Periodic table (Allotropes)

 See also: Template:Periodic_table and Atomic radius



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 1n shell consists of the 1s orbital.

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

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

The 4n 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.

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".



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.



It is actually the "normal" Zeeman effect that is Anomalous.

The "normal" Zeeman effect appears to be due to hybridization.



The radial quantum number nr is equal to the number of nodes in the radial wavefunction.
 * nr = 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:
 * 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.

metals]] earth metals]] ! style="vertical-align:middle; " | 8 ! style="vertical-align:middle; " | 7 ! style="vertical-align:middle; " | 7 ! style="vertical-align:middle; " | 6 Lanthanide (Rare-earth element) ! style="vertical-align:middle; " | 6 ! style="vertical-align:middle; " | 5 ! style="vertical-align:middle; " | 5 ! style="vertical-align:middle; " | 4 element]] metals]] Very high thermal conductivity boiling point ! style="vertical-align:middle; " | 4 ! style="vertical-align:middle; " | 3 ! style="vertical-align:middle; " | 3 ! style="vertical-align:middle; " | 2 Gases]] ! style="vertical-align:middle; " | 2 ! style="vertical-align:middle; " | 1 ! style="vertical-align:middle; " | 1
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 * colspan=14 | Actinide
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 * colspan=14 |
 * [[Wikipedia:Rare-earth element|Rare-earth
 * [[Wikipedia:Rare-earth element|Rare-earth
 * colspan=3 | Transition metals
 * colspan=3 | 18-electron rule
 * [[Wikipedia:Noble metal|Noble
 * [[Wikipedia:Noble metal|Noble
 * Very low
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 * colspan=10 rowspan=3 | Atomic radii.svg
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 * colspan=4 | Octet rule
 * Halogens
 * [[Wikipedia:Noble Gas|Noble
 * Halogens
 * [[Wikipedia:Noble Gas|Noble
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ξ = c/(2a √8/√3)-1