Atomic radius

See also:

Template:Periodic table (Allotropes)

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#bottom
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 m_j.
In high magnetic fields (The right side of the image below) electrons with opposite spins (m_s) become separated and the Hyperfine structure corresponds to m_ℓ.
m_ℓ + m_s = m_j. 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 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:

Atomic Number Element symbol Atomic mass Allotrope:Atomic Radius Crystal lattice Atomic packing factor

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.

																											Acceptor (P-type)	Semi- conductor	Donor (N-type)	Note that due to sp3 hybridization the  end wraps back around to the beginning ↘
Strong magnetic field																											-1⁄2	-3⁄2	-3⁄2	-1⁄2	1⁄2	3⁄2		3⁄2	1⁄2	mℓ
						"normal" Zeeman effect → sp3 hybridization? →																					-1⁄2	-1⁄2	1⁄2	1⁄2	1⁄2	1⁄2		-1⁄2	-1⁄2	ms
	Weak magnetic field																										-1	-2	-1	0	1	2		1	0	mj
	mℓ + ms = mj					Note the one electron that switches from orange to yellow
ℓ	3						↓									2											1							0		ℓ
mℓ	3	2	1	0	-1	-2	-3	-3	-2	-1	0	1	2	3		2	1	0	-1	-2	-2	-1	0	1	2		1	0	-1	-1	0	1		0	0	mℓ
ms	-1⁄2	-1⁄2	-1⁄2	-1⁄2	-1⁄2	-1⁄2	-1⁄2	1⁄2	1⁄2	1⁄2	1⁄2	1⁄2	1⁄2	1⁄2		-1⁄2	-1⁄2	-1⁄2	-1⁄2	-1⁄2	1⁄2	1⁄2	1⁄2	1⁄2	1⁄2		-1⁄2	-1⁄2	-1⁄2	1⁄2	1⁄2	1⁄2		-1⁄2	1⁄2	ms
mj	5⁄2	3⁄2	1⁄2	-1⁄2	-3⁄2	-5⁄2	-7⁄2	-5⁄2	-3⁄2	-1⁄2	1⁄2	3⁄2	5⁄2	7⁄2		3⁄2	1⁄2	-1⁄2	-3⁄2	-5⁄2	-3⁄2	-1⁄2	1⁄2	3⁄2	5⁄2		1⁄2	-1⁄2	-3⁄2	-1⁄2	1⁄2	3⁄2		-1⁄2	1⁄2	mj
J	5⁄2						7⁄2									3⁄2				5⁄2							1⁄2		3⁄2					1⁄2		J
	f 5⁄2						f 7⁄2									d 3⁄2				d 5⁄2							p 1⁄2		p 3⁄2					s 1⁄2
	1	2	3	4	5	6	7	8	9	10	11	12	13	14		1	2	3	4	5	6	7	8	9	10		1	2	3	4	5	6		1	2
8	89 Ac 227.0278 1.8829 Å fc-c 0.74	90 Th 232.0377 α:1.8027 Å fc-c 0.74 β:1.7848 Å bc-c 0.68	91 Pa 231.0359 α:1.6112 Å bc-t(0.82) 0.696	92 U 238.0289 α:1.1358 Å bc-ortho 0.293 β:1.4457 Å unknown 0.547 γ:1.5304 Å bc-c 0.68	93 Np 237.0482 α:1.4918 Å bc-ortho 0.717 β:1.3882 Å unknown 0.547 γ:1.5278 Å bc-c 0.68	94 Pu 244.0642 α:0.9662 Å mono(102°) 0.183 β:1.3733 Å ec-mono 0.47 γ:1.5951 Å fc-ortho 0.357 δ:1.6556 Å fc-c 0.74 δ':1.6366 Å bc-t(1.33) 0.72 ε:1.59 Å bc-c 0.68	95 Am 243 α:1.7393 Å dh-cp 0.74	96 Cm 247 α:1.7409 Å dh-cp 0.74 β:1.7464 Å fc-c 0.74	97 Bk 247 α:1.7037 Å dh-cp 0.74	98 Cf 251 α:1.7014 Å dh-cp 0.74	99 Es 252 2.036 Å fc-c 0.74	100 Fm 257	101 Md 258	102 No 259		103 Lr 266	104 Rf 267	105 Db 268	106 Sg 269	107 Bh 270	108 Hs 277	109 Mt 278	110 Ds 281	111 Rg 282	112 Cn 285		113 Nh 286	114 Fl 289	115 Mc 290	116 Lv 293	117 Ts 294	118 Og 294		Alkali metals	Alkaline earth metals	8
7	57 La 138.9055 α:1.8824 Å dh-cp 0.74	58 Ce 140.116 β:1.8373 Å dh-cp 0.74 γ:1.8296 Å fc-c 0.74	59 Pr 140.9077 α:1.8331 Å dh-cp 0.74	60 Nd 144.242 α:1.8266 Å dh-cp 0.74	61 Pm 144.9128 α:1.8164 Å dh-cp 0.74	62 Sm 150.36 α:1.8075 Å tri-cp 0.74	63 Eu 151.964 1.9893 Å bc-c 0.68	64 Gd 157.25 1.8072 Å h-cp 0.74	65 Tb 158.9254 1.7863 Å h-cp 0.74	66 Dy 162.5 1.7795 Å h-cp 0.74	67 Ho 164.9303 1.7704 Å h-cp 0.74	68 Er 167.259 1.7613 Å h-cp 0.74	69 Tm 168.9342 1.7508 Å h-cp 0.74	70 Yb 173.054 1.9467 Å fc-c 0.74		71 Lu 174.9668 1.7391 Å h-cp 0.74	72 Hf 178.49 1.5854 Å h-cp 0.74	73 Ta 180.9479 1.4342 Å bc-c 0.68	74 W 183.84 1.3744 Å bc-c 0.68	75 Re 186.207 1.3789 Å h-cp 0.74	76 Os 190.23 1.3561 Å h-cp 0.74	77 Ir 192.217 1.3613 Å fc-c 0.74	78 Pt 195.084 1.3912 Å fc-c 0.74	79 Au 196.9666 1.446 Å fc-c 0.74	80 Hg 200.592 α:1.5118 Å rhomb(71°) 0.608		81 Tl 204.3835 1.7209 Å h-cp 0.74	82 Pb 207.2 1.7552 Å fc-c 0.74	83 Bi 208.9804 1.8107 Å rhomb(57°) 0.696	84 Po 208.9824 α:2.382 Å fcc+alv 0.74	85 At 209.9871 2.1393 Å fc-c 0.74	86 Rn 222.0176 2.4629 Å fc-c 0.74		87 Fr 223.0197	88 Ra 226.0254 2.2356 Å bc-c 0.68	7
6	Actinide Lanthanide (Rare-earth element)															39 Y 88.9058 1.8056 Å h-cp 0.74	40 Zr 91.224 1.6071 Å h-cp 0.74	41 Nb 92.9064 1.4332 Å bc-c 0.68	42 Mo 95.95 1.3666 Å bc-c 0.68	43 Tc 97.9072 1.3637 Å h-cp 0.74	44 Ru 101.07 1.3425 Å h-cp 0.74	45 Rh 102.9055 1.3486 Å fc-c 0.74	46 Pd 106.42 1.3794 Å fc-c 0.74	47 Ag 107.8682 1.4487 Å fc-c 0.74	48 Cd 112.414 1.567 Å h-cp 0.74		49 In 114.818 1.4527 Å fc-t(1.52) 0.487	50 Sn 118.71 α:2.3009 Å d-c 0.74 β:1.5951 Å fc-t(0.55) 0.623	51 Sb 121.76 1.7147 Å rhomb(57°) 0.695	52 Te 127.6 1.627 Å rhomb(87°) 0.526	53 I 126.9045 2.1828 Å fc-ortho 0.507	54 Xe 131.293 2.3641 Å fc-c 0.74		55 Cs 132.9055 2.6667 Å bc-c 0.68	56 Ba 137.327 2.1796 Å bc-c 0.68	6
5																21 Sc 44.9559 1.6458 Å h-cp 0.74	22 Ti 47.867 1.4655 Å h-cp 0.74	23 V 50.9415 1.3128 Å bc-c 0.68	24 Cr 51.9961 1.2527 Å bc-c 0.68	25 Mn 54.938 α:1.2598 Å bc-c 0.68 β:1.2728 Å bc-c 0.68 γ:1.3695 Å fc-c 0.74 δ:1.338 Å bc-c 0.68	26 Fe 55.845 1.2448 Å bc-c 0.68	27 Co 58.9332 1.2546 Å h-cp 0.74	28 Ni 58.6934 1.2495 Å fc-c 0.74	29 Cu 63.546 1.2817 Å fc-c 0.74	30 Zn 65.38 1.3946 Å h-cp 0.74		31 Ga 69.723 α:1.6034 Å fc-ortho 0.437	32 Ge 72.63 2.0061 Å d-c 0.74	33 As 74.9216 α:1.4974 Å rhomb(54°) 0.647	34 Se 78.971 grey:1.5111 Å rhomb(93°) 0.526	35 Br 79.904 2.0245 Å fc-ortho 0.526	36 Kr 83.798 2.1745 Å fc-c 0.74		37 Rb 85.4678 2.4774 Å bc-c 0.68	38 Sr 87.62 2.1576 Å fc-c 0.74	5
4																Rare-earth element		Transition metals			18-electron rule			Noble metals Very high thermal conductivity	Very low boiling point		13 Al 26.9816 1.4358 Å fc-c 0.74	14 Si 28.085 1.9257 Å d-c 0.74	15 P 30.9738 α:1.6482 Å bc-c 0.68 β:0.9524 Å triclinic 0.138 γ:1.5067 Å unknown 0.547 black:1.3763 Å fc-ortho 0.285 red:1.0477 Å mono(106°) 0.219	16 S 32.0675 α:1.6502 Å fc-ortho 0.362 β:1.5014 Å mono(93°) 0.477	17 Cl 35.4515 1.9767 Å fc-ortho 0.518	18 Ar 39.948 2.0389 Å fc-c 0.74		19 K 39.0983 2.3137 Å bc-c 0.68	20 Ca 40.078 1.9815 Å fc-c 0.74	4
3																											5 B 10.8135 α:1.0747 Å rhomb(58°) 0.708 β:1.071 Å rhomb(65°) 0.665	6 C 12.0106 Di:1.2647 Å d-c 0.74 Gr:0.7125 Å graphite 0.256	7 N 14.0069 1.725 Å h-cp 0.74	8 O 15.9994 2.025 Å fcc+alv 0.74	9 F 18.9984 1.9553 Å fcc+alv 0.74	10 Ne 20.1797 1.7043 Å fc-c 0.74		11 Na 22.9898 1.8632 Å bc-c 0.68	12 Mg 24.3055 1.6062 Å h-cp 0.74	3
2																											Octet rule				Halogens	Noble Gases		3 Li 6.9675 1.5259 Å bc-c 0.68	4 Be 9.0122 1.1306 Å h-cp 0.74	2
1																																		1 H2 1.008 1.9002 Å h-cp 0.74	2 He 4.0026 1.8506 Å h-cp 0.74	1

ξ = c/(2a √8/√3)-1

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