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  • Law of the Squares
  • Atomic Dumbbells
  • To the power of Rhombuses
  • Cwantum’s RhombicStars

Atomic Dumbbells

Electron Shells

Atomic electron shell study has the rule 2n².

This rule is listed for each element.


The first maximum shell is 2 Helium.

1 Hydrogen 1

2 Helium 2


The second maximum shell is 10 Neon.
3 Lithium 2,1
4 Beryllium 2,2
5 Boron 2,3
6 Carbon 2,4

7 Nitrogen 2,5

8 Oxygen 2,6

9 Fluorine 2,7

10 Neon 2,8


The third maximum shell is 18 Argon

11 Sodium 2,8,1
12 Magnesium 2,8,2 

13 Aluminium 2,8,3
14 Silicon 2,8,4
15 Phosphorus 2,8,5

16 Sulphur 2,8,6

17 Chlorine 2,8,7

18 Argon 2,8,8

Rule 2c²

Add a Nucleus and half the count.

Using brackets to indicate shells, adding a central nucleus and halving the electron shell count in whole numbers changes the presentation.


Representations of Electrons (E) can constructed as a Dumbbell.

By adding that central nucleus, Protons (Z) and Neutrons (N) can be included in notation.


The first maximum shell surrounding the nucleus is element 2 Helium.


1 Hydrogen 1. (E(Z:N)0)

2 Helium 2. (E(Z:N)E)

Protons, Neutrons and Electrons

A stable Atom has the same number of protons as electrons. The number of neutrons determine the isotope.


After looking at hydrogen‘s isotopes here, I will use the neutron count of the most abundant stable isotope.


1 Hydrogen 1. (1(1:N)0)


Changing the notation to include the type of electron orbital (spdf).

1 Hydrogen 1. (s(1:0)0)

                   Ion ((1:0))

          Protium (s(1:0)0) stable.

       Deuterium (s(1:1)0) stable.

            Tritium (s(1:2)0) radioactive.

Atomic docking ports

Hydrogen has a vacant docking port in its shell, to highlight that vacant docking port, the 0 electron in (s(1:0)0) is replaced by a hook, a question mark.

A right way up question mark on the left ?, and an upside down question mark ¿ on the right. (s(1:0)¿) or (?(1:0)s). This implies the electrons orbit the nucleus.


Vacant docking ports are replaced with question marks for higher elements.

Elements 1 to 10

1 Hydrogen 1. (s(1:0)¿) +s orbital. 

2 Helium 2. (s(2:2)s) +s full shell.


3 Lithium 2,1. (???s(s(3:4)s)¿¿¿¿) +s

4 Beryllium 2,2. (???s(s(4:5)s)s¿¿¿) +s

5 Boron 2,3. (??ps(s(5:6)s)s¿¿¿) +p

6 Carbon 2,4. (??ps(s(6:6)s)sp¿¿) +p

7 Nitrogen 2,5. (?pps(s(7:7)s)sp¿¿) +p

8 Oxygen 2,6. (?pps(s(8:8)s)spp¿) +p

9 Fluorine 2,7. (ppps(s(9:10)s)spp¿) +p

10 Neon 2,8. (ppps(s(10:10)s)sppp) +p full shell

Elements 11 to 18

11 Sodium 2,8,1 +s

(???s(4(1(11:12)1)4)¿¿¿¿) 

12 Magnesium 2,8,2 +s

(???s(4(1(12:12)1)4)s¿¿¿) 

13 Aluminium 2,8,3 +p

(??ps(4(1(13:14)1)4)s¿¿¿) 

14 Silicon 2,8,4 +p

(??ps(4(1(14:14)1)4)sp¿¿) 

15 Phosphorus 2,8,5 +p

(?pps(4(1(15:16)1)4)sp¿¿) 

16 Sulphur 2,8,6 +p

(?pps(4(1(16:16)1)4)spp¿)

17 Chlorine 2,8,7 +p

(ppps(4(1(17:18)1)4)spp¿)

18 Argon 2,8,8 +p full shell

(ppps(4(1(18:22)1)4)sppp)

Elements 19 to 36

19 Potassium 2,8,8,1 +s

(???s(ppps(4(1(19:20)1)4)sppp)¿¿¿¿)

20 Calcium 2,8,8,2 +s

(???s(ppps(4(1(20:20)1)4)sppp)s¿¿¿)

21 Scandium 2,8,9,2 +d

(???s(dppps(4(1(21:24)1)4)sppp)s¿¿¿)

22 Titanium 2,8,10,2 +d

(???s(dppps(4(1(22:26)1)4)spppd)s¿¿¿)

23 Vanadium 2,8,11,2 +d

(???s(ddppps(4(1(23:28)1)4)spppd)s¿¿¿)

24 Chromium 2,8,13,1 -s +2d

(???s(dddppps(4(1(24:28)1)4)spppdd)¿¿¿¿)

25 Manganese 2,8,13,2 +s

(???s(dddppps(4(1(25:30)1)4)spppdd)s¿¿¿)

26 Iron 2,8,14,2 +d

(???s(dddppps(4(1(26:30)1)4)spppddd)s¿¿¿)

27 Cobalt 2,8,15,2 +d

(???s(ddddppps(4(1(27:32)1)4)spppddd)s¿¿¿)

28 Nickel 2,8,16,2 +d

(???s(ddddppps(4(1(28:30)1)4)spppdddd)s¿¿¿)

29 Copper 2,8,18,1 -s +2d

(???s(dddddppps(4(1(29:34)1)4)spppddddd)¿¿¿¿)

30 Zinc 2,8,18,2 +s

(???s(9(4(1(30:34)1)4)9)s¿¿¿)

31 Gallium 2,8,18,3 +p

(??ps(9(4(1(31:38)1)4)9)s¿¿¿)

32 Germanium 2,8,18,4 +p

(??ps(9(4(1(32:42)1)4)9)sp¿¿)

33 Arsenic 2,8,18,5 +p

(?pps(9(4(1(33:42)1)4)9)sp¿¿)

34 Selenium 2,8,18,6 +p

(?pps(9(4(1(34:46)1)4)9)spp¿)

35 Bromine 2,8,18,7 +p

(ppps(9(4(1(35:44)1)4)9)spp¿)

36 Krypton 2,8,18,8 +p full shell

(ppps(9(4(1(36:48)1)4)9)sppp)

Elements 37 to 54

37 Rubidium 2,8,18,8,1 +s

(???s(ppps(9(4(1(37:48)1)4)9)sppp)¿¿¿¿)

38 Strontium 2,8,18,8,2 +s

(???s(ppps(9(4(1(38:50)1)4)9)sppp)s¿¿¿)

39 Yttrium 2,8,18,9,2 +d

(???s(dppps(9(4(1(39:50)1)4)9)sppp)s¿¿¿)

40 Zirconium 2,8,18,10,2 +d

(???s(dppps(9(4(1(40:50)1)4)9)spppd)s¿¿¿)

41 Niobium 2,8,18,12,1 -s +2d

(???s(ddppps(9(4(1(41:52)1)4)9)spppdd)¿¿¿¿)

42 Molybdenum 2,8,18,13,1 +d

(???s(dddppps(9(4(1(42:56)1)4)9)spppdd)¿¿¿¿)

43 Technetium 2,8,18,13,2 +s

(???s(dddppps(9(4(1(43:55)1)4)9)spppdd)s¿¿¿)

44 Ruthenium 2,8,18,15,1 -s +2d

(???s(ddddppps(9(4(1(44:58)1)4)9)spppddd)¿¿¿¿)

45 Rhodium 2,8,18,16,1 +d

(???s(ddddppps(9(4(1(45:58)1)4)9)spppdddd)¿¿¿¿)

46 Palladium 2,8,18,18 -s +2d

(dddddppps(9(4(1(46:60)1)4)9)spppddddd)

47 Silver 2,8,18,18,1 +s

(???s(9(9(4(1(47:60)1)4)9)9)¿¿¿¿)

48 Cadmium 2,8,18,18,2 +s

(???s(9(9(4(1(48:66)1)4)9)9)s¿¿¿)

49 Indium 2,8,18,18,3 +p

(??ps(9(9(4(1(49:66)1)4)9)9)s¿¿¿)

50 Tin 2,8,18,18,4 +p

(??ps(9(9(4(1(50:70)1)4)9)9)sp¿¿)

51 Antimony 2,8,18,18,5 +p

(?pps(9(9(4(1(51:70)1)4)9)9)sp¿¿)

52 Tellurium 2,8,18,18,6 +p

(?pps(9(9(4(1(52:78)1)4)9)9)spp¿)

53 Iodine 2,8,18,18,7 +p

(ppps(9(9(4(1(53:74)1)4)9)9)spp¿)

54 Xenon 2,8,18,18,8 +p full shell

(ppps(9(9(4(1(54:78)1)4)9)9)sppp)

Elements 55 to 86

55 Caesium 2,8,18,18,8,1 +s

(???s(ppps(dddddppps(9(4(1(55:78)1)4)9)spppddddd)sppp)¿¿¿¿)

56 Barium 2,8,18,18,8,2 +s

(???s(ppps(dddddppps(9(4(1(56:82)1)4)9)spppddddd)sppp)s¿¿¿)

57 Lanthanum 2,8,18,18,9,2 +d

(???s(dppps(dddddppps(9(4(1(57:82)1)4)9)spppddddd)sppp)s¿¿¿)

58 Cerium 2,8,18,19,9,2 +f

(???s(dppps(fdddddppps(9(4(1(58:82)1)4)9)spppddddd)sppp)s¿¿¿)

59 Praseodymium: 2,8, 18,21,8,2 -d +2f

(???s(ppps(ffdddddppps(9(4(1(59:82)1)4)9)spppdddddf)sppp)s¿¿¿)

60 Neodymium: 2,8,18,22,8,2 +f

(???s(ppps(ffdddddppps(9(4(1(60:82)1)4)9)spppdddddff)sppp)s¿¿¿)

61 Promethium: 2,8,18,23,8,2 +f

(???s(ppps(fffdddddppps(9(4(1(61:84)1)4)9)spppdddddff)sppp)s¿¿¿)

62 Samarium: 2,8,18,24,8,2 +f

(???s(ppps(fffdddddppps(9(4(1(62:90)1)4)9)spppdddddfff)sppp)s¿¿¿)

63 Europium 2,8,18,25,8,2 +f

(???s(ppps(ffffdddddppps(9(4(1(63:90)1)4)9)spppdddddfff)sppp)s¿¿¿)

64 Gadolinium 2,8,18,25,9,2 +d

(???s(dppps(ffffdddddppps(9(4(1(64:94)1)4)9)spppdddddfff)sppp)s¿¿¿)

65 Terbium 2,8,18,27,8,2 -d +2f

(???s(ppps(fffffdddddppps(9(4(1(65:94)1)4)9)spppdddddffff)sppp)s¿¿¿)

66 Dysprosium 2,8,18,28,8,2 +f

(???s(ppps(fffffdddddppps(9(4(1(66:98)1)4)9)spppdddddfffff)sppp)s¿¿¿)

67 Holmium (Ho): 2,8,18,29,8,2 +f

(???s(ppps(ffffffdddddppps(9(4(1(67:98)1)4)9)spppdddddfffff)sppp)s¿¿¿)

68 Erbium (Er): 2,8,18,30,8,2 +f

(???s(ppps(ffffffdddddppps(9(4(1(68:98)1)4)9)spppdddddffffff)sppp)s¿¿¿)

69 Thulium (Tm): 2,8,18,31,8,2 +f

(???s(ppps(fffffffdddddppps(9(4(1(69:100)1)4)9)spppdddddffffff)sppp)s¿¿¿)

70 Ytterbium (Yb): 2,8,18,32,8,2 +f

(???s(ppps(fffffffdddddppps(9(4(1(70:104)1)4)9)spppdddddfffffff)sppp)s¿¿¿)

71 Lutetium (Lu): 2,8,18,32,9,2 +d

(???s(dppps(16(9(4(1(71:104)1)4)9)16)sppp)s¿¿¿)

72 Hafnium 2,8,18,32,10,2 +d

(???s(dppps(16(9(4(1(72:108)1)4)9)16)spppd)s¿¿¿)

73 Tantalum 2,8,18,32,11,2 +d

(???s(ddppps(16(9(4(1(73:108)1)4)9)16)spppd)s¿¿¿)

74 Tungsten 2,8,18,32,12,2 +d

(???s(ddppps(16(9(4(1(74:110)1)4)9)16)spppdd)s¿¿¿)

75 Rhenium 2,8,18,32,13,2 +d

(???s(dddppps(16(9(4(1(75:112)1)4)9)16)spppdd)s¿¿¿)

76 Osmium (Os) 2,8,18,32,14,2 +d

(???s(dddppps(16(9(4(1(76:116)1)4)9)16)spppddd)s¿¿¿)

77 Iridium (Ir) : 2,8,18,32,15,2 +d

(???s(ddddppps(16(9(4(1(77:116)1)4)9)16)spppddd)s¿¿¿)

78 Platinum (Pt) 2,8,18,32,17,1 -s +2d

(???s(dddddppps(16(9(4(1(78:117)1)4)9)16)spppdddd)¿¿¿¿)

79 Gold (Au) 2,8,18,32,18,1  +d

(???s(dddddppps(16(9(4(1(79:118)1)4)9)16)spppddddd)¿¿¿¿)

80 Mercury 2,8,18,32,18,2 +s

(???s(9(16(9(4(1(80:122)1)4)9)16)9)s¿¿¿)

81 Thallium (Tl) 2,8,18,32,18,3 +p

(??ps(9(16(9(4(1(81:124)1)4)9)16)9)s¿¿¿)

82 Lead 2,8,18,32,18,4 +p

(??ps(9(16(9(4(1(82:126)1)4)9)16)9)sp¿¿)

83 Bismuth (Bi) 2,8,18,32,18,5 +p

(?pps(9(16(9(4(1(83:126)1)4)9)16)9)sp¿¿)

84 Polonium (Po) 2,8,18,32,18,6 +p

(?pps(9(16(9(4(1(84:125)1)4)9)16)9)spp¿)

85 Astatine (At) 2,8,18,32,18,7 +p

(ppps(9(16(9(4(1(85:125)1)4)9)16)9)spp¿)

86 Radon 2,8,18,32,18,8 +p

(ppps(9(16(9(4(1(86:136)1)4)9)16)9)sppp)

Elements 87 to 118

87 Francium 2,8,18,32,18,8,1 +s

(???s(ppps(dddddppps(16(9(4(1(87:136)1)4)9)16)spppddddd)sppp)¿¿¿¿)

88 Radium 2,8,18,32,18,8,2 +s

(???s(ppps(dddddppps(16(9(4(1(88:138)1)4)9)16)spppddddd)sppp)s¿¿¿)

89 Actinium 2,8,18,32,18,9,2 +d

(???s(dppps(dddddppps(16(9(4(1(89:138)1)4)9)16)spppddddd)sppp)s¿¿¿)

90 Thorium (Th) 2,8,18,32,18,10,2 +d

(???s(dppps(dddddppps(16(9(4(1(90:142)1)4)9)16)spppddddd)spppd)s¿¿¿)

91 Protactinium 2,8,18,32,20,9,2 -d +2f

(???s(dppps(fdddddppps(16(9(4(1(91:150)1)4)9)16)spppdddddf)sppp)s¿¿¿)

92 Uranium (U) 2,8,18,32,21,9,2 +f

(???s(dppps(ffdddddppps(16(9(4(1(92:146)1)4)9)16)spppdddddf)sppp)s¿¿¿)

93 Neptunium (Np) 2,8,18,32,22,9,2 +f

(???s(dppps(ffdddddppps(16(9(4(1(93:144)1)4)9)16)spppdddddff)sppp)s¿¿¿)

94 Plutonium (Pu) 2,8,18,32,24,8,2 -d +2f

(???s(ppps(fffdddddppps(16(9(4(1(94:150)1)4)9)16)spppdddddfff)sppp)s¿¿¿)

95 Americium 2,8,18,32,25,8,2 +f

(???s(ppps(ffffdddddppps(16(9(4(1(95:148)1)4)9)16)spppdddddfff)sppp)s¿¿¿)

96 Curium 2,8,18,32,25,9,2 +d

(???s(dppps(ffffdddddppps(16(9(4(1(96:151)1)4)9)16)spppdddddfff)sppp)s¿¿¿)

97 Berkelium (Bk) 2,8,18,32,27,8,2 -d +2f

(???s(ppps(fffffdddddppps(16(9(4(1(97:150)1)4)9)16)spppdddddffff)sppp)s¿¿¿)

98 Californium (Cf) 2,8,18,32,28,8,2 +f

(???s(ppps(fffffdddddppps(16(9(4(1(98:153)1)4)9)16)spppdddddfffff)sppp)s¿¿¿)

99 Einsteinium (Es) 2,8,18,32,29,8,2 +f

(???s(ppps(ffffffdddddppps(16(9(4(1(99:153)1)4)9)16)spppdddddfffff)sppp)s¿¿¿)

100 Fermium (Fm) 2,8,18,32,30,8,2 +f

(???s(ppps(ffffffdddddppps(16(9(4(1(100:157)1)4)9)16)spppdddddffffff)sppp)s¿¿¿)

101 Mendelevium (Md) 2,8,18,32,31,8,2 +f

(???s(ppps(fffffffdddddppps(16(9(4(1(101:157)1)4)9)16)spppdddddffffff)sppp)s¿¿¿)

102 Nobelium (No) 2,8,18,32,32,8,2 +f

(???s(ppps(fffffffdddddppps(16(9(4(1(102:157)1)4)9)16)spppdddddfffffff)sppp)s¿¿¿)

103 Lawrencium (Lr) 2,8,18,32,32,9,2 +d

(???s(dppps(16(16(9(4(1(103:163)1)4)9)16)16)sppp)s¿¿¿)

104 Rutherfordium (Rf) 2,8,18,32,32,10,2 +d

(???s(dppps(16(16(9(4(1(104:157)1)4)9)16)16)spppd)s¿¿¿)

105 Dubnium (Db) 2,8,18,32,32,11,2 +d

(???s(ddppps(16(16(9(4(1(105:163)1)4)9)16)16)spppd)s¿¿¿)

106 Seaborgium (Sg) 2,8,18,32,32,12,2 +d

(???s(ddppps(16(16(9(4(1(106:163)1)4)9)16)16)spppdd)s¿¿¿)

107 Bohrium (Bh) 2,8,18,32,32,13,2 +d

(???s(dddppps(16(16(9(4(1(107:163)1)4)9)16)16)spppdd)s¿¿¿)

108 Hassium (Hs) 2,8,18,32,32,14,2 +d

(???s(dddppps(16(16(9(4(1(108:169)1)4)9)16)16)spppddd)s¿¿¿)

109 Meitnerium (Mt) 2,8,18,32,32,15,2 +d

(???s(ddddppps(16(16(9(4(1(109:169)1)4)9)16)16)spppddd)s¿¿¿)

110 Darmstadtium (Ds) 2,8,18,32,32,16,2 +d

(???s(ddddppps(16(16(9(4(1(110:171)1)4)9)16)16)spppdddd)s¿¿¿)

111 Roentgenium (Rg) 2,8,18,32,32,17,2 +d

(???s(dddddppps(16(16(9(4(1(111:171)1)4)9)16)16)spppdddd)s¿¿¿)

112 Copernicium (Cn), 2,8,18,32,32,18,2 +d

(???s(dddddppps(16(16(9(4(1(112:173)1)4)9)16)16)spppddddd)s¿¿¿)

113 Nihonium (Nh) 2,8,18,32,32,18,3 +p

(??ps(9(16(16(9(4(1(113:173)1)4)9)16)16)9)s¿¿¿)

114 Flerovium (Fl) 2,8,18,32,32,18,4 +p

(??ps(9(16(16(9(4(1(114:175)1)4)9)16)16)9)sp¿¿)

115 Moscovium (Mc) 2,8,18,32,32,18,5 +p

(?pps(9(16(16(9(4(1(115:175)1)4)9)16)16)9)sp¿¿)

116 Livermorium (Lv) 2,8,18,32,32,18,6 +p

(?pps(9(16(16(9(4(1(116:177)1)4)9)16)16)9)spp¿)

117 Tennessine (Ts) 2,8,18,32,32,18,7 +p

(ppps(9(16(16(9(4(1(117:177)1)4)9)16)16)9)spp¿)

118 Oganesson (Og) 2,8,18,32,32,18,8 +p

(ppps(9(16(16(9(4(1(118:176)1)4)9)16)16)9)sppp)

Summary of Full Electron Shells

                                  (1²(0²)1²)

                              (2²(1²(0²)1²)2²)

                          (2²(2²(1²(0²)1²)2²)2²)

                      (2²(3²(2²(1²(0²)1²)2²)3²)2²)

                  (2²(3²(3²(2²(1²(0²)1²)2²)3²)3²)2²)

              (2²(3²(4²(3²(2²(1²(0²)1²)2²)3²)4²)3²)2²)

         (2²(3²(4²(4²(3²(2²(1²(0²)1²)2²)3²)4²)4²)3²)2²)

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