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Periodic Table
Band Theory, Metal
Solid State
X-ray Diffraction
Specific Heats of Solids and Phonons
2-D Superconductivity
Josephson Junction and SQUID
Hall Effect (Classical and Quantum)

Periodic Table

In the mid 19th century, scientists were confronted with a mountain of seemingly unconnected chemical data - a situation similar to the particle physics in mid 20th century. In 1869 the Russian chemist Mendeleyev successfully organized the various chemical elements into a Periodic Table. Similar elements are arranged in vertical columns and the properties of the elements change
Periodic Table 1 Periodic Table 2 progressively across the row. The Periodic Table in Figure 13-01a is the modern version; while Figure 12-19 depicts the simpler one. The atomic number is the number of positive charges in the atomic nucleus. Atomic masses refer to the masses of neutral atoms, including the masses of the nucleus, the electrons and the mass equivalent of their binding energies. It is expressed in mass units such that the mass of the most abundant type of carbon is exactly 12.00 u (1 u = 1.66x10-24 gm).

Figure 13-01a Periodic Table,
Modern [view large image, 1 MB]

Figure 13-01b Periodic Table,
Unconventional [view large image]

Also see "Extension of the Periodic Table".

It was discovered later that not all of the atoms of a particular element have the same mass. The different varieties (different number of neutrons, same number of protons) of the same element are called its isotopes. The atomic masses now appear in the Periodic Table is the average atomic mass weighted by the abundance of each isotope. Unfortunately, the abundance depends on location where the sample is taken (ultimately depends on the process that created, transported or aggregated the material). The International Union of Pure and Applied Chemistry (IUPAC) has decided in 2011 to list atomic weight in lower and upper bounds, e.g., (1.00784;1.00811) for hydrogen. The affected elements include H, Li, B, C, S, and N. Elements with only one stable isotope such as F, Al, Na, Au and 17 others, are exempted from this ongoing change. And some highly radioactive elements exist too fleetingly for their atomic weights even to be defined.

Periodic Table, Comical 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. None of the elements are edible (as suggested in Figure 13-01c). They could be burning, toxic, poisonous,

Figure 13-01c Periodic Table, Comical [view large image]

radioactive or metallic (Figure 13-01d). Human consume mostly organic compounds such as proteins, carbohydrate, or fat. We also take in some inorganic compounds, e.g., the "Calcium, Magnesium, Zinc"
pills, which actually contain Calcium Carbonate (CaCO3), Magnesium Oxide (MgO), and Zinc Gluconate (C12H22O14Zn). Perhaps the table salt (NaCl) is the most favorite inorganic substance. Water (H2O) is very important, but tasteless.

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.

Zeeman Effects 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 13-01c1,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 with given (s, p, ...)

Figure 13-01c1 Zeeman Effects [view large image]

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 13-01c1,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 mj = +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 13-01c2,a shows the many causes that split the levels to the order of 5x10-5 ev and collectively called fine structures. The contributions include :
Hyperfine and Fine Structures
  1. The relativistic correction to the electron's kinetic energy.
  2. The Spin-Orbit correction.
  3. The "Darwin Term" correction by smearing out the electrostatic interaction between the electron and nucleus.
  4. The Anomalouus Zeeman effects of an external magnetic field.
  5. The Lamb Shift from vacuum fluctuation of virtual particles (courtesy of QED).

Figure 13-01c2 Fine and Hyperfine Structures [view large image]

Figure 13-01c2,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

Note: Small inserts in the 2nd column depict the corresponding atomic structures with the semi-classical view in term of orbital motion, and quantum view in term of probability density.
High-tech Elements Export Quota 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).
Electronic Junks 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 [view large image]

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.
On March 13 2012, the U.S., Japan and EU filed a WTO (World Trade Organization) complaint vs. China. They accuse China of hoarding the valuable minerals for its own use. The aim is to pressure China to lift export limits on rare earth minerals. But the Chinese government retorts that, the restrictions are motivated by environmental concerns (?).

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