emission line spectra. Of larger significance was
the inability of the model to explain much of the emission spectra for multielectron atoms. The resolution of these issues fell into place with the full
quantum mechanical treatment (particle/wave duality) of the constituents
of the atom. The full solution of the Schrödinger equation for the hydrogen
atom is one of the canonical problems of a Quantum Mechanics course, and
we will not repeat it here. We will simply use the results to finish the story
of the atomic spectroscopy and help understand the categorization scheme
of the periodic table.
Using wave mechanics, every electron in an atom is characterized by four
quantum numbers. The size, shape, and spatial orientation of an electron’s
probability density are specified by three of these quantum numbers. Bohr
energy levels separate into electron subshells, and quantum numbers dictate
the number of states within each subshell. Shells are specified by a principle
26
The Elements
quantum number n, which may take on integral values beginning with unity;
sometimes these shells are designated by the letters K, L, M , N , O and so on,
which corresponds respectively, to n =0, 1, 2, ,3, 4, 5, .... Note also that this
quantum number, and it only, is also associated with the Bohr model. This
quantum number is related to the distance of an electron from the nucleus.
The second quantum number, l, signifies the subshell, which is denoted
by a lowercase letter – an s, p, d, or f ; it is related to the shape of the
electron subshell. In addition, the number of these subshells is restricted by
the magnitude of n. l < n, so the number of subshells available is n − 1.
The number of energy states for each subshell is determined by the third
quantum number, ml . ml can take on values from −l to l, so for a given l
there are 2l + 1 energy states available. For an s subshell, there is a single
energy state, where as for p, d, and f subshells, three, five and seven states
exist, respectively. In the absence of an external magnetic field, the states
within each subshell are identical. However, when a magnetic field is applied
these subshells states split each state assuming a slightly different energy.
Associated with each electron is a spin moment, which must be oriented
either up or down. Related to this spin moment is the fourth quantum
number, ms , for which two values are possible (+1/2 and −1/2), one for
each of the spin orientations.
A schematic energy level diagram for the various shells and subshells using
the quantum mechanical model is shown in Figure 2.7. Several features of the
diagram are worth noting. First, the smaller the principle quantum number,
the lower the energy level; for example, the energy of a 1s state is less than
that of a 2s state. Second, within each shell, the energy of a subshell level
increases with the value of the l quantum number. Finally, there may be
overlap in the energy of a state in one shell with states in an adjacent shell,
which is especially true of the d and f states; for example, the energy of the
3d state is greater than that for the 4s.
The discussion up to this point has dealt primarily with electron states –
values of energy that are permitted for electrons. To determine the manner
in which these states are filled with electrons, we use the Pauli exclusion
principle, another quantum mechanical concept. This principle stipulates
that no two electrons can have the same set of quantum numbers. This means
that each electron state (a specific n, l, and ml set of quantum numbers) can
hold no more than two electrons, which must have opposite spins (so that
ms is not the same). This, s, p, d and f subshells may each accommodate,
respectively, a total of 2, 6, 10 and 14 electrons.
27
Chapter 2
Figure 2.7: Schematic representation of the relative energies of the electrons
for the various shells and subshells
Of course, not all possible states in an atom are filled with electrons.
The electrons fill up the lowest possible energy states in the electron shells
and subshells, two electrons (having opposite spin) per state. When all the
electrons occupy the lowest possible energies in accord with the foregoing
restrictions, an atom is said to be in its ground state. However, electron
transitions to higher energy states are possible, and are responsible for electrical and optical properties of a material. The electron configuration of an
atom represents the manner in which these states are occupied. In the conventional notation the number of electrons in each subshell is indicated by
a superscript after the shell-subshell designation. For example, the electron
configurations for hydrogen, helium and sodium are, respectively, 1s1 , 1s2
and 1s2 2s2 2p6 3s1 .
At this point, comments regarding these electron configurations are necessary. First, the valence electrons are those that occupy the outermost shell.
28
The Elements
These electrons are extremely important as they participate in the bonding
between atoms to form atomic and molecular aggregates. Furthermore, many
of the physical and chemical properties of solids are based on these valence
electrons.
In addition, some atoms have what is termed stable electron configurations; that is, the states within the outermost or valence electron shell are
completely filled. Normally this corresponds to the occupation of just the
s and p states for the outermost shell by a total of eight electrons, as in
neon, argon, and krypton; on exception is helium, which contains only two
1s electrons. These elements are the inert, or noble, gases which are virtually
unreactive chemically.
With this knowledge of electron configuration, it is possible to arrange
the elements into a periodic table with increasing atomic number, in seven
horizontal rows called periods (connected to the principle quantum number
n). The arrangement is such that all elements arranged in a given column
or group have similar valence electron structures, as well as chemical and
physical properties. These properties change gradually, moving horizontally
across the period and vertically down each column.
2.4
The Modern Periodic Table
The modern explanation of the pattern of the periodic table is that the
elements in a group have similar configurations of the outermost electron
shells of their atoms: as most chemical properties are dominated by the
orbital location of the outermost electron. The last major changes to the
periodic table resulted from Glenn Seaborg’s work in the middle of the 20th
Century (see Figure 2.8). Starting with his discovery of plutonium in 1940,
he discovered all the transuranic elements from 94 to 102. He reconfigured
the periodic table by placing the actinide series below the lanthanide series.
In 1951, Seaborg was awarded the Nobel Prize in chemistry for his work.
Element 106 has been named seaborgium (Sg) in his honor.
The elements positions in Group 8A (or sometimes called Group 0), the
rightmost group, are the inert gases, which have filled electron shells and
stable electron configurations. Group VIIA and VIA are one and two electrons deficient, respectively, from having stable structures. The Group VIIA
elements (F, Cl, Br, I and At) are sometimes termed the halogens.1 The
1
The term halogen originates from 18th century scientific French nomenclature based
29
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I
Chapter 2
Figure 2.8: Modern periodic table, (from www.dayah.com/periodic)
The Elements
alkali2 and alkaline earth3 metals (Li, Na, K, Be, Mg, Ca, etc...) are labeled
as Groups IA and IIA, having, respectively, one and two electrons in excess
of stable structures. The elements in the three long periods, Group IIIB
through IIB are termed the transition metals, which have partially filled d
electron states and in some cases one or two electrons in the next higher
energy shell. Groups IIA, IVA and VA (B, Si, Ge, As, etc.) display characteristics that are intermediate between metals and nonmetals by virtue of
their valence electron structures.
2.4.1
Group naming schemes
There are three ways of numbering the groups of the periodic table, one
using Hindu-Arabic numerals and the other two using Roman numerals. The
Roman numeral names are the original traditional names of the groups; the
Arabic numeral names are those recommended by the International Union
of Pure and Applied Chemistry (IUPAC) to replace the old names in an
attempt to reduce the confusion generated by the two older, but mutually
confusing, schemes.
There is considerable confusion surrounding the two old systems in use
(old IUPAC and CAS) that combined the use of Roman numerals with letters.
In the old IUPAC system the letters A and B were designated to the left (A)
and right (B) part of the table, while in the CAS system the letters A and
B were designated to main group elements (A) and transition elements (B).
The former system was frequently used in Europe while the latter was most
common in America. The new IUPAC scheme was developed to replace both
systems as they confusingly used the same names to mean different things.
The periodic table groups are as follows (in the brackets are shown the
old systems: European and American):
• Group 1 (IA,IA): the alkali metals or hydrogen family/lithium family
on erring adaptations of Greek roots; the Greek word halos meaning ”salt”, and genes
meaning ”production” referring to elements which produce a salt in union with a metal.
2
The word ”alkali” is derived from Arabic Al Qaly = ”the calcined ashes”, referring to
the original source of alkaline substances. Ashes were used in conjunction with animal fat
to produce soap, a process known as saponification.
3
The alkaline earth metals are named after their oxides, the alkaline earths, whose oldfashioned names were beryllia, magnesia, lime, strontia and baryta. These oxides are basic
(alkaline) when combined with water. ”Earth” is an old term applied by early chemists
to nonmetallic substances that are insoluble in water and resistant to heating–properties
shared by these oxides.
31
Chapter 2
• Group 2 (IIA,IIA): the alkaline earth metals or beryllium family
• Group 3 (IIIA,IIIB): the scandium family
• Group 4 (IVA,IVB): the titanium family
• Group 5 (VA,VB): the vanadium family
• Group 6 (VIA,VIB): the chromium family
• Group 7 (VIIA,VIIB): the manganese family
• Group 8 (VIII): the iron family
• Group 9 (VIII): the cobalt family
• Group 10 (VIII): the nickel family
• Group 11 (IB,IB): the coinage metals (not an IUPAC-recommended
name) or copper family
• Group 12 (IIB,IIB): the zinc family
• Group 13 (IIIB,IIIA): the boron family
• Group 14 (IVB,IVA): the carbon family
• Group 15 (VB,VA): the pnictogens (not an IUPAC-recommended name)
or nitrogen family
• Group 16 (VIB,VIA): the chalcogens or oxygen family
• Group 17 (VIIB,VIIA): the halogens or fluorine family
• Group 18 (Group 0): the noble gases or helium family/neon family
32
The Elements
2.5
2.5.1
Trends through the periodic table
Atomic radii
Atomic radius tends to decrease on passing along a period of the periodic
table from left to right, and to increase on descending a group, see Figure 2.9.
The electrons in an atom are arranged in shells which are, on average, further
and further from the nucleus, and which can only hold a certain number of
electrons. Each new period of the periodic table corresponds to a new shell
which starts to be filled up, and so the outermost electrons are further and
further from the nucleus as a group is descended. Passing along a period
from left to right, the nuclear charge increases while the electrons are still
entering the same shell: the effect is that the physical size of the shell (and
hence of the atom) decreases in response.
The increasing nuclear charge is partly counterbalanced by the increasing
number of electrons in a phenomenon that is known as shielding, which is
why the size of atoms usually increases as a group is descended. However,
there are two occasions where shielding is less effective: in these cases, the
atoms are smaller than would otherwise be expected.
Lanthanide contraction
The electrons in the 4f -subshell, which is progressively filled from cerium (Z
= 58) to lutetium (Z = 71), are not particularly effective at shielding the
increasing nuclear charge from the sub-shells further out. The elements immediately following the lanthanides have atomic radii which are smaller than
would be expected and which are almost identical to the atomic radii of the
elements immediately above them. Hence hafnium has virtually the same
atomic radius (and chemistry) as zirconium, and tantalum has an atomic
radius similar to niobium, and so forth. The effect of the lanthanide contraction is noticeable up to platinum (Z = 78), after which it is masked by a
relativistic effect known as the inert pair effect.
d-Block contraction
The d-block contraction is less pronounced than the lanthanide contraction
but arises from a similar cause. In this case, it is the poor shielding capacity of
the 3d-electrons which affects the atomic radii and chemistries of the elements
33
Chapter 2
Figure 2.9: Periodic table of empirically measured atomic radius in picometres (pm) (from www.dayah.com/periodic).
immediately following the first row of the transition metals, from gallium (Z
= 31) to bromine (Z = 35).
2.5.2
Ionization energy
The ionization energy I is defined as the energy that must be supplied in
order to completely remove an electron from an atom. The first ionization
energy is the energy required to remove one electron from the neutral parent
atom. The second ionization energy is the energy required to remove a second
valence electron from the univalent ion to form the divalent ion, and so on.
Successive ionization energies increase.
As can be seen from Figure 2.10 The decrease in atomic radius also causes
the ionization energy to increase when moving from left to right across a
period. The more tightly bound an element is, the more energy is required
to remove an electron. Group I elements have low ionization energies because
the loss of an electron generates an ion with a stable closed shell. Working
down a group, each successive element has a lower ionization energy because
34
The Elements
Figure 2.10: Periodic table of measured first ionization energies in kJ/mol
(1kJ/mol = 0.010364 eV/atom (from www.dayah.com/periodic)
it is easier to remove an electron since the atoms are less tightly bound.
Note the ionization energy of hydrogen is 13.6 eV. The energy of the 1s state
discussed earlier.
There are two exceptions to the general trends. The first is that the
energy to remove the first electron to fill the p subshell is less than the
energy to remove the last electron to fill the s subshell. For example, the
first ionization energy of Be is greater than that of B. The second is that after
all the p subshell orbitals have been filled with one electron (which requires
3 electrons) the addition of the fourth electron will be to a state that already
has an electron of opposite spin. The electron-electron repulsion of this paired
state makes it easier to remove the outermost, paired electron (this is Hunds
rule, which we cover in the magnetism chapter). This last exception holds
for periods 2, 3 and 4.
2.5.3
Electron affinity
Electron affinity, A, reflects the ability of a neutral atom to accept an elec35
Chapter 2
tron. It is the energy change that occurs when an electron is added to a
gaseous atom. Atoms with stronger effective nuclear charge have greater
electron affinity. Some generalizations can be made about the electron affinities of certain groups in the periodic table, see Figure 2.11. The Group
IIA elements, the alkaline earths, have low electron affinity values. These
elements are relatively stable because they have filled s subshells. Group
VIIA elements, the halogens, have high electron affinities because the addition of an electron to an atom results in a completely filled shell. Group
VIII elements, noble gases, have electron affinities near zero, since each atom
possesses a filled shell and will not accept an electron readily. Elements of
other groups have low electron affinities.
As for ionization potential, there are two exceptions to the general trends.
The first is that the Groups 13-17 the elements in the first period have lower
electron affinities than the elements below them in their respective groups.
The second is that elements with particularly stable electron configurations,
filled or exactly half filled subshells (Be, Mg, Mn Tc, Zn, Cd, N, etc...) also
have very low electron affinity.
2.5.4
Electronegativity
Electronegativity is a chemical property which describes the power of an
atom in a molecule to attract electrons towards itself. Electronegativity is not
strictly an atomic property, but rather a property of an atom in a molecule:
the equivalent property of a free atom is its electron affinity. It is to be
expected that the electronegativity of an element will vary with its chemical
environment, but it is usually considered to be a transferable property, that
is to say that similar values will be valid in a variety of situations.
First proposed by Linus Pauling in 1932, electronegativity cannot be directly measured and must be calculated from other atomic or molecular properties. Several methods of calculation have been proposed and, although
there may be small differences in the numerical values of the electronegativity, all methods show the same periodic trends between elements.
The most commonly used method of calculation is that originally proposed by Pauling. This gives a dimensionless quantity, commonly referred
to as the Pauling scale, on a relative scale running from 0.7 to 4.0 (hydrogen
= 2.2). When other methods of calculation are used, it is conventional (although not obligatory) to quote the results on a scale which covers the same
36
The Elements
Figure 2.11: The electron affinity of elements. The data are quoted in
kJ/mole (1kJ/mole = 0.010364 eV/atom). Elements with a value of zero
are expected to have electron affinities close to zero on quantum mechanical grounds. Elements with no values presented are synthetically
made elements - elements not found naturally in the environment (from
www.dayah.com/periodic).
range of numerical values: this is known as an electronegativity in Pauling
units.
In general, electronegativity increases on passing from left to right along
a period, and decreases on descending a group, see Figure 2.12. Hence,
fluorine is undoubtedly the most electronegative of the elements while cesium
is the least electronegative, at least of those elements for which substantial
data are available. There are some exceptions to this general rule. Gallium
and germanium have higher electronegativities than aluminum and silicon
respectively because of the d-block contraction.
In inorganic chemistry it is common to consider a single value of the electronegativity to be valid for most ”normal” situations. While this approach
has the advantage of simplicity, it is clear that the electronegativity of an
element is not an invariable atomic property and, in particular, increases
37
Chapter 2
Figure 2.12: Periodic table of electronegativity using the Pauling scale
with the oxidation state of the element. Allred used the Pauling method
to calculate separate electronegativities for different oxidation states of the
handful of elements (including tin and lead) for which sufficient data was
available. However, for most elements, there are not enough different covalent compounds for which bond dissociation energies are known to make this
approach feasible. This is particularly true of the transition elements, where
quoted electronegativity values are usually, of necessity, averages over several
different oxidation states and where trends in electronegativity are harder to
see as a result.
2.5.5
Other Periodic Tables
Since 1869, numerous table designs have been proposed to demonstrate the
periodic law. I have collected a couple here.
• Physicists Periodic Table
Figure 2.13 shows Timmothy Stowe’s physicists periodic table. This
table depicts periodicity in terms of the four quantum numbers. As you
move down the planes, the principle quantum number, n, increases. In
38
The Elements
Figure 2.13: The physicists periodic table, by Timmothy Stowe.
each plane the color depicts l and the direction in and out of the page
depicts ml (which is labeled m in the legend. ml = 0 is the only choice
for l = 0 or s subshell. For the d subshell (pinkish color in the table)
ml = −2, −1, 0, 1, 2. The left and right direction depict ms which is
labeled as s in the caption. Notice that you can only ever have 2 values
of ms for any other set of quantum numbers, so for any given plane
(n) and color (l), and front to back position (ml ) there are only two
elements indicated, each with a different ms .
• Triangular Periodic Table
Figure 2.14 shows an example is based on the work of Emil Zmaczynski
and graphically reflects the process of the construction of electronic
shells of atoms.
39
Chapter 2
Figure 2.14: The triangular periodic table by Emil Zmaczynski
• Spiral Periodic Table
Figure 2.15 was devised by Theodor Benfey and depicts the elements
as a seamless series with the main group elements radiating from the
center with the d- and f-elements filling around loops.
• The Mayan Periodic Table
Figure 2.16, named for its similarity to the ancient Mesoamerican calendar, is based on electron shells. The shells are shown as concentric
circles. Each row in the tabular form is shown as a ring.
The noble gases are in the vertical column above the center of the chart.
The elements to the right of a noble gas have one extra electron, the
elements directly on the left need one electron to fill their outer shell.
What does this chart show better then the traditional table? (1) The
reactivity of the elements. The elements closest to the noble gases are
so close to becoming a noble gas they can taste it. This makes them
more eager, more reactive, since all they need is to gain or lose one
electron. As you move away from the noble gases along the concentric
circles, the elements get less and less reactive, since they are so far from
being a noble gas, they don’t really think it is worth the effort. (2) The
proportions of compounds. The proportion of elements can be guessed
by looking at the ’hops’ that an element must take to get to the noble
40
The Elements
Figure 2.15: Spiral periodic table.
gases. The guideline is that for elements to combine, one should be
from the left and one from the right. The number of hops an atom
takes to get to the vertical line must equal the number its partner on
the other side takes, since one is gaining an electron and one is losing
one. Aluminum needs three hops left to get vertical, and Oxygen needs
just two. Since the number of hops needs to be the same on both
sides, we need two Aluminum atoms to make the journey and three
Oxygen to make it equal. This implies Al(2)O(3) is a good possibility
for a compound. This guideline only works for elements fairly near the
noble gases. This chart is a only a rough guide since the inner shells of
elements are not always filled before the outer shells.
41
Chapter 2
Figure 2.16: Mayan Periodic Table. Radioactive elements are underlined in
red. Synthetic elements are underlined in blue. The Noble gases are in bold.
42