Atoms

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Periodic Table

			and the mass equivalent of their binding energies. It is expressed in units such that the mass of the most abundant type of carbon is exactly 12.00 u (1 u = 1.66x10-24 gm). Figure 13-01b is the same table in more colorful style, while Figure 13-01c is another classification scheme by filling up the electron configuration according to increasing energy levels.
Figure 13-01a Periodic Table, Modern [view large image]	Figure 13-01b Periodic Table, Unconventional [view large image]	Figure 13-01c E-Config Table	Also see "Extension of the Periodic Table".

Figure 13-01a includes data for the boiling point, melting point, density, acidity, basicity, crystal structure, and electronegativity (tendency to keep electrons) of the elements. The s, p, d, and f letters in the electronic configuration designate the orbital quantum number l = 0, 1, 2, 3, ... respectively for the outer shell electrons. A new designation of the groups has a number ranged from 1 to 18. Figure 13-01b is an unconventional Periodic Table. It specifies the phase (solid, liquid, or gas) of the element at room temperature, whether the element is radioactive or man-made, as well as its usage (in daily life) or occurrence (in nature). The original version in pdf format, and other Periodic Table in words are available from: http://elements.wlonk.com. Other kinds of Periodic Table may incorporate properties such as atomic radius, covalent radius, ionization potential, specific heat, heat of vaporization, heat of fusion, electrical conductivity, and thermal conductivity etc. The filling sequence in Figure 13-01c shows

Figure 13-01c1 Periodic Table, Comical

clearly that the electrons in each atom arrive at their most stable configuration (the ground state) by occupying the lowest possible energy levels.

The regular pattern in the periodic table is related to the states of the electrons in an atom. It is specified by four quantum numbers. The principal quantum number n determines the energy level; its value runs from 1, 2, 3, ... For each n, the orbital quantum number l = 0, 1, 2, ... (n-1) designated by s, p, d, ... ; it is related to the magnitude of angular momentum. Then for each l, the magnetic quantum number m can be -l, -l+1, ...l-1, l; it is related to the z component of the angular momentum. The spin quantum number s is either +1/2 or -1/2.

For n = 1, l = 0, m = 0, there is only 2 possible quantum states for the electron, with s = +1/2 and -1/2 respectively. For n = 2, l = 0, m = 0 and l =1, m = -1, 0, +1; there is a total of 2 + 6 = 8 possible quantum states. Therefore, it requires 2 electrons to complete the shell for n = 1, and 8 electrons to complete the shell for n = 2, ...and so on. The orbital quantum number l is often designated by a letter, s for l = 0, p for l = 1, d for l = 2, and f for l = 3 ...

The quantum number l is non-additive (e.g., two of the quantum numbers l₁, l₂ are added as vectors, they can take on the values of l₁+l₂, l₁+l₂-1, ..., |l₁-l₂| ) while m is additive (e.g., m' = m₁ + m₂ only) and relates to an Abelian group (e.g., the two dimensional rotation about the z-axis). States having the same non-additive quantum numbers but differing from each other by their additive quantum numbers are said to belong to the same multiplet. The number of members of a multiplet is called its multiplicity. For a given multiplet l the multiplictiy is equal to 2l+1.

When the multiplet levels have the same eigen-energy, they are degenerate, which can be lifted via either external perturbation such as a magnetic field or internally by interaction between parts within the atom. The Zeeman effects in Figure 13-01c2,a shows the interaction between the magnetic field B and the magnetic dipole moment associated with the orbital angular momentum L. It splits a single level

Figure 13-01c2 Zeeman Effects [view large image]

with given (s, p, ...) into levels according to the formula (2+1). However there would not be so many line splitting as the transition is restricted by the selection rule ml = 0, 1. Simply put, selection rules are the consequence of something that has to be conserved before and after the transition.

In anomalous Zeeman effect, the electron spin S is also involved in the interaction, then it is the total angular momentum J = L + S and its z components that has to be taken into consideration (Figure 13-01c2,b). According to the rule of vector addition, the two levels involve in the sodium D1 line splitting are J = 0 + 1/2 = 1/2, and J = 1 - 1/2 =1/2 and m_j = +1/2, -1/2 for each level.

Beside the external perturbations to lift the degeneracy, there are many effects internally that can split the levels. Figure 13-01c3,a shows the many causes that split the levels to the order of 5x10^-5 ev and collectively called fine structures. The contributions include :

	The relativistic correction to the electron's kinetic energy. The Spin-Orbit correction. The "Darwin Term" correction by smearing out the electrostatic interaction between the electron and nucleus. The Anomalouus Zeeman effects of an external magnetic field. The Lamb Shift from vacuum fluctuation of virtual particles (courtesy of QED).
Figure 13-01c3 Fine and Hyperfine Structures [view large image]	Figure 13-01c3,b shows the interaction between the electron spin and nuclear spin producing splitting of the order 5x10-6 ev. Astronomers use the 21 cm line emission to plot the hydrogen cloud distribution of the Milky Way (see insert).

The atom tends to lost the outer electrons if the number is far from a complete shell or sub-shell such as the elements in the beginning of a series. It gradually develops a preference for accepting more electrons to complete the outer shell as the progression moves toward the end of a series. This property is responsible for all the chemical reactions, which form molecules with a tendency of completing the shell (energy levels with similar energy, usually with the same value of n) or subshell (energy levels having almost the same energy, usually with the same values of l). A stable atomic configuration is also achieved by completing a shell or sub-shell as illustrated in Table 13-01 below by the inert elements (the rule becomes more complicated in the advanced series as the electrons with high l tend to intermingle with each others), which do not react chemically:

n	..., l	..., (2l+1)x2	Electron Configuration of the Inert Element
1	0	2	He (2)=2
2	0, 1	2, 6	Ne (2)+(2+6)=10
3	0, 1, 2	2, 6, 10	Ar (2)+(2+6)+(2+6)=18
4	0, 1, 2, 3	2, 6, 10, 14	Kr (2)+(2+6)+(2+6+10)+(2+6)=36
5	0, 1, 2, 3, 4	2, 6, 10, 14, 18	Xe (2)+(2+6)+(2+6+10)+(2+6+10)+(2+6)=54
6	0, 1, 2, 3, 4, 5	2, 6, 10, 14, 18, 22	Rn (2)+(2+6)+(2+6+10)+(2+6+10+14)+(2+6+10)+(2+6)=86

Table 13-01 Electron Configuration of the Inert Elements

The elements in the periodic table has been classified broadly into metals, non-metals and metalloids as discussed in Topic-12. The more refined classification is to categorize according to groups (in new designation from 1 to 18). A summary is given for each group here. It then follows with a table (attached to the main text as a "flap") listing the elements within. For Groups 3 - 12 only the more common elements are presented. The table is intended to supplement the conventional periodic table with information on electron orbitals, emission spectrum, some common chemical compounds, the application to nature and in our daily life. The pictures on orbitals and spectrum are taken from "The Elements, A Visual Exploration of Every Known Atom in the Universe" by Theodore Gray. The followings is a summary of the information in these tables:


1. The atomic radius is not well defined as the electron density does not have a sharp boundary in quantum theory. Theoretical

   		calculation defines it as the maximum radial density in the outermost shells. The result is shown in Figure 13-01d for most of the elements. Measured radii are added (within parenthses) for those with missing data. Experimental data are usually obtained by measuring the distance between two atoms (and then divided by 2). It is rather obvious that there are discrepancies in these two kinds of measurements. Figure 13-01e depicts the energy levels of the subshells and the outermost filling blocks (subshells) in the periodic table.
   Figure 13-01d Atomic Radii [view large image]	Figure 13-01e Subshell Energy Levels

   
   
2. The general trends of the radii are decreasing size from Group 1 to Group 18 and the reverse from Period 1 to 7. Such phenomena are the results of three competing causes :
   • Electron shells increase the radii down each period (column).
   • Nuclear charge attracts the electrons to make the radii smaller along each column and row.
   • Electron shielding by inner electrons reduces the effect of increasing nuclear charge.
   
   
3. Figure 13-01e shows the increase in energy (less binding) as more subshells are filled by electrons. Thus, the ionization energies (binding energy) are inversely proportion to the radii of the atoms (such relationship is exact for the Bohr model of the hydrogen atom). Consequently, most of the metallic elements are good electric and thermal conductors since they possess loosely bound outermost electrons to move up to the conduction band. Near the end of the d-block transition metals (Group 11 and 12), they all become excellent conductors as there are 10 valence electrons available for the conduction band. Some of the Group 13 to 17 elements is high in electronegativity - meaning that they rather accept electrons than donate them to the conduction band - and thus turn into metalloids or diatomic gases. The Group 18 elements of inert gases have fully occupied shells or subshells, they don't interact with other elements and not even to themselves. Thus they exist as monoatomic gases.



4. The emission spectrum of the elements is used to identify unknown substance. A crude and cheap method to detect metal ions is the flame test, which heats the sample on a loop of platinum wire moistened with hydrochloric acid (HCl) in a colorless flame. Figure 13-01f shows the color of the flame from sodium carbonate (Na₂CO₃) and copper sulfate (CuSO₄). The color of the flame is determined by the dominant emission line of the metallic element. However, the color is only a

   		qualitative indicator, since many different metals may emit similar color. A more reliable method is the spectroscope shown in Figure 13-01g. The source is in the form of low pressure gas inside a discharge tube . A slit or two is used to collimate the light into parallel beam (for a sharp image). The different emission lines are separated by a prism. It is widely used in science and engineering.
   Fig. 13-01f Flame Test	Figure 13-01g Spectroscope [view large image]	For example, the emission spectrum of the quasar 3C273 looks suspiciously like the Balmer series spectrum of the hydrogen atom but the wavelength of each line is not the same as the one shown in

   		Figure 13-01h taken in the laboratory. It turns out that the ratios of the wavelengths are identical, the lines has been red shifted by a factor of (1 + z), where z is the amount of redshift, as the quasar is recessing from us in the cosmic expansion (Figure 13-01i).
   Figure 13-01h Hydrogen Emission Spectrum [view large image]	Figure 13-01i 3C273 Emission Spectrum [view large image]

   
   
5. The quantum theory of hydrogen atom has related the energy levels of the electron to the wavelength of the emission lines in

   well organized series. Most of the other elements produce randomly distributed emission lines since the displacement of just one electron opening up numerous ways the other electron(s) can jump from one energy level to another. The group 13 elements and a few others seem to be the exception. They appear to be hydrogen-like with one outer electron moving around a core. Figure 13-01j illustrates a few of the possible ways the electrons can move around generating a number of emission lines after an electron at the core has been excited to higher energy level.

   Figure 13-01j Orbitals and Spectrum [view large image]

   
   
6. An article in the July 12-18, 2014 issue of NewScientist lists five problems with the Periodical Table :
   
   

   The atomic weight is not universal as explained earlier. The Rare Earth and Actinide series can be arranged in either electron configurations or chemical properties. The position of H and He is ambiguous as they can be in group 17 and 2 respectively as well according to the number of electron(s) in the outer shell. The line between metal and non-metal is defined by the ambient conditions on Earth's surface. The elements can assume very different forms under different pressure and temperature. The relativistic speed of the inner most electrons in heavy elements (with atomic number >79) changes the chemical properties of the elements. The Table has no end in sight (see "Stable Nucleus").

   Figure 13-01k Problems with Periodic Table [view large image]

   
   
   
7. Group 1 elements (known as alkali metals) are silvery colored, soft, low density metals, which react readily with halogens to form ionic salts, and with water to form strongly alkaline (basic) hydroxides. These elements all have one electron in their outermost shell, so the energetically preferred state of achieving a filled electron shell is to lose one electron to form a singly charged positive ion. Their softness and ractivity increase down the group. Lithium is a soft metal (see Figure 13-02a) with such low density that it floats in water. It reacts vigorously with water to produce hydrogen gas, and with oxygen to form

Li2O, such that it is never found in its free state in nature. Hydrogen (water creator in Greek), with a solitary electron, nominally belongs in the alkali metals group. However, removal of that single electron requires considerably more energy than for the other alkali metals. Like the halogens, only one additional electron is required to fill in the outermost shell of the hydrogen atom, so hydrogen can be regarded in some respects as behaving like a halogen; its elemental form is a diatomic gas, and it can even form salts (called hydrides) with the alkali metals, where the metal has donated an electron to the hydrogen, almost as if hydrogen were actually a halogen.

Figure 13-02a Lithium

See more in Group 01 Elements.



Group 2 elements have one more electron in their outer shells than group 1 elements. Although they are reactive, the extra electron makes them less reactive than group 1 elements. The reactivity of these elements increases down the group. They are found in compounds, which form important rocks in the Earth's crust. This gives rise to the group's alternative name, the "alkaline earth" metals. The emerald (Be3(Al,Cr)2Si6O18) is the green variety of beryl (see Figure 13-02b), the mineral that is the principal source of beryllium.

Figure 13-02b Beryl

See more in Group 02 Elements.


8. Group 3 -12 are the transition elements, which are usually hard, tough and shiny. They are less reactive and have greater

   densities than group 1 or 2 elements. Group 11 includes the traditional coinage metals such as copper, silver, and gold (see Figure 13-02c). They are also known as the "noble metals". They are all relatively inert, hard-to-corrode metals which have been used for minting coins, hence their name. Many metals form coloured compounds, (e.g., iron pyrite), and many metals have a coloured sheen. These metals, especially silver, have unusual properties that make them essential for industrial applications outside of their monetary or decorative value. They are all excellent conductors of electricity. The most conductive of all metals are silver, copper and gold in that order. Silver is the most thermally conductive element, and is

   Figure 13-02c Gold

   also the most light reflecting element. Silver also has the unusual property that the tarnish on the surface is still highly electrically conductive.

   In Group 3 - 12, the Transition Metals fill up the 3d, 4d, 5d sub-shells (10 slots each), while the Lanthanides, Actinides fill up the 4f, 5f sub-shells (14 slots each) respectively. See more in Group 03-12 Elements, also "Atomic Emission Spectrum" for coverage of almost all groups, and "NIST, Atomic Spectra Dataabse" for more accurate information).
   
   
9. Group 13 elements are called light metals. Boron is a hard, brittle, non-metallic element. It is found in nature usually in combination with oxygen. The compound boric oxide is important in making heat-resistant glass. Boric acid is commonly used as eyewash and antiseptic. The compound borax (boron combined with oxygen, water, and sodium) is

useful as a cleaning agent and water softener. Aluminum, which is right beneath boron, is by its position a metalloid. But the properties of aluminum are usually those of metals. Aluminum is the most abundant metal and the third most abundant element in the earth's crust. Aluminum is found as aluminum oxide in the ore called bauxite. Aluminum is extremely valuable in industry (see Figure 13-02d). It is light, strong, and does not tarnish in air. It is a good conductor and is used in wiring, airplane parts, household items. The other members of the boron family ...gallium, indium, and thallium, are metals. Gallium shares many chemical properties with aluminum. It is an extremely soft metal that can be cut with a knife. It also has an extremely low melting point of 29.8oC. Gallium arsenide (GaAs) can

Figure 13-02d Aluminum

function as a "laser diode" and convert electricity directly into a beam of laser light.

See more in group 13 Elements.


10. Group 14 is the carbon family. It includes the elements carbon, silicon, germanium, tin, and lead. Carbon can combine with other elements in a great variety of ways - in millions of carbon compounds called "organic compounds", which form the basis for life. Carbon exists in its free state in several different forms. The most spectacular of these forms is diamond, the hardest of materials (see Figure 13-02e1). In the form of graphite, the carbon atoms arrange themselves in layer, like the pages of a book. Because the forces between them are not very strong, the layers slide easily over one another, making graphite soft and slippery. It is useful as a lubricant and as a writing material in pencils. Silicon is the second most abundant

		element in the earth's crust. Silicon is used in glass and in cement. Glass is produced by mixing silica (sand - SiO2), soda ash (sodium carbonate - Na2CO3) and limestone (calcium carbonate - CaCO3) in a ratio of 60:80:5 and heated to the melting point of 2500oF. The final product is a supercooled liquid called glass which can be made to be colourful or to have special property by adding impurities (see Figure 13-02e2). Silicon is also used in solar cells, which convert the energy of sunlight into electric energy. Germanium is a metalloid used in transistors, which are devices found in many electronic instruments, such as radios and televisions. Tin is a metal which
Figure 13-02e1 Carbon [view large image]	Figure 13-02e2 Glass	resists rusting and corrosion. The most dense element in the carbon family is the metal lead (Pb), which can form poisonous compounds.

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11. Group 15 is the nitrogen family. This group is sometimes referred to as pnictogens (choke generator in Greek as nitrogen was discovered in 1772 by demonstrating that it can asphyxiate a mouse). It consists of nitrogen, phosphorus, arsenic, antimony, and bismuth. Although a relatively unreactive gas, nitrogen forms hundreds of thousands of compounds that are of crucial importance for agriculture and industry. Considering the stability of nitrogen itself, some of these compounds are, ironically, extremely unstable and explosive. Despite the lack of reactivity of nitrogen, nature has developed several mechanisms (such as lightning) for converting nitrogen for use by living cells. The process of converting nitrogen from the atmosphere into usable nitrogen compounds is called nitrogen "fixing". Phosphorus (bearer of light in Greek) is a non-metal that glows in

dark and bursts into flames in warm air (see Figure 13-02f). It is used in the military to make incendiary bomb. Arsenic is a brittle, crystalline solid at room temperature. It is often thought of as a semi-metal, or metalloid. For example, it is a poor conductor of electricity, yet it has a steel-gray color. In the form of arsenious oxide, it is a well-known poison. It is used as a weed killer and insecticide. Arsenic has become a material of great importance in the world of solid-state electronics. Small amounts of arsenic are added to such semi-conductors as germanium and silicon to transform them into transistors.

Figure 13-02f Phosphorus

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12. Group 16 consists of the elements Oxygen (O), Sulfur (S), Selenium (Se), Tellurium (Te), and the radioactive Polonium (Po). Their compounds, particularly the sulfides, selenides and tellurides are collectively known as chalcogenides. The

name is generally considered to mean "ore former" (from the Greek chalcos "ore" and -gen "formation"). Oxygen and sulfur (see Figure 13-02g) are nonmetals, polonium is a true metal, and selenium and tellurium are metalloid semiconductors (i.e., their electrical properties are between those of a metal and an insulator). Nevertheless, tellurium, as well as selenium, is often referred to as a metal when in elemental form. Chalcogenides are quite common as minerals, e.g., FeS2 pyrite is an iron ore and AuTe2 gave its name to the gold rush town of Telluride, Colorado in the USA. The oxidation number of the chalcogen is generally -2 in a chalcogenide but other values (e.g. -1 in pyrite) can be attained. The highest oxidation number +6 is found in sulfates, selenates and tellurates, e.g., in Na2SeO4 - sodium selenate.

Figure 13-02g Sulfur

See more in group 16 Elements.


13. Group 17 elements are known as the halogens (salt creator). These elements are diatomic molecules in their natural form. They require one more electron to fill their outer electron shells, and so have a tendency to form a singly-charged negative ion. This negative ion is referred to as a halide ion, which tend to form ionic compounds with metals. Salts containing these ions are known as halides. Halogens form covalent compounds with non-metals. Examples include

    most carbon-containing, or organohalogen, molecules. Organohalogen chemicals (such as DDT, PCB, CFC, ...) are often believed to be solely industrial compounds, but many living organisms and geological phenomena also produce them naturally. In the case of plants and animls (such as sponges, corals, seaweeds, evergreen trees, some arthropods, and some frogs), the substance is produced for defence against predators and parasites. The halogens become less reactive, and their melting points increase further down the group. For example, fluorine is a yellow gas at room temperature, whereas bromine is a liquid, and iodine is a black solid (see Figure 13-02h).

    Figure 13-

    02h Iodine

    See more in group 17 Elements.
    
    

    Group 18 contains the noble or inert gases. Their outer electron shells are full, which makes it difficult for them to gain or lose electrons. They are therefore almost totally unreactive and non-flammable. The neon signs contain neon gas that glows in orange-red color (see Figure 13-02i) when it is energized by an electrical discharge. Every gas, when excited, radiates its own characteristic color. Argon, for example, produces a purple light, while xenon produces a blue-green light.

    Figure 13-02i Neon

    See more in group 18 Elements.
    
    

		The 21st century ushers in an era of handheld electronics and green machines. The new technologies use materials other than the traditional steel or gold. Suddenly some obscure metals appear on the scene (or laterally on the touchscreen). These elements used to be the by-products of smelting. Now they are the primary ores in short supplies as demand soared.
Figure 13-02j High-tech Elements [view large image]	Figure 13-02k Export Quota [view large image]	In 2010, the US Department of Energy compiled a list of 14 high-tech elements in danger of supply disruption for the green technology (Figure 13-02j).

One of the problems is the introduction of export quotas by China (Figure 13-02k), which currently mines over 90% of the supply of rare earth elements. The insert in Figure 13-02k shows the low-tech smelting of lanthanum in Inner Mongolia. In theory the shortfall could be covered by reopening some of those closed ores suspended over environmental concerns about radioactive contamination or toxicity. Another way is to recycle the used parts.

Figure 13-02l Recycling Electronic Junks

But the process would ruin the place and poison its inhabitants as shown in Figures 13-02l taken from a remote village in South-East China. Figure 13-02j also shows the special (and wonderful) properties of some high-tech elements.

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