Periodic table (Allotropes)

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Electrons exist as "clouds" of charge surrounding the positively charged nucleus. In the Bohr model each cloud is prevented from collapsing into the nucleus by its Clifford rotation. In reality only the 2 electrons of the lowermost cloud (*n* = 1) are supported in this way. All other clouds (*n* > 1) are resting on top the the ground shell; repelled from the ground shell by some sort of quantum force. The angular momentum of the electron = ħ.

The 1*n* shell consists of the **1s** orbital.

The 2*n* shell consists of the **2p** and **2s** orbitals.

The 3*n* shell consists of the **3d**, **3p** and **3s** orbitals.

The 4*n* shell consists of the **4f**, **4d**, **4p** and **4s** orbitals.

*n* + *ℓ* gives the order in which the orbitals are filled.

*n* + *ℓ* probably corresponds to the charge distribution of the electron.

*n* probably corresponds to the mass distribution of the electron.

The orbitals with the largest *n* correspond to the outer solid "surface" of the atom (where the valence electrons are located). The charge of the electrons can, and normally does, exist well outside of this solid "surface". (Not only are charge and mass not colocated but they do not need to share a common center either. In fact they can be separated quite far from each other. This is what makes fusion possible at such low temperatures found in the center of the sun.)

The **s** orbital (*ℓ* = 0) consists of only the **s** 1⁄2 orbital.

The **p** orbital (*ℓ* = 1) splits into **p** 1⁄2 and **p** 3⁄2.

The **d** orbital (*ℓ* = 2) splits into **d** 3⁄2 and **d** 5⁄2.

The **f** orbital (*ℓ* = 3) splits into **f** 5⁄2 and **f** 7⁄2.

This is known as the Fine structure.

**s** 1⁄2 and **p** 1⁄2 have almost the same "energy" level. (See Lamb shift)
**p** 3⁄2 and **d** 3⁄2 have the same "energy" level (ie. frequency).
**d** 5⁄2 and **f** 5⁄2 have the same "energy" level.

In the presence of a magnetic field each of the above levels splits into many separate "energy" levels.

This is called the Zeeman effect and it results in the Hyperfine structure.

In low magnetic fields (The left side of the image below) the Hyperfine structure corresponds to *mj*.

In high magnetic fields (The right side of the image below) electrons with opposite spins (*ms*) become separated and the Hyperfine structure corresponds to *mℓ*.

*mℓ* + *ms* = *mj*. See Spin–orbit coupling and Angular momentum coupling

Note the one electron that switches from one group to the other.

The radial quantum number *n**r* is equal to the number of nodes in the radial wavefunction.

*n**r* = *n* - *ℓ* - 1

Not all transitions between orbitals are allowed. See Selection rule.

Note: The atoms of a diamond cubic crystal are not all the same size. There are 2 different sizes. The large atoms form an fcc crystal and the smaller atoms occupy the large voids.

Chart below:

 Allotrope:Atomic Radius/Radius of ground shell
Crystal lattice

Vertical axis = *n* + *ℓ*
Background color indicates how far the crystal structure is from close packed. In other words, how distorted the lattice is.
Atomic radius is calculated from the Atomic volume.
Atomic volume is calculated by dividing the Atomic mass by the Density and multiplying by the Atomic packing factor.

ξ = c/(2a √8/√3)-1

Purge

## References

Data retrieved from \*http://wwwhomes.uni-bielefeld.de/achim/ele\_structures.html which lists as its references:

* http://cst-www.nrl.navy.mil/lattice/struk/atype.html
* http://www.chem.qmul.ac.uk/iupac/AtWt/
* http://www.chemistry.ohio-state.edu/~woodward/ch754/str\_cp.htm
* http://invsee.asu.edu/nmodules/carbonmod/crystalline.html
* http://www.siliconfareast.com/lattice\_constants.htm
* http://www.uni-konstanz.de/FuF/chemie/felsche/3D\_FEST/MET/BI.HTML
* http://www.uni-konstanz.de/FuF/chemie/felsche/3D\_FEST/NICHT/SE.HTML
* http://www.techniklexikon.net/d/antimon/antimon.htm
* http://www.platinummetalsreview.com/pdf/pmr-v33-i1-014-016.pdf

Platinum Metals Rev., 1989, V. 33, (1), p. 14-16 "Densities of Osmium and Iridium", By J. W. Arblaster
* http://www.francoiscardarelli.ca/PDF\_Files/MAH\_2E\_Sample\_Chapter\_Appendices\_Index.pdf
* http://www.nature.com/srep/2011/110919/srep00096/full/srep00096.html