Eight Steps in the History of the Earth

1. The Big Bang	2.Star Formation
3. Supernova Explosion	4. Solar Nebula Condenses
5. Sun & Planetary Rings Form	6. Earth Forms
7. Earth's Core Forms	8. Oceans & Atmosphere Forms

             Astronomers and physicists denote the build-up of heavier elements from lighter ones as "nucleosynthesis".
Only the very lightest elements (Hydrogen, Helium and Lithium [2]) were created at the time of the Big Bang and therefore
present in the early universe.All the other heavier elements we now see around us were produced at a later time by nucleosynthesis inside stars. In those"element factories", nuclei of the lighter elements are smashed together whereby they become the nuclei of heavier ones - this process is known as nuclear fusion. In our Sun and similar stars, Hydrogen is being fused into Helium. At some stage, Helium is fused into Carbon, then Oxygen, etc.
The fusion process requires positively charged nuclei to move very close to each other before they can unite. But with
increasing atomic mass and hence, increasing positive charge of the nuclei, the electric repulsion between the nuclei becomes
stronger and stronger.
In fact, the fusion process only works up to a certain mass limit, corresponding to the element Iron. All elements that are
heavier than Iron cannot be produced via this path.
The following pictures show the distribution curves of the relative abundance of the elements in the "visible" universe:

The understanding of the origin of the elements, that is their sites of origin, the variety of processes involved, and the epochs in
the evolutionary history of the universe when they occurred, is one of  the greatest achievement of modern science. The
importance of this endeavor is not only in its ability to provide answers to questions such as “where did we come from", but
also in its being the prime tool for setting the time markers that delineate cosmic evolution. Research over the past half century
has clarified  much of the situation. The cosmic rays, high energy particles that pervade our Galaxy, not only provide a direct
sample of cosmic matter carrying information on the processes that produce the elements, but also play a major role in the
synthesis of the light elements, lithium, beryllium and boron. As we shall see, investigations with powerful ground and space
based telescopes of the abundances of these elements have led to entirely new insights into the origin of the cosmic rays.

Element Genesis
We now know that nucleosynthesis, the genesis of the chemical elements and their isotopes, took place both universally,
shortly after the Big Bang, as well as in stars, much later. Isotopes of the same element have the same atomic number but
different masses.
Hydrogen is by far the most abundant element in the universe; it accounts for approximately 93% of the total number of atoms and 76% of the total mass. Helium comes in at a distant second at about 7% of the number and 23% of the mass. 
In general the abundance of the elements drops off exponentially as the atomic mass increases ( simply said: atomic mass is the sum of the protons and neutrons in the atom's nucleus ) the exponential fall is continuous throughout the periodic table until it hits the iron group. (Look at the chart below and you can see a spike at atomic mass 56) These elements are approximately 10,000 times more abundant than their neighbors. This is the only perturbation in the fairly smooth distribution curve. When one does an analysis of the the distribution curve some interesting facts can be seen, such as 99% of the universe's weight comes from hydrogen and helium and all the atoms with a greater atomic number than iron makes up less than a millionth of the universe's total (visible) weight.
1.1 Nucleosynthesis of the light elements
In the first few minutes after the Big Bang, at temperatures exceeding 109 K, several of the lightest elements and their isotopes
were created. Most of the helium (He), essentially all of the deuterium (2H, the heavy isotope of hydrogen) and some lithium
were thus produced. Lithium has two stable isotopes, 7Li and 6Li, but the relevant nuclear processes are such that the Big
Bang produced significant amounts of only the heavier one. Beryllium has one stable isotope (9Be), while boron has two (10B
and 11B). These light elements were not produced in significant  quantities in the Big Bang. Likewise, because of the rapid
expansion of the universe and the concomitant decrease of the density and temperature, neither were the heavier elements (C,
O , etc.). These, so-called metals, have been and still are synthesized much later in the interior of stars, as well as in stellar
explosions (supernovae) that are the death throes of the most massive stars.

The idea that the synthesis of all the elements was associated with the origin of the Universe came from George Gamow and
his co-workers in the late 1940's. A competing theory at that time was that of Fred Hoyle, which maintained that all the
elements are synthesized in stars in galaxies. The strongest argument against an initial, universal synthesis of all the elements is
the fact that very significant variations of elemental abundances are observed in stars of different ages, indicating that
nucleosynthesis is an ongoing process. Indeed, the theories of stellar evolution, supernova dynamics and Galactic chemical
evolution are capable of accounting for many the observed elemental abundances at a great variety of astronomical sites. These
theories are based in large part on the pioneering work in the 1950's of Margaret and Geoff Burbidge, Willie Fowler and Fred
Hoyle, and independently that of Al Cameron.

On the other hand, there are several isotopes whose abundances cannot be understood by stellar nucleosynthesis. Even
though deuterium is produced in stellar interiors, it is also very rapidly destroyed. But in the Big Bang, deuterium produced by
the capture of neutrons on protons, can survive under certain conditions on the universal density which allow the synthesized 2H
to escape destruction owing to the rapid expansion of the universe. In fact, the observed deuterium abundance in the solar
system, in the Galaxy and even in distant extragalactic space, is one of the best indicators of the overall matter density of the
universe.

The other light elements, Li, Be and B, hold a unique place among the elements. Even though their abundances are
exceedingly low, only about 10-9 that of H and about 10-6 that of the next heavier elements C, N and O, they play important
roles both in cosmology and cosmic-ray origin. Li, Be and B are very easily destroyed in stellar interiors, and they are not
generated in the normal course of stellar nucleosynthesis, which proceeds directly from helium to carbon via the fusion of
three alpha particles (helium nuclei). 7Li is somewhat of an exception, as it is produced via the fusion of the two helium
isotopes, 3He and 4He, in giant stars and supernovae. Thus, until about 1970, the origin of Li, Be and B remained a mystery.
At that time, Hubert Reeves, Willie Fowler and Fred Hoyle suggested that these light elements could be produced in nuclear
interactions of cosmic rays with the atoms of the gas and dust that pervade interstellar space in galaxies (the interstellar
medium). The cosmic rays, high energy particles most likely accelerated by shock waves produced by supernovae, also
pervade interstellar space.
1.2 The nucleosynthesis of heavy elements
How were those heavy elements we now find on the Earth produced in the first place? From where comes the
Zirconium in artificial diamonds, the Barium that colours fireworks, the Tungsten in the filaments in electric bulbs? Which
process made the Lead in your car battery?
Synthesizing the Chemical Elements
The Sun and Solar System abundances are the result of MANY cycles of element production  and dispersal in stars. We are literally made of star dust.
We already have a way to mix in "new" Helium, Carbon and Oxygen. All stars with initial masses <8M. end their lives on the Asymptotic Giant Branch (AGB). Main-sequence, (red giant branch )RGB , (horizontal-branch) HB and (asymptotic giant branch) AGB stars produce these elements, deep convection mixes some into the envelopes of the AGB stars and then Planetary  Nebulae carry these elements into the interstellar medium to be mixed into the next generations of stars.
Low-mass stars make He, C, and O, and deliver these via stellar winds and planetary nebulae.
To make the heavier elements up to Iron requires nucleosynthesis in massive stars and delivery via stellar   winds or, more spectacularly, Supernova (SN) explosions.
Supernova(SN)

The structure of all stars is determined by the battle between gravity and radiation pressure arising from internal energy generation. In the early stages of a star's evolution the energy generation in its centre comes from the conversion of hydrogen into helium. For stars with  masses of about 10 times that of the Sun this continues for about ten million years.
Supernovae are vast explosions in which a whole star is blown up. They are mostly seen in  distant galaxies as `new' stars appearing close to the galaxy of which they are members. They  are extremely bright, rivalling, for a few days, the combined light output of all the rest of the  stars in the galaxy. After this time all the hydrogen in the centre of such a star is exhausted and hydrogen `burning'  can only continue in a shell around the helium core. The core contracts under gravity until its  temperature is high enough for helium `burning', into carbon and oxygen, to occur. The helium  `burning' phase also lasts about a million years but eventually the helium at the star's centre is  exhausted and it continues, like the hydrogen `burning', in a shell. The core again contracts until it is hot enough for the conversion of carbon into neon, sodium and magnesium. This lasts for about 10 thousand years.
Type I supernova (SNII)
This pattern of core exhaustion, contraction and shell `burning' is repeated as neon is converted  into oxygen and magnesium (lasting about 12 years), oxygen goes to silicon and sulphur  (about 4 years) and finally silicon goes to iron, taking about a week.  No further energy can be obtained by fusion once the core has reached iron and so there is now no radiation pressure to balance the force of gravity. The crunch comes when the mass of iron reaches 1.4 solar masses. Gravitational compression heats the core to a point where it endothermically decays into neutrons. The core collapses from half the Earth's diameter to about 100 kilometres in a few tenths of a second and in about one second becomes a 10 kilometre diameter neutron star. This releases an enormous amount of potential energy primarily in the form of neutrinos which carry 99% of the energy.
  A shock wave is produced which passes, in 2 hours, through the outer layers of the star causing fusion reactions to occur. These form the heavy elements. In particular the silicon and sulphur, formed shortly before the collapse, combine to give radioactive nickel and cobalt which are responsible for the shape of the light curve after the first two weeks.
  When the shock reaches the star's surface the temperature reaches 200 thousand degrees and  the star explodes at about 15000 kilometres/sec. This rapidly expanding envelope is seen as the initial rapid rise in brightness. It is rather like a huge fireball which rapidly expands and thins allowing radiation from deeper in towards the centre of the original star to be seen. Subsequently most of the light comes from energy released by the radioactive decay of cobalt and nickel produced in the explosion.
Type I supernova (SNI)
The origin of a Type I supernova is an old, evolved binary system in which at least one component is a white dwarf star. White dwarf stars are very small compact stars which have collapsed to a size about one tenth that of the Sun. They represent the final evolutionary stage of all low-mass stars. The electrons in a white dwarf are subject to quantum mechanical constraints (the matter is called degenerate) and this state can only be maintained for star  masses less than about 1.4 times that of the Sun.

SN are like a production and delivery system for the elements.
What about those elements more massive than Fe? Supposedly equilibrium reactions don't work to  produce elements on the other side of the binding energy curve beyond Fe. It turns out that in the excitement of SN explosions there are many non-equilibrium reactions that build up very massive elements.
In some cases these elements are stable, in many cases they are not and the process of radioactive decay of heavy elements is just Nature's way of getting back into equilibrium.
The two principal paths to building "trans-Fe" elements are the s-process and the r-process.
1.S(slow)-process is the Slow addition of neutrons to nuclei with the neutron subsequently undergoing a  &beta;-decay (ejection of an e-) to change into a p+. This way atoms can slowly slowly walk their way  up the Periodic table. It is much easier to add the chargeless neutron to a nucleus than it is a p+.

          ⁵⁶Fe₂₆ + 3n₀ -> ⁵⁹Fe₂₆

          ⁵⁹Fe₂₆ -> ⁵⁹Co₂₇ + e_-1 + n₀;

This works up to around Bismuth at atomic #83 and is though to occur in SNI and also in AGB stars  during the thermal pulse stage.
There is some direct evidence for the S-process occuring in some AGB stars. Technetium with atomic  #43 is an S-process element that has a radioactive half-life of ~200,000 years. It has been detected in AGB stars that are MUCH older than that! The only thing that could be going on is the production of    Tc in the star and then mixing of this to the surface via convection.

2.R(rapid)-process is the Rapid addition of neutrons to existing nuclei. The idea is that you add a bunch of  neutrons which then start to decay into protons via &beta;-decay in the nucleus. This increases the atomic number and is the way to produce the really heavy stuff.
The R-process occurs only (we think) in SN and mostly in SNII. The evidence for R-process occuring is less direct. First, we see elements like Gold which are thought to only be produced via the R-process. It is also true that if we look at the oldest stars in the Galaxy, which were formed after only one or two SNII (these come from massive stars that have very short lives) had enriched the interstellar medium, the abundance of Iron is very low, but the abundaces of R-process elements are only moderately low.
If we look at the Crab nebula which is the expanding remnant of the 1054 A.D. explosion we see  processed material from deep in the star that went SN, but mostly this is the result of the equilibrium  fusion in the "onion skin".

             Elements                                  # of Protons                              Production Site
                  Hydrogen                                       1                                                     Big Bang
                  He                                                 2                                                     Big Bang + stars
                  Carbon, Oxygen                             6, 8                                                low- and high-mass stars
                  Neon - Fe                                     10 - 26                                            high-mass stars
                  Cobalt - Bismuth                            27 - 84                                            s- and r-process; AGB and SNe
                  Polonium - Uranium                        84 - 92                                            r-process in SNe
 

Stability of the Elements and Their Isotopes

The Segré chart of the nuclides. Stable nuclei are shown in black.

As the neutron excess in stable nuclei increases with mass, then accordingly nuclei with equal numbers of protons and neutrons (N=Z) become increasingly exotic compared to the line of beta stable nuclei, and consequently more difficult to produce and investigate experimentally. The neutron separation energy (S_n) is the amount of energy required to remove a neutron from the nucleus, and is equal to the difference in binding of the nucleus with and without the neutron. Similarly, the proton separation energy (S_p) is the energy required to remove a proton. The limits of the existence of nuclei are defined to be where the separation energy of the last nucleon is zero, and are referred to as driplines. The proton dripline is on the neutron-deficient side of the stable nuclei and is predicted to cross the N=Z line somewhere just above ¹⁰⁰Sn.

Nuclear Binding Energy

To compute the nuclear binding energy, simply total up the masses of the protons and neutrons in a nucleus and compare it to the mass of the nucleus.

• Proton mass: 1.00728 amu
• Neutron mass: 1.00867 amu

• Mass of the nucleus is not generally equal to the total mass of its individual neutrons and protons
• For a stable element the nucleus mass is less than the total mass of its nucleons
• This mass difference  leads to the binding energy of the nucleus
• Binding energy represents the energy needed to break a stable atom into Hydrogen (proton and an electron) and neutrons

A negative value of  indicates an unstable nucleus
 To calculate the energy released, calculate the mass defect(), then multiply by 931.5 MeV/amu

Nuclear Reactions
Light nuclides undergo fusion or bombardment to convert to other nuclides closer to the maximum value
Heavy nuclides undergo fission to give nuclides closer to the maximum value If a nuclear reaction gives products with a higher nuclear binding energy, then energy is  released by the reaction.

Nuclear Fusion Reactions
Nuclear energy, measured in millions of electron volts (MeV), is released by the fusion of two light nuclei, as when two heavy hydrogen nuclei, deuterons (H), combine in the reaction

producing a helium-3 atom, a free neutron (n), and 3.2 MeV, or 5.1 × 10^-13 J (1.2 × 10^-13 cal).
Nuclear Fission Reactions
Nuclear energy is also released when the fission (breaking up of ) of a heavy nucleus such as ²³⁵U is induced by the absorption of a neutron as in

producing cesium-140, rubidium-93, three neutrons, and 200 MeV, or 3.2 × 10^-11 J (7.7 × 10^-12 cal). A nuclear fission reaction releases 10 million times as much energy as is released in a typical chemical reaction. The two key characteristics of nuclear fission important for the practical release of nuclear energy are both evident in equation (2). First, the energy per fission is very large. In practical units, the fission of 1 kg (2.2 lb) of uranium-235 releases 18.7 million kilowatt-hours as heat. Second, the fission process initiated by the absorption of one neutron in uranium-235 releases about 2.5 neutrons, on the average, from the split nuclei. The neutrons released in this manner quickly cause the fission of two more atoms, thereby releasing four or more additional neutrons and initiating a self-sustaining series of nuclear fissions, or a chain reaction, which results in continuous release of nuclear energy.
Nuclear Forces
Within the incredibly small nuclear size, the two strongest forces in nature are pitted against each other. When the balance is broken, the resultant radioactivity yields particles of enormous energy.

Magic Numbers.
In the atomic shell model, the shells are filled with electrons in order of increasing energy until they completely fill a closed shell, producing the inert core of a noble gas. These elements have highly stable properties, such as low ionic radius and high ionisation energy. As further electrons are added to shells outside the core, the atomic properties are primarily determined by these valence electrons. The shell model arises from observation of similar phenomena in nuclei, with certain numbers of
nucleons being particularly stable, these numbers are called `magic numbers',

Nuclei with either numbers of protons or neutrons equal to Z, N =2, 8, 20, 28, 50, 82, or 126 exhibit certain properties which are analogous to closed shell properties in atoms, including anomalously low masses, high natural abundances and high energy first excited states. The effect can be seen in a plot of separation energy versus increasing N or Z (figure 2.3) [52]. This is similar to the ionisation energy of an atom with increasing mass, ie. there is a gradual increase with a definite sharp drop off at each of the magic numbers, corresponding to the filling of major nuclear shells.
Radioactivity
     The nuclei of elements exhibiting radioactivity are unstable and are found to be undergoing continuous disintegration (i.e.,  gradual breakdown). The disintegration proceeds at a definite  rate characteristic of the particular nucleus; that is, each radioactive isotope has a definite lifetime. However, the time  of decay of an individual nucleus is unpredictable. The lifetime of a radioactive substance is not affected in any way by any physical or chemical conditions to which the substance may be subjected.
Types of ionising radiation:

X-rays and gamma rays, like light, represent energy transmitted in a wave without the movement of material, just as heat and light from a fire or the sun travels through space. X-rays and gamma rays are virtually identical except that X-rays do not come from the atomic nucleus. Unlike light, they both have great penetrating power and can pass through the human body. Thick barriers of concrete, lead or water are used as protection from them.
Alpha particles have a positive electrical charge and are emitted from naturally occurring heavy elements such as uranium and radium, as well as from some man-made elements. Because of their relatively large size, alpha particles collide readily with matter and lose their energy quickly. They therefore have little penetrating power and can be stopped by the first layer of skin or a sheet of paper.
However, if they are taken into the body, for example by breathing or swallowing, alpha particles can affect the body's cells. Inside the body, because they give up their energy over a relatively short distance, alpha particles can inflict more biological damage than other radiations.
Beta particles are fast-moving electrons ejected from the nuclei of atoms. These particles are much smaller than alpha particles and can penetrate up to 1 to 2 centimetres of water or human flesh. Beta particles are emitted from many radioactive elements. They can be stopped by a sheet of aluminium a few millimetres thick.
Cosmic radiations consist of a variety of very energetic particles including protons which bombard the earth from outer space. They are more intense at higher altitudes than at sea level where the earth's atmosphere is most dense and gives the greatest protection.
Neutrons are particles which are also very penetrating. On earth, they mostly come from the splitting, or fissioning, of certain atoms inside a nuclear reactor. Water and concrete are the most commonly used shields against neutron radiation from the core of the nuclear reactor.
It is important to understand that ionising radiation does not cause the body to become radioactive.
1.3 The classification of the elements
Periodic Table
History
 In the early 1800's Dobereiner noted that similar elements often had  relative atomic masses, and DeChancourtois made a cylindrical table  of elements to display the periodic reoccurrence of properties.
     Cannizaro determined atomic weights for the 60 or so elements   known in the 1860s, then a table was arranged by Newlands, with the  elements given a serial number in order of their atomic weights,  beginning with Hydrogen.   This made evident that "the eighth element, starting from a given  one, is a kind of repetition of the first", which Newlands called the Law of Octaves.
            Both Meyer and Mendeleyev constructed periodic tables independently, Meyer more impressed by the periodicity of physical properties, while Mendeleyev was more interested in the chemical properties.
          "...if all the elements be arranged in order of their atomic  weights a periodic repetition of properties is obtained." - Mendeleyev
            Mendeleyev published his periodic table & law in 1869 and forecast the properties of missing elements, and chemists began to appreciate it when the discovery of elements predicted by the table took place. Periodic table have always been related to the way scientists thought about the shape and structure of the atom, and has changed accordingly.
Dimitri Mendeleev

Dimitri Mendeleev created this, the original, periodic table.

Reihen

Gruppe I. - R2O

Gruppe II. - RO

Gruppe III. - R2O3

Gruppe IV. RH4 RO2

Gruppe V. RH3 R2O5

Gruppe VI. RH2 RO3

Gruppe VII. RH R2O7

Gruppe VIII. - RO4

1

H = 1

2

Li = 7

Be = 9,4

B = 11

C = 12

N = 14

O = 16

F = 19

3

Na = 23

Mg = 24

Al = 27,3

Si = 28

P = 31

S = 32

Cl = 35,5

4

K = 39

Ca = 40

- = 44

Ti = 48

V = 51

Cr = 52

Mn = 55

Fe = 56, Co=59 Ni=59, Cu=63

5

(Cu = 63)

Zn = 65

- = 68

- = 72

As = 75

Se = 78

Br = 80

6

Rb = 85

Sr = 87

?Yt = 88

Zr = 90

Nb = 94

Mo = 96

- = 100

Ru=104, Rh=104 Pd=106, Ag=108

7

Ag = 108

Cd = 112

In = 113

Sn = 118

Sb = 122

Te = 125

J = 127

8

Cs = 133

Ba = 137

?Di = 138

?Ce = 140

-

-

-

-  -  -  -

9

(-)

-

-

-

-

-

-

10

-

-

?Er = 178

?La = 180

Ta = 182

W = 184

-

Os=195, Ir=197, Pt=198, Au=199

11

(Au = 199)

Hg = 200

Tl = 204

Pb = 207

Bi = 208

-

-

12

-

-

-

Th = 231

-

U = 240

-

-  -  -  -

Organization of the Modern Periodic Table
The `modern' periodic table is very much like a later table by Meyer, arranged, as was Mendeleyev's, according to the size of the atomic weight, but with Group 0 added by Ramsay. Later, the table was reordered by Mosely according to atomic numbers (nuclear charge) rather than by weight.
     The Periodic Law revealed important analogies among the 94 naturally occurring elements, and stimulated renewed interest in  Inorganic Chemistry in the nineteenth century which has carried into
the present with the creation of artificially produced, short lived elements of `atom smashers' and supercolliders of high energy  physics.
     Harry D. Hubbard, of the United States National Bureau of Standards, modernized Mendeleyev's periodic table, and his first work was  published in 1924. This was known as the "Periodic Chart of the  Atoms".
            Into the 1930s the heaviest elements were being put up in the body of the periodic table, and Dr.Glenn T.Seaborg in 1968  "plucked those out" while working with Fermi in Chicago, naming them the Actinide series,  which later permitted proper placement of subsequently 'created'      elements - the Transactinides, changing the periodic table yet again.  These elements were shown separate from the main body of the  table.
          The Alexander Arrangement of the Elements, a three-dimensional periodic chart designed and patented by Roy Alexander and introduced in 1994, retains the separate Lanthanide and Actinide series, but integrates them at the same time, made possible by using all three dimensions  Further improvement provided by the Alexander Arrangement of the Elements is location of all the element data blocks in a continuous sequence according to atomic numbers while retaining all accepted property interrelationships.  This eases use & understanding of the immense correlative power of
the periodic chart in teaching, learning, and working with chemistry.
             Periodic table is an arrangement of all known element according to their atomic number and chemical properties. This table contains vertical columns called groups and horizontal columns called periods. All elements in a group have similar chemical properties. These groups are number from 1 - 8, left to right and some of groups have their own names.

group I - alkali metal: Li, Na, K Rb, Cs, Fr

group II - alkaline earth metals: Be, Mg, Ca, Sr, Ba, Ra

group VII - Halogens: Cl, Br, I, At

group VIII - Noble gases: He, Ne, Ar, Kr, Xe, Rn

In addition to groups in the periodic table there are three blocks of elements called transition elements, Lanthanoides and Actinoides

Most of the elements in the periodic table are metals. They are found to the left of the table.

The non-metals are found to the top right side of the periodic table. Metals loose electrons to form cations, while non-metals gain electrons to form anions. The bonding between metals and non-metals are usually ionic bond. Ionic bond is a due to attraction of charges of cations and anions. Covalent bonds are found in molecular compounds formed by non - metal reacting with non - metals.

Periodic Spiral: Is a textually rich, highly informative tool for exploring the chemical elements. An    electronic learning application that’s both powerful and easy to use, Periodic Spiral combines a feature-packed interface with a unique design of the periodic table.
          In conventional versions of the Mendeleyevian periodic table, the lanthanons and the actinons are poorly integrated. Moreover, the traditional and alternative placements of hydrogen neither effectively convey the element's unique status nor indicate its chemical similarities and partial affinities to the noble gases, the halogens and the alkali metals. Periodic Spiral illustrates more clearly hydrogen's ambiguous relation to the noble gases, halogens and chalcogens while recognizing its relation to the alkali metals; it also fully integrates the lanthanons and actinons into the design.
 

The Periodic Table of the Elements

---

http://www.chemicalelements.com/elements/

The existing periodic table of the elements is more than 100 years old and is outdated.

The Current Periodic Table

Accordingly, the process of element-building is comparable to a mass which falls under the influence of gravity as
follows:

The alkali metals, found in group 1 of the periodic table (formerly  known as group IA), are very reactive metals that do not
occur  freely in nature. These metals have only one electron in their outer shell. Therefore, they are ready to lose that one
electron in ionic bonding with other elements. As with all metals, the alkali metals are malleable, ductile, and are good
conductors of heat and  electricity. The alkali metals are softer than most other metals.Cesium and francium are the most
reactive elements in this group. Alkali metals can explode if they are exposed to water.
 The Alkali Metals are:  Lithium, Sodium,   Potassium,  Rubidium,   Cesium,  Francium
The alkaline earth elements are metallic elements found in the
                              second group of the periodic table. All alkaline earth elements
                              have an oxidation number of +2, making them very reactive.
                              Because of their reactivity, the alkaline metals are not found free
                              in nature.

                              The Alkaline Earth Metals are:

                                   Beryllium
                                   Magnesium
                                   Calcium
                                   Strontium
                                   Barium
                                   Radium
Transition Elements
The 38 elements in groups 3 through 12 of the periodic table are called "transition metals". As with all metals, the transition  elements are both ductile and malleable, and conduct electricity  and heat. The interesting thing about transition metals is that their  valence electrons, or the electrons they use to combine with other  elements, are present in more than one shell. This is the reason  why they often exhibit several common oxidation states. There are three noteworthy elements in the transition metals family.
 These elements are iron, cobalt, and nickel, and they are the only  elements known to produce a magnetic field.
The Transition Metals:

Scandium  Titanium  Vanadium  Chromium  Manganese  Iron  Cobalt  Nickel  Copper  Zinc  Yttrium  Zirconium  Niobium  Molybdenum  Technetium  Ruthenium  Rhodium  Palladium   Silver

Cadmium  Hafnium  Tantalum  Tungsten  Rhenium  Osmium  Iridium  Platinum  Gold  Mercury  Rutherfordium  Dubnium  Seaborgium  Bohrium  Hassium  Meitnerium  Ununnilium  Unununium  Ununbium

Other Metals
The 7 elements classified as "other metals" are located in groups 3, 14, and 15. While these elements are ductile and malleable,  they are not the same as the transition elements. These  elements, unlike the transition elements, do not exhibit variable  oxidation states, and their valence electrons are only present in  their outer shell. All of these elements are solid, have a relatively  high density, and are opaque. They have oxidation numbers of  +3, ±4, and -3.
 The "Other Metals" are:

Aluminum  Gallium   Indium  Tin  Thallium  Lead  Bismuth

Metalloids
Metalloids are the elements found along the stair-step line that  distinguishes metals from non-metals. This line is drawn from  between Boron and Aluminum to the border between Polonium  and Astatine. The only exception to this is Aluminum, which is  classified under "Other Metals". Metalloids have properties of both  metals and non-metals. Some of the metalloids, such as silicon  and germanium, are semi-conductors. This means that they can  carry an electrical charge under special conditions. This property  makes metalloids useful in computers and calculators
 The Metalloids are:

Boron  Silicon  Germanium  Arsenic  Antimony Tellurium Polonium

Non-metals
Non-metals are the elements in groups 14-16 of the periodic  table. Non-metals are not able to conduct electricity or heat very  well. As opposed to metals, non-metallic elements are very brittle,  and cannot be rolled into wires or pounded into sheets. The  non-metals are exist in two of the three states of matter at room temperature: gases (such as oxygen) and solids (such as  carbon). The non-metals have no metallic luster, and do not  reflect light. They have oxidation numbers of ±4, -3, and -2.
 The Non-Metal elements are:

Hydrogen  Carbon  Nitrogen  Oxygen  Phosphorous  Sulfur  Selenium

The halogens
The halogens are five non-metallic elements found in group 17 of   the periodic table. The term "halogen" means "salt-former" and  compounds containing halogens are called "salts". All halogens   have 7 electrons in their outer shells, giving them an oxidation  number of -1. The halogens exist, at room temperature, in all  three states of matter:
                                    Solid- Iodine, Astatine
                                    Liquid- Bromine
                                    Gas- Fluorine, Chlorine
 The Halogens are:
                                    Fluorine
                                    Chlorine
                                    Bromine
                                    Iodine
                                    Astatine
Noble Gases
The six noble gases are found in group 18 of the periodic table.  These elements were considered to be inert gases until the  1960's, because their oxidation number of 0 prevents the noble  gases from forming compounds readily. All noble gases have 8  electrons in their outer shell, making them stable.
                                    Helium
                                    Neon
                                    Argon
                                    Krypton
                                    Xenon
                                    Radon
Inner-transition Elements
The thirty rare earth elements are composed of the lanthanide and actinide series. One element of the lanthanide series and most of the elements in the actinide series are called trans-uranium, which means synthetic or man-made. All of the rare earth metals are found in group 3 of the periodic table, and   the 6th and 7th periods.
The Rare Earth Elements
The Rare Earth Elements are made up of  two series of elements, the Lanthanide and Actinide Series.
The Rare Earth Elements are:
 
 

Lanthanide Series	Actinide Series
Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium  Thulium Ytterbium  Lutetium	Actinium Thorium  Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium

The structure of hydrogenic atoms
1.4 Some principles of quantum mechanics
Wave-Particle Duality of Matter and Energy
Arbert Einstein
Energy and matter we have learnt from Einstein's theories are analagous, matter can be simply
described in terms of energy. So far we have only discovered two ways in which energy can be
transfered. These are particles and waves. Wave theory applies to electromagnetic radiation. EMR can also be described as particles.
quanta :A particles of light energy.
Quantum: One particle of light with a certain energy.
Photon: A stream of Quanta
Wave theory could be applied to electrons.
What is a wave-mechanical model?
motions of a vibrating string shows one dimensional motion.
Energy of the vibrating string is quantized
Energy of the waves increased with the nodes.
Nodes are places were string is stationary.
Number of nodes gives the quantum number.  One dimensional motion gives  one quantum number.

Wave properties of Electron
The electron is clearly a particle as the experiments of J J Thomson show. He calculated that there was a clear e/m ratio and that the charge on any electron is 1.6E-19 Coulombs. However, experiments by Davisson and Germer show that electrons can display diffraction, an obvious wave property. The first complete evidence of deBroglie's hyprothesis came from two physicists working at the Bell Laboratories in the USA in 1926. Using beams as Thomson did in electron diffraction they scattered electrons off Nickel crystals and analysed how the electrons were more likely to appear at certain angles than others. De Broglie suggested that electrons have wave properties to account for why their energy was quantized.  He reasoned that the electron in the hydrogen atom was fixed in the space  around the nucleus. He felt that the electron would best be  represented as a standing wave. As a standing wave, each electron’s   path must equal a whole number times  the wavelength.

Electrons as de Broglie waves

  l = wavelength, meters
  h = Plank’s constant
  m = mass, kg
  v = frequency, m/s

Returning now to the problem of the atom, it was realized that if, for the moment, we pictured the electron not as a particle but as a wave, then it was possible to get stable configurations. Imagine trying to establish a wave in a circular path about a nucleus. One possibility might be as below.

 An unstable wave orbit

For this configuration, when one starts the wave at a given point, one ends up after one complete revolution at a different point on the wave. The incoming wave will then be out of phase with the original wave, and destructive interference will occur.
However, certain stable configurations are possible, as is illustrated below.

 A stable wave orbit

In this case, the wave ends up in phase with the original wave after one complete revolution, and constructive interference results. Such a pattern would result in a stable orbit. This type of wave is called a standing wave, and are common in other contexts; for example, they can be established on a string attached to a wall if the string is moved up and down at exactly the right speed (such a wave would appear not to be moving, which is why it's called a standing wave).
The Heisenberg Uncertainty Principle
There is a theoretical limit on the exactness with which a particle can be pinned-down (usually in terms of its position and momentum):
                  Dx.Dp > h/2p
where Dx is the uncertainty in position and Dp the uncertainty in momentum.

The Schrödinger Wave Equation and Its Significance

The Schrödinger Wave Equation
 In its most general form the equation looks like this:

 H is called the Hamiltonian operator and represents a series of mathematical operations that must be performed on Y which will give back Y multiplied by an energy E for the electron. Only Y functions for which this is true are "proper" wave-functions, called "eigenfuctions" and the E's that go with them are called "eigenvalues". ("Eigen" is German for "unique".)

 H is defined for the system being described, for example one nucleus and one electron (hydrogen) or two nuclei and one electron (H₂⁺), so the trick is to find the eigenfunctions which work.
 Let's see how this works in a model system - not an electron, but a vibrating string:
The Vibrating String and the "Particle in a One-dimensional Box"

The following diagrams illustrate vibrations on stretched strings. The two curves indicate the extremes of the motion, and the formulae apply to the red one.

y = sin(1px/l)

y = sin(2px/l)

y = sin(3px/l)

 

y = sin(npx/l)

.........(1)

dy/dx = (np/l)cos(npx/l)

 d²y/dx² = -(n²p²/l²)sin(npx/l) = -(n²p²/l²)y

d²y/dx² = -(4p²/l²)y

l = h/mv

d²y/dx² = -(4m²v²p²/h²)y

d²y/dx² + d²y/dy² + d²y/dz² + (8p²m/h²)(E - V)y = 0

y = wave function
E = total energy
V = potential energy

 The diagrams below represent extremes of motion of vibrating drumskins. Play with the applet to make sure you understand which are which. Each mode of vibration is characterized by two quantum numbers, one of which defines the number of circular nodes, and one of which defines the number of linear nodes.

One circular node (at the drumskin's edge)

Two circular nodes (one at the drumskin's edge plus one more)

Three circular nodes (one at the drumskin's edge plus two more)

One transverse node (plus a circular one at the drumskin's edge)

Two transverse nodes (plus one at the drumskin's edge)

Two transverse nodes plus two circular nodes

These vibrations are much easier to visualize when animated.
Separation of the Eigenfunctions into Radial and Angular Components
 It turns out to be much easier to solve the three-dimensional Schrödinger equation if it is transformed to polar coordinates:

Radial probability function electron in 2s orbital
Radial probability function electron in 3s orbital

Nodes in the Y
Total nodes     = n -1
Radial nodes   = n -1- l
Angular nodes = l
Eg 4d orbital:
Total nodes     = 4 -1  = 3
Radial nodes   = n -1- l = 4-1-2 = 1
Angular nodes = l = 2

Probability functions R² and 4pr²R²
 (These diagrams were constructed using the program Mathcad)
 
 

Meaning of Quantum Numbers
Schrodinger's model was based on standing wave properties of electrons similar to a vibrating guitar string and the momentum considering electron as a particle. The difference in the treatment electronic waves was that electrons show three dimensional motion and vibrating string showed one-dimensional motion.Energy of the vibrating string is quantized (quantified) energy of the waves increased with the nodes. Nodes are places were string is stationary. The number of nodes was called the quantum number. One-dimensional motion gives one quantum number.
Quantum numbers n, l and m_l
Principal quantum number,  n
Tells the size of an orbital and largely determines its energy.
 n = 1, 2, 3, ……
n value could be 1, 2, 3, 4, 5, . . . . etc.
Angular momentum,  l
The azimuthal  or angular quantum number l can take values l = (n-1), (n-2), (n-3), ... ¥
 It defines the orbital type or sub-shell:
The number of subshells that a principal level contains.  It tells the shape of the orbitals.  l = 0 to n - 1
 

Magnetic quantum number, m_l
Describes the direction that the orbital projects in space.

 m_l = l to +l  (all integers, including zero)
m_l values depends on l value:  can have -l . , 0 . . . +l values of ml
For example, if l = 2, then m_l would have values of -2, -1, 0, 1 and 2.
Knowing all three numbers provide us with a picture of all of the orbitals.

The magnetic quantum number m_l can take values l, (l-1), (l-2) ... 0 ... -l
 This quantum number can only be associated with a specific orbital for the case m_l = 0. The orbitals defined by other values are functions involving -1^½ i.e. they are imaginary. The orbitals we can visualize and draw are obtained by mathematically "mixing" the imaginary functions, so that the one-on-one correspondence is lost. For example, the 2p_z orbital goes with m_l = 0 but the other two are mixtures.
 The rule for obtaining the possible values of m_l from l does tell us how many orbitals of a particular type we can construct, for example, if l = 3, m_l can be 3, 2, 1, 0, -1, -2, and -3 corresponding to the 7 f-orbitals.
In each of the following cases, the full name of the orbital includes the value of n followed by the orbital symbol. The symbol is followed by a subscript that is derived from simplified approximate functions that mimic the real ones called Slater orbitals.
 The principal quantum number n can take values n = 1, 2, 3, ... ¥

 The magnetic quantum number m_l can take values l, (l-1), (l-2) ... 0 ... -l
 This quantum number can only be associated with a specific orbital for the case m_l = 0. The orbitals defined by other values are functions involving -1^½ i.e. they are imaginary. The orbitals we can visualize and draw are obtained by mathematically "mixing" the imaginary functions, so that the one-on-one correspondence is lost. For example, the 2p_z orbital goes with m_l = 0 but the other two are mixtures.

 The rule for obtaining the possible values of m_l from l does tell us how many orbitals of a particular type we can construct, for example, if l = 3, m_l can be 3, 2, 1, 0, -1, -2, and -3 corresponding to the 7 f-orbitals.

In each of the following cases, the full name of the orbital includes the value of n followed by the orbital symbol. The symbol is followed by a subscript that is derived from simplified approximate functions that mimic the real ones called Slater orbitals.
Spin Quantum Number
m_s should always be -1/2 or +1/2
For the electron  3 Quantum numbers for motion in 3 dimension (x, y, z directions in space) are necessary. Fourth Quantum number was necessary due to spin motion of the electron. According to wave-mechanical model an electron has four Quantum numbers (Q.N.): n = Principle Q.N.; l =Angular Momentum Q.N.; m_l = Magnetic Q.N.; m_s = Spin Q.N.
Schrödinger introduced the notion of treating  electrons as standing waves - a novel move away from thinking of electrons as  particles.

Each electron can be described in terms of Wave function y its quantum numbers.  (n, l, m_l, m_s),
 y² is proportional probablity of finding the electron in a given volume. Max Born Interpretation:  y² = atomic orbital
Electrons travel in three dimensions therefore three quantum numbers are needed three to describe, x, y, z, and fourth is needed for the spin. Four quantum numbers of an electron describe an orbital currently used to explain the arrangement, bonding and spectra of atoms.
 

1.5 Atomic orbitals
Shapes of the Atomic Orbitals
s-Orbitals
These orbitals are spherically symmetrical. They have n - 1 spherical nodes (excluding the one at r = ¥). Notice that the maximum in r²R²(r) occurs at increasing distances from the nucleus with n. Most of the electron density is contained outside the nodal spheres.Electrons surrounding atoms are concentrated into regions of space called atomic orbitals. The Heisenberg uncertainty principle states that it is impossible to know both the location and the momentum of an atomic particle, but it is possible to describe the probability that the electron will be found within a given region of space. The boundries of an atomic orbital are commonly drawn to the region of 90% probability; there is a 90% probability that at any given time, the electron will be within the specified boundry.
The electronic configuration of carbon is 1s² 2s² 2sp³. Atomic orbitals with s-character have spherical symmetry and a representation of the surface of the carbon 1s orbital is shown below. The wave properties of electrons make the description of the 2s orbital slightly more complex than the corresponding 1s orbital, in that, within the 2s sphere there is a region in which the amplitude of the electron standing wave falls to zero, that is, there is zero probability of finding the electron in this node region.
p-Orbitals

These orbitals each have one planar node (in xy,xz or yz) as well as n - 2 spherical nodes (excluding the one at r = ¥). They are named for the axes perpendicular to their nodes (p_x, p_y and p_z. Remember that these orbitals all have a three-dimensional shape with cylindrical symmetry i.e. sections through them parallel to the nodal planes have circular symmetry
 

The electron densities along the x, y and z axes of the 2p orbitals are clearly shown in the figure; the nodes are the points at the origin and at these points, there is zero probability of finding the electron.

d-Orbitals
 It is not possible to mathematically construct 5 equivalent looking real orbitals from the imaginary solutions to the wave equation. The conventional choice is to depict four that have equivalent shapes with two planar nodes each and a fifth with a conical node. The four are named for the plane defined by a pair of axes which does not define a planar node (d_xy, d_x²-z², d_xz, d_yz). The fifth orbital is cylindrically symmetrical about the z axis with a conical node (at 2z²-x²-y² = 0) and is called the d_z² orbital. The d-orbitals have n - 3 spherical nodes.
Shown below are the set of 3d orbitals. From the top 3d_z², 3d_x²-y², 3d_xz, 3d_yz and 3d_xy:
 
 

Many-electron atoms
Stuctures of Atoms with Many Electrons
 
 

 Firstly, note that for a one electron atom or ion, the energy is only a function of n. For atoms with many electrons this remains the overbearing trend, but penetration effects have a profound effect on the actual ordering:
1.6 Penetration and shielding
Radial Penetration of the Wave Functions
 The order can be rationalized by setting up a core of electrons and then considering where the next might go. This is illustrated in Text Figure 1.18. Notice that the added electron would penetrate more deeply into the core in the orbital with the lowest l (s more than p more than d). Do not be mislead by the position of the main maximum in each curve: it is the little "bumps" towards the nucleus that make the difference. Since the stabilization of the electron is directly related to the nuclear charge it "feels" (the effective nuclear charge), the greater the penetration, the better.
Effective Nuclear charge (Z_eff):
Nuclear charge felt by electrons. Z_eff is less than atomic number (Z) since in polyelectronic atoms electrons screen each other from the nucleus.
Many atomic properties are directly related to the magnitude of Z_eff. Variation of Z_eff has been used to explain atomic property trends going across a period or down a group in the periodic table.

Z_eff increase going across a period

Z_eff decrease going down a group

1. If the electron is one of two 1s electrons, the shielding constant s is 0.30 - stop here, otherwise:

 
2. All the other electrons in groups to the right of the electron in question have zero contribution to s.

 
3. Each electron in the same (ns,np) group has contribution 0.35 to s.

 
4. Each electron in the n-1 shell contributes 0.85.

 
5. All those electrons in shells n-2 or lower contribute 1.0 to s.

1. All electrons in groups higher than the electron in question contribute zero to s.

 
2. Each electron in the same group contributes 0.35 to s.

 
3. All those in groups to the left contribute 1.0 to s.

         Argon - Find the effective nuclear charge experienced by one of the outermost 3p electrons.
                     Configuration: (1s²)(2s²2p⁶)(3s²3p⁶)

 Other electrons in the same group = 7 x 0.35 = 2.45
Electrons in the next shell (n = 2) down = 8 x 0.85 = 6.8
Electrons in shells (n = 1) further left = 2 x 1.0 = 2.20

 Therefore s = 11.25 and Z* = 18 - 11.25 = 6.75

Zinc - Find the effective nuclear charge experienced by one of the 4s electrons.
          Configuration: (1s²)(2s²2p⁶)(3s²3p⁶)(3d¹⁰)(4s²)

Other electrons in the same group = 1 x 0.35 = 0.35
Electrons in the next shell (n = 3) down = 18 x 0.85 = 15.30
Electrons in shells (n = 2,1) further left = 10 x 1.0 = 10.00

 Therefore s = 11.25 and Z* = 30 - 25.65 = 4.35

Zinc - Find the effective nuclear charge experienced by one of the 3d electrons.

Configuration: (1s²)(2s²2p⁶)(3s²3p⁶)(3d¹⁰)(4s²)

 Electrons in groups to the right (4s¹) contribute nothing.
Other electrons in the same group (3d) = 9 x 0.35 = 3.15
Electrons in the remaining groups to the left = 18 x 1.00 = 18.00

 Therefore s = 11.25 and Z* = 30 - 21.35 = 21.15

1. The Pauli Exclusion Principle. There is one more quantum number called the spin quantum number m_s which can take values -½ or -½ (for electrons). No two electrons can have the same four quantum numbers so an orbital can "hold" only two electrons. (i.e. Only two electrons can be described by the same spacial wave function.) This rule cannot be broken.

 
2. The Aufbau principle. Electron configurations are built up by filling the lowest energy orbitals first (provided the energy differences are significant). Remember this rule gives only the ground state. Other excited configurations which do not violate the Pauli princple are possible.

 
3. Hund's (first) rule. Where orbitals have the same energy (are degenerate) or nearly so, they will be filled one electron in each, with parallel spins, before pairing begins. Other configurations are excited states i.e. not forbidden.

• Use periodic table
• Periodic table is divided into orbital blocks
• Each period:represents a shell or n
• Start writing electron configuration
• Using following order
• 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d… (building up (Auf Bau)
• principle:)

 What is Pauli Exclusion Principle?
If two or more orbitals exist at the same energy level, they are degenerate. Do not pair the electrons until you have to.
Electrons in an atom cannot have all four of their quantum numbers equal.
Eg. He:  1s2 electron orbital                            n      l         m_l            m_s
                                              __________________________________
                                                        1    1s¹  1      0          0             1/2 ( ¯ )
                                                        2    1s²  1      0          0            -1/2 ( ­ )

Hund’s Rule
Rule to fill electrons into p,d,f orbitals containing more than one sublevel of the same energy.

Electrons will spread over all available (3 ps, 5ds, 7fs) and try to have parallel spins.

p, d, f orbitals have more than one energy sublevels.

When they are filled, Hund's rule is followed.

Elecronic configuration using the periodic table

• To write the ground-state electron configuration of an element:
• Starting with hydrogen, go through the elements in order of increasing atomic number
• As you move across a period
• Add electrons to the ns orbital as you pass through groups IA (1) and IIA (2).
• Add electrons to the np orbital as you pass through Groups IIIA (13) to 0 (18).
• Add electrons to (n-1) d orbitals as you pass through IIIB (3) to IIB(12) and add electrons to (n-2) f orbitals as you pass through the f -block.

 O  1s² 2s² 2p⁴
 Ti  1s² 2s² 2p⁶ 3s² 3p⁶ 3d² 4s²
 Br  1s² 2s²2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁵
Core format
 O  [He]  2s² 2p⁴
 Ti  [Ar]  3d² 4s²
 Br  [Ar]  3d¹⁰ 4s² 4p⁵

Elements of Period Two
 

Lithium Beryllium	Z=3 Z=4 (L-shell, part)	1s22s1 1s22s2	The effect of the greater penetration of the 2s orbital favours it over the 2p as the home for the next two electrons.
Boron to Neon	Z=5 to Z=10 (L-shell, then rest)	1s22s22p1 to 1s22s22p6	Add one electron to each 2p orbital, spins parallel, until each of the three has one electron, and then begin pairing. If it is necessary to be specific, use a diagram showing individual orbitals and electron spins as arrows. It does not matter which combination of orbitals are chosen when a choice exists, nor which spin is chosen, as long as they are parallel as far as possible.

Elements of Period Three
 

Sodium to Argon

Z=11 to Z=18 (M-shell)

[neon]3s1 to [Neon]3s23p6

These follow the pattern of the period from lithium to neon. The core, [neon] means the configuration of neon.

Elements of Period Four
 For this period, the 3d orbitls become very close in energy to the 4s orbitals, and eventually dip below them leading to a couple of "anomalies" in the configurations. (These anomalies are a source of exam questions, but otherwise have little significance.) The filling order continues as follows:
 
 

Potassium to Calcium	Z=19 to Z=20	[argon]4s1 to [argon]4s2	As expected.
Scandium to Vanadium	Z=21 to Z=23	[argon]4s23d1 to [argon]4s23d3	As expected if 3d comes above 4s but below 4p (an accident of nature).
Chromium	Z=24	[argon]4s13d5	This is a manifestation of Hund's rule. It is as if the 4s and 3d orbitals are nearly degenerate (have the same energy) so the electrons are unpaired as far as possible.
Manganese to Nickel	Z=25 to Z=28	[argon]4s23d5 to [argon]4s23d8	These continue the expected trend if 3d is once again just above the 4s
Copper	Z=29	[argon]4s13d10	At this point the 3d orbital energy has dipped below the 4s and stays there. The 3d electrons become core electrons and have only a minor effect on the chemistry of the succeeding elements.
Zinc	Z=30	[argon]4s23d10	Zinc is divalent like calcium, but is "soft" due to the extra d polarizable electrons.
Gallium to Krypton	Z=31 to Z=36	[argon]3d104s24p1 to [argon]3d104s23p6	The expected order resumes.

The Elements of Period Five

 The elements of thise period show analogous configurations including an anomalous configuration for molybdenum (like chromium) and silver (like copper).

 The Elements of Period Six

 The trends are not unlike period five, but after lanthenum, come the 14 lanthanide elements where the 4f orbitals are being filled. There are anomalies in this series associated with the half-filled f-orbitals, and again at the end of the filling of the 5d orbitals for gold (like copper and silver).

 The Elements of Period Seven

 There are similarities to period six, with another set of 14 elements where the 5f orbitals are being filled, the actinides which follow actinium. Little is known of the chemistry of the short-lived radioactive elements beyond Z=104.

 N.B.
 The anomalies in ground state configurations of the neutral atoms are not important in the chemistry of the atoms in their compounds. In particular, for ions of the transition elements (incomplete d orbitals) their configuration is always derived by assuming that the (n-1)d subshell lies below the ns. Remember this when dealing with bonding in transition metal complexes.

Exception to Building Up Principle!

Transition Metal Elements
Electronic Configuration of d-block and f-block elements
d⁵ or  d¹⁰ and f⁷ or f¹⁴  are stable
 Cr :[Ar] 3d⁴ 4s² wrong
 Cr :[Ar] 3d⁵ 4s¹ correct
 Cu :[Ar] 3d⁹ 4s² wrong
 Cu :[Ar] 3d¹⁰ 4s¹ correct

1. The different interpenetrations of the atomic orbitals. Overall "sizes" are a function of R(r)² while orientation is a function of Q(q)²F(f)².
2. We know the filling order.
3. We can estimate effective nuclear charges.

We also know the occupancy of the individual orbitals which may come into play.

Different Types of Atomic Radii in the way they are measured:

tomic Radii

 There are several types of radii in common use according to the circumstances:

1. Covalent Radii: Radii based on covalently liked atoms in covalently bonded molecules.Single-bond (and multiple) covalent radii (r_cov) are appropriate for covalent bonds and are obtained experimentally starting with homonuclear bond lengths divided by two, and building from there.
2. van der Waals Radii: Radii based on non bonded atoms in solids. Van der Waals radii (r_vdw) are appropriate for estimating unconstrained non-bonded contacts and have features in common with the ionic radii. Similarly they are difficult to estimate.
3. Metallic Radii (12-coordinate):Radii based on metallic solids. Metallic radii similar to covalent radii but apply to metallic elements in the solid state.

4. Ionic Radii: Radii basesd on bond distances in ionic solids. Ionic radii (r_ion) are used in ionic compounds to predict closest approach of ions. It may be assumed that such radii are additive. The ionic radii depend on the oxidation state of the ion and its coordination number (number of nearest neighbours). The tabulated values are ususally for the six-coordinate configuration.
 It is more difficult to generate a self-consistent set because more assumtions about what is actually touching what have to be made.

• Cations are always smaller than the corresponding neutral atom and anions are always larger.Van der Waal's radii are alway bigger than covalent radii.
• Radii generally increase down a group. Radii generally decrease across a period (from left to right).
• There are anomalies which can be blamed on the intervention of a transition series, for example Al and Ga are virtually the same size in their covalent compounds.

Tables of Radii

Carbon-based Covalent Radii

1.1 Single bond radii (pm)

Element H
Radius* 29.9
 
Element Be      B       C       N       O       F 
Radius  106     83.0    76.7    70.2    65.9    61.9 
Source  b       a       a       a       a       a 
 
Element         Al      Si      P(III)  S(II)   Cl 
Radius          118     109.0   108.8   105.2   102.3 
Source          b       a       a       a       a 
 
Element         Ga      Ge      As(III) Se(II)  Br 
Radius          125     122     119.6   120.3   119.9 
Source          b       b       a       a       a 
 
Element         In      Sn      Sb(III) Te(II)  I 
Radius          141     139     137     139.1   139.5 
Source          b       b       b       a       a

Sources:

• a: From tabulations and averages of C(sp3)-X distances in Allen, F.H., Kennard, O., Watson, D.G., Brammer, L., Orpen, A.G., & Taylor, R. (1987) J.Chem. Soc. Perkin II, p. S1, subtracting 76.7pm for the radius of carbon.
• b: From individual CH3-X distances, again subtracting 76.7pm.

1.2 Multiple bond radii (pm)

Element         C       N       O
Single          76.7    70.2    65.9
Double          66.1    61.8    54.9
Triple          59.1    54.5

Source:

• Allen et al. (1987), as section A.1.1

2 Van der Waals radii

Element         N       O       F
Radius          155     152     147
 
Element Si      P       S       Cl
Radius  210     180     180     175
 
Element Ge      As      Se      Br
Radius  195     185     190     185
 
Element Sn      Sb      Te      I       Xe*
Radius  210     205     206     198     200
 
Element         Bi
Radius          215

• Bondi,A. (1964) J.Phys. Chem. 68, 441.

3 Metallic radii (12-coordinate) (pm)

Elem.   Rad.    Elem.   Rad.    Elem.   Rad.    Elem.   Rad.
        
Ag      144.5   Fe      127.4   Nb      146.8   Sn      162.3
Al      143.2   Ga      141.1   Nd      182.1   Sr      215.1
Au      144.2   Gd      180.2   Ni      124.6   Ta      146.7
Ba      224.3   Hf      158.0   Os      135.3   Tb      178.2
Be      112.8   Hg      157.3   Pb      175.0   Tc      136.0
Bi      170     Ho      176.6   Pd      137.6   Th      179.8
Ca      197.4   In      166.3   Pm      181.0   Ti      146.2
Cd      156.8   Ir      135.7   Pr      182.8   Tl      171.6
Ce      182.5   K       237.6   Pt      138.7   Tm      174.6
Co      125.2   La      187.7   Rb      254.6   U       156     
Cr      128.2   Li      156.2   Re      137.5   V       134.6
Cs      273.1   Lu      173.4   Rh      134.5   W       140.8
Cu      127.8   Mg      160.2   Ru      133.9   Y       180.1
Dy      177.3   Mn      126.4   Sb      159     Yb      174.0
Er      175.7   Mo      140.0   Sc      164.1   Zn      139.4
Eu      204.2   Na      191.1   Sm      180.2   Zr      160.2

4 Ionic radii

Elem.   Rad.    Elem.   Rad.    Elem.   Rad.    Elem.   Rad.
Ag(+1)  129     Er(+3)  103.0   Mn(+3) 72/78.5* Ta(+3)  86
Al(+3)  67.5    Eu(+2)  131     Mo(+3)  83      Tb(+3)  106.3
Au(+1)  151     Eu(+3)  108.7   Na(+1)  116     Th(+4)  108     
Au(+3)  99      Fe(+2) 75/92.0* Nb(+3)  86      Ti(+2)  100     
Ba(+2)  149     Fe(+3) 69/78.5* Nd(+3)  112.3   Ti(+3)  81.0
Be(+2)  59      Ga(+3)  76.0    Ni(+2)  83.0    Ti(+4)  74.5
Bi(+3)  117     Gd(+3)  107.8   Pb(+2)  133     Tl(+1)  164     
Ca(+2)  114     Hf(+4)  85      Pd(+2)  100     Tl(+3)  102.5
Cd(+2)  109     Hg(+1)  133     Pm(+3)  111     Tm(+3)  102.0
Ce(+3)  115     Hg(+2)  116     Pr(+3)  113     U(+3)   116.5
Ce(+4)  101     Ho(+3)  104.1   Pt(+2)  94      U(+4)   103     
Co(+2) 79/88.5* In(+3)  94.0    Rb(+1)  166     V(+2)   93      
Co(+3) 68.5/75* Ir(+3)  82      Rh(+3)  80.5    V(+3)   78.0
Cr(+2) 87/94*   K(+1)   152     Ru(+3)  82      Y(+3)   104.0
Cr(+3)  75.5    La(+3)  117.2   Sb(+3)  90      Yb(+2)  116     
Cs(+1)  181     Li(+1)  90      Sc(+3)  88.5    Yb(+3)  100.8
Cu(+1)  91      Lu(+3)  100.1   Sm(+3)  109.8   Zn(+2)  88.0
Cu(+2)  87      Mg(+2)  86.0    Sr(+2)  132     Zr(+4)  86      
Dy(+3)  105.2   Mn(+2)  81/97.0*                        
* Low spin and high spin values (section 8.2.3)

4.2 Anion radii (6-coordinate) (pm)

Elem.   Rad.    Elem.   Rad.    
Cl(-1)  167     O(-2)   126     
Br(-1)  182     S(-2)   170     
F(-1)   119     Se(-2)  184     
I(-1)   206     Te(-2)  207

Periodic Properties: Ionization Energy
It is defined as the energy required to remove the outermost electron from a gaseous atom. A "gaseous atom" means an atom that is all by itself, not hooked up to others in a solid or a liquid. When enough energy is added to an atom the outermost electron can use that energy to pull away from the nucleus completely (or be pulled, if you want to put it that way), leaving behind a positively charged ion. That is why it's called ionization, one of the things formed in the process is an ion. The ionization energy is the exact quantity of energy that it takes to remove the outermost electron from the atom.

In your lab work on atomic spectra you observed that a gas would conduct electricity and emit light when it was subjected to a high voltage. When there is little or no voltage applied to the gas in the tubes, no light is emitted and the gas does not conduct electricity. One method for measuring the ionization energy of a gas is to slowly increase the voltage applied to it until it does conduct electricity and emit light. The voltage at which that occurs can be used to calculate the ionization energy.

If the ionization energy is high, that means it takes a lot of energy to remove the outermost electron. If the ionization energy is low, that means it takes only a small amount of energy to remove the outermost electron.

 Let’s use your understanding of atomic structure to make some predictions. Think for a minute about how ionization energy would be affected by three of the factors we were talking about earlier: (1) nuclear charge, (2) number of energy levels, and (3) shielding.

Defined as the Quantity of energy required to remove an electron from an atom is directly related to Z_eff . Ionization potential increase going across a period and decrease going down a group.
As the effective nuclear charge increases, the attraction between the nucleus and the electrons increases and it requires more energy to remove the outermost electron and that means there is a higher ionization energy. As you go across the periodic table, nuclear charge is the most important consideration. So, going across the periodic table, there should be an increase in ionization energy because of the increasing nuclear charge.

Going down the table, the effect of increased nuclear charge is balanced by the effect of increased shielding, and the number of energy levels becomes the predominant factor. With more energy levels, the outermost electrons (the valence electrons) are further from the nucleus and are not so strongly attracted to the nucleus. Thus the ionization energy of the elements decreases as you go down the periodic table because it is easier to remove the electrons. Another way of looking at that is that if you are trying to take something from the first energy level, you have to take it past the second, the third, the fourth and so on, on the way out. But if something is already in the third or fourth energy level, it doesn't have to be taken as far to get away from the nucleus. It is already part way removed from the nucleus.
The first ionization enthalpies most effectively illustrate all these effects.

1. There is always a general trend to increase the enthalpy across a period. This is the effect of steadily increasing effective nuclear charge. Note the rise from Li to Ne for example.
2. Due to the larger size of orbitals in succeeding periods, the outermost electrons are always less tightly held than those of the elements in the same group. Note that sodium (Z* = 2.2) is lower than lithium (Z* = 1.3), and argon (Z* = 6.75) is lower than neon (Z* = 5.85) so it is not just a matter of effective nuclear charge.
3. The estimation of effective nuclear charge is not sufficiently sensitive (using th above rules) to allow for the effect of changing subshell within a period. Note the drop from Be to B.

There is another discontinuity at the half-filled p-subshell, e.g. nitrogen to oxygen, and less well defined ones at the half-filled d and f-subshellss. This occurs when pairing begins and electrons are forced into the same orbital.

The electrons removed when nitrogen and oxygen are ionized also come from 2p orbitals.

But there is an important difference in the way electrons are distributed in these atoms. Hund's rules predict that the three electrons in the 2p orbitals of a nitrogen atom all have the same spin, but electrons are paired in one of the 2p orbitals on an oxygen atom.

Hund's rules can be understood by assuming that electrons try to stay as far apart as possible to minimize the force of repulsion between these particles. The three electrons in the 2p orbitals on nitrogen therefore enter different orbitals with their spins aligned in the same direction. In oxygen, two electrons must occupy one of the 2p orbitals. The force of repulsion between these electrons is minimized to some extent by pairing the electrons. There is still some residual repulsion between these electrons, however, which makes it slightly easier to remove an electron from a neutral oxygen atom than we would expect from the number of protons in the nucleus of the atom.

Periodic Properties: Electron Affinity

Atoms can also gain electrons to form negatively charged ions (anions)

It is also called Electron Attachment Enthalpies
 These correspond to the process:

X(g)   +   e^-(g)    X^-(g)

It is possible to measure the enthalpy of this process directly in very few cases. The elements which normally form cations have positive DH_EA and the elements which normally form di- or trianions ususally have positive DE_EA for the second and third electron attachment steps in spite of their stability in ionic compounds. It would be nice to have more because one of the scales of elecronegativity uses them. The electron affinity is the energy change associated with an atom or ion in the gas state gaining an electron. Defined as the energy released/absorbed when a gaseous atom gains an electron. Electron affinity is directly related to Z_eff. Electron affinity value could either be + or -, therefore care should be exercised when predicting the trends.

• For all positively charged ions, and most neutral atoms, energy is released when an electron is added

Thus, we say that chlorine has an electron affinity of -328 kJ/mol.
The greater the attraction for the electron, the more exothermic the process. For anions and some neutral atoms, added an electron is an endothermic process, i.e. work must
be done to force an electron onto the atom. This results in the formation of an unstable anion.

     The halogens, which are one electron short of a completely filled p subshell have the greatest
     attraction for an electron (i.e. the electron affinity has the largest negative magnitude)

     In adding an electron they achieve a stable electron configuration like the noble gases
     The 2A and 8A groups have filled subshells (s, and p, respectively) and therefore, an
     additional electron must reside in a higher energy orbital. Adding an electron to these groups
     is an endothermic process

Across a period, value of electron affinity generally decrease (going from a small positive value to a larger negative value represents a decrease) Going down a group Electron Affinity values increase.
Electronegativity:
These measure the tendency for one element of a bonded pair to attract the electrons associated with the bond to itself. The polarity of a bond, that is its ionic character is assessed by comparing the two electronegativities of the two bonded atoms. It is also possible to assign an electronegativity to a chemical group e.g. CH₃.  In LiH molecule, it would seem that the bonding orbital places more electron density on the hydrogen than on the lithium since the orbital shape describes the probability of finding the electrons. As a result, the hydrogen end of the moelcule would be slightly negative and the lithium end would be slightly positive.This situation is called a polar bond in which the electrons in the bond are being shared, but not equally shared.

In almost every case in which a bond is formed between two different atoms the resulting bond will be polar.

I
In the 1930's, Linus Pauling (1901 - 1994), an American chemist who won the 1954 Nobel Prize, recognized that bond polarity resulted from the relative ability of atoms to attract electrons. Pauling devised a measure of this electron attracting power which he called "electronegativity" which he defined as the "power of an atom in a molecule to attract electrons to itself." Electronegativity only has meaning in a bond.

The table below presents the electronegativities for the main group elements.

Electronegativity

H = 2.1	x	x	x	x	x	x
Li = 1.0	Be = 1.5	B = 2.0	C = 2.5	N = 3.0	O = 3.5	F = 4.0
Na = 0.9	Mg = 1.2	Al = 1.5	Si = 1.8	P = 2.1	S = 2.5	Cl = 3.0
K = 0.8	Ca = 1.0	Ga = 1.6	Ge = 1.8	As = 2.0	Se = 2.4	Br = 2.8
Rb = 0.8	Sr = 1.0	In = 1.7	Sn = 1.8	Sb = 1.9	Te = 2.1	I = 2.5
Cs = 0.7	Ba = 0.9	Tl = 1.8	Pb = 1.9	Bi = 1.9	Po = 2.0	At = 2.2

Generally, the electronegativity increases moving left to right across a row, and decreases going down the table. Notice that this trend is violated by the Group 13 metals for which the electronegativity drops from B to Al as expected, but hen rises slightly going down to Tl. This effect is due to the intervention of the d electrons and other effects that come into play with very large atoms.
The transition metals are not presented in this chart to conserve room, but their values range from 1.0 to about 2.4.

There have been several methods used to generate numerical electronegativity scales:
Pauling Electronegativity, c_p
           Pauling electronegativity has been calculated based on energetics of bond formation is the first electronegativity scale.
c_p  are commonly used in tables to make decisions about bond polarities. Pauling reasoned that the dissociation energy of a covalent bond, D_theo(A-B), if it were perfectly covalent, could be calculated as the average of the experimental dissociation energies D_exp(A-A) and D_exp(B-B). Partially ionic bonds would have higher observed dissociation energies D_exp(A-B). Therefore the difference between D_exp(A-B) and D_theo(A-B), D_(A-B), will be proportional to the difference in electronegativities c_A and c_B.
 For example, the bond energies of H-H and F-F are, respectively, 436 and 158 kJ mol^-1. If H-F were perfectly covalent, which is not, the bond energy ought to be (436 x 158)^½ = 262 kJ mol^-1. (Pauling used the "geometric" mean rather than the "arithmetic" mean, (436 + 158)/2 = 297 kJ mol^-1, because, by weighting the smaller number more, it gives better results.) The experimental H-F bond energy is 566 kJ mol^-1 so the difference, 566 - 262 = 304 kJ mol^-1 is proportional to the difference c_F - c_H.
 The formula which Pauling used to express this was:

Mulliken Electronegativity, c_M
                   This scale is based on the average of the ionization enthalpy and the negative of the electron attachment enthalpy.  R.S. Mulliken proposed an electronegativity scale in which the Mulliken electronegativity, c_M is related to the electron affinity EA_v (a measure of the tendency of an atom to form a negative species) and the ionization  potential IE_v (a measure of the tendency of an atom to form a positive species) by the equation:

A strong tendency to gain electrons is characterized by a large negativeDH_EA and a large positive DH_IE will go with a reluctance to lose electrons, both of which will contribute to an element showing a large electronegativity. The method makes gfreat sense but is limited by the lack of electron attachment enthalpy data.

 DH_IE - DH_EA depends on specific valence state - so for trigonal boron   compounds, a values of electronegativity can be defined for sp² hybrid orbitals. If the values of IE and EA are in units of MJ mol^-1, then the  Mulliken electronegativity c_M can be expressed on the Pauling scale by  the relationship:

               c_p = 1.35  c_M^1/2 - 1.37

The Allred-Rochow electronegativity-  c_AR.
The underlying theoretical concept is that an electron close to the surface of an atom i.e. a bonding electron is held there by the effective nuclear charge it experiences, and the force resisting its removal is given by:

               c_AR =  0.359(Z*/r²) + 0.744
Assuming the electronegativity is proportional to this force, and adding constants to bring the Allred-Rochow scale into correspondence with the Pauling scale (i.e. F = 4.00 and H = 2.22) gives:
The Allen Scale
 This scale, which is designed only for the representative (main group) elements, comes back to the use of ionization enthalpy data. In this case the weighted average DH_IE for the s and p valence electrons, obtained from (atomic) spectroscopic data is used:

where n and m are the numbers of s and p electrons, respectively. Allen's numbers do not differ much from the other scales.

Polarizability

The ease with which the charge distribution in a molecule can be distorted by an external electric field is called
its polarizability ('squashiness' of its e- cloud). The greater the polarizability, the more easily its e- cloud can be
distorted.  Larger molecules tend to have greater polarizabilities - they have more e- and their e- are further from the nuclei
e.g. I₂ is more polarizable than F₂. Measures the ease of distortion of an atom in an electric field. If the frontier orbitals are not widely separated, then the atom will be more polarizable. This happens more for heavier elements. Atoms resistant to polariation are "hard", while atoms which are easily polarized are "soft".

Recommended Questions from Shriver and Atkins:
 
 

	"Exercises"
1.1, 1.2	These questions are about nuclear chemistry.
1.3 - 1.19	You should be able to answer all these important questions. They could be on exams.
	"Problems"
1.1	This could be done using the equations in Table 1.2 but is well beyond the scope of this course!
1.2	This question is asking you to distinguish between the radial wavefunction and the radial distribution function.
1.3	You have to calculate the ionization energy of an excited H atom, and then explain the comparative values of all three species.
1.4	This is a question about photoelectron spectroscopy. The difference between the energy of the irradiating photons (use E = hn and c = nl), and the kinetic energy (use E = ½mv2) of the ejected electrons corresponds to their ionization energy. The main problem here is just to get everything into the same units.
1.5, 1.6	Do not waste your time with these questions unless you are headed for a career as a chemisry teacher!
1.7 - 1.9	These are more nuclear chemistry questions: not covered in 2001.
1.10	Shielding is a concept that some students find difficult. You should probably be able to take a shot at this.
1.11	Tricky little question unless you get the ground state configurations written down correctly.
1.12	You should be able to do this, although you need not memorize the mathematical functions.
1.13	An interesting question but a bit to philosophical for Chem 481!

 Please return to the referring document and note the hypertext link that led you here.