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Electron shell

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Electron shell

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This article is about the orbits of electrons. For valence shell, see Valence electron.
“Atomic shell” redirects here. For the weapon, see Nuclear artillery.

In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom’s nucleus. The closest shell to the nucleus is called the “1 shell” (also called the “K shell”), followed by the “2 shell” (or “L shell”), then the “3 shell” (or “M shell”), and so on farther and farther from the nucleus. The shells correspond to the principal quantum numbers (n = 1, 2, 3, 4 …) or are labeled alphabetically with the letters used in X-ray notation (K, L, M, …).

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2) electrons.[1] For an explanation of why electrons exist in these shells see electron configuration.[2]

Each shell consists of one or more subshells, and each subshell consists of one or more atomic orbitals.

History

The shell terminology comes from Arnold Sommerfeld’s modification of the Bohr model. Sommerfeld retained Bohr’s planetary model, but added mildly elliptical orbits (characterized by additional quantum numbers ℓ and m) to explain the fine spectroscopic structure of some elements.[3] The multiple electrons with the same principal quantum number (n) had close orbits that formed a “shell” of positive thickness instead of the infinitely thin circular orbit of Bohr’s model.

The existence of electron shells was first observed experimentally in Charles Barkla’s and Henry Moseley’s X-ray absorption studies. Barkla labeled them with the letters K, L, M, N, O, P, and Q.[4] The origin of this terminology was alphabetic. A “J” series was also suspected, though later experiments indicated that the K absorption lines are produced by the innermost electrons. These letters were later found to correspond to the n values 1, 2, 3, etc. They are used in the spectroscopic Siegbahn notation.

Subshells

3D views of some hydrogen-like atomic orbitals showing probability density and phase (g orbitals and higher are not shown).

Each shell is composed of one or more subshells, which are themselves composed of atomic orbitals. For example, the first (K) shell has one subshell, called 1s; the second (L) shell has two subshells, called 2s and 2p; the third shell has 3s, 3p, and 3d; the fourth shell has 4s, 4p, 4d and 4f; the fifth shell has 5s, 5p, 5d, and 5f and can theoretically hold more in the 5g subshell that is not occupied in the ground-state electron configuration of any known element.[2] The various possible subshells are shown in the following table:

Subshell label

Max electrons
Shells containing it
Historical name
s
0
2
Every shell
 sharp
p
1
6
2nd shell and higher
 principal
d
2
10
3rd shell and higher
 diffuse
f
3
14
4th shell and higher
 fundamental
g
4
18
5th shell and higher (theoretically)
(next in alphabet after f)[5]The first column is the “subshell label”, a lowercase-letter label for the type of subshell. For example, the “4s subshell” is a subshell of the fourth (N) shell, with the type (s) described in the first row.
The second column is the azimuthal quantum number (ℓ) of the subshell. The precise definition involves quantum mechanics, but it is a number that characterizes the subshell.
The third column is the maximum number of electrons that can be put into a subshell of that type. For example, the top row says that each s-type subshell (1s, 2s, etc.) can have at most two electrons in it. In each case the figure is 4 greater than the one above it.
The fourth column says which shells have a subshell of that type. For example, looking at the top two rows, every shell has an s subshell, while only the second shell and higher have a p subshell (i.e., there is no “1p” subshell).
The final column gives the historical origin of the labels s, p, d, and f. They come from early studies of atomic spectral lines. The other labels, namely g, h and i, are an alphabetic continuation following the last historically originated label of f.

Number of electrons in each shell

Each subshell is constrained to hold 4ℓ + 2 electrons at most, namely:

Each s subshell holds at most 2 electrons
Each p subshell holds at most 6 electrons
Each d subshell holds at most 10 electrons
Each f subshell holds at most 14 electrons
Each g subshell holds at most 18 electrons

Therefore, the K shell, which contains only an s subshell, can hold up to 2 electrons; the L shell, which contains an s and a p, can hold up to 2 + 6 = 8 electrons, and so forth; in general, the nth shell can hold up to 2n2 electrons.[1]

Shellname
Subshellname
Subshellmaxelectrons
Shellmaxelectrons
K
1s
2
2
L
2s
2
2 + 6 = 8
2p
6
M
3s
2
2 + 6 + 10= 18
3p
6
3d
10
N
4s
2
2 + 6 + 10 + 14= 32
4p
6
4d
10
4f
14
O
5s
2
2 + 6 + 10 + 14 + 18 = 50
5p
6
5d
10
5f
14
5g
18

Although that formula gives the maximum in principle, in fact that maximum is only achieved (by known elements) for the first four shells (K, L, M, N). No known element has more than 32 electrons in any one shell.[6][7] This is because the subshells are filled according to the Aufbau principle. The first elements to have more than 32 electrons in one shell would belong to the g-block of period 8 of the periodic table. These elements would have some electrons in their 5g subshell and thus have more than 32 electrons in the O shell (fifth principal shell).

Subshell energies and filling order

Further information: Aufbau principle
For multielectron atoms n is a poor indicator of electron’s energy. Energy spectra of some shells interleave.
The states crossed by same red arrow have same n+ℓ{\displaystyle n+\ell } value. The direction of the red arrow indicates the order of state filling.

Although it is sometimes stated that all the electrons in a shell have the same energy, this is an approximation. However, the electrons in one subshell do have exactly the same level of energy, with later subshells having more energy per electron than earlier ones. This effect is great enough that the energy ranges associated with shells can overlap.

The filling of the shells and subshells with electrons proceeds from subshells of lower energy to subshells of higher energy. This follows the n + ℓ rule which is also commonly known as the Madelung rule. Subshells with a lower n + ℓ value are filled before those with higher n + ℓ values. In the case of equal n + ℓ values, the subshell with a lower n value is filled first.

List of elements with electrons per shell

The list below gives the elements arranged by increasing atomic number and shows the number of electrons per shell. At a glance, the subsets of the list show obvious patterns. In particular, every set of five elements (in

  electric blue) before each noble gas (group 18, in   yellow) heavier than helium have successive numbers of electrons in the outermost shell, namely three to seven.

Sorting the table by chemical group shows additional patterns, especially with respect to the last two outermost shells. (Elements 57 to 71 belong to the lanthanides, while 89 to 103 are the actinides.)

The list below is primarily consistent with the Aufbau principle. However, there are a number of exceptions to the rule; for example palladium (atomic number 46) has no electrons in the fifth shell, unlike other atoms with lower atomic number. Some entries in the table are uncertain, when experimental data is unavailable. (For example, the elements past 108 have such short half-lives that their electron configurations have not yet been measured.)

Z
Element
No. of electrons/shell
Group
1
Hydrogen
1
1
2
Helium
2
18
3
Lithium
2, 1
1
4
Beryllium
2, 2
2
5
Boron
2, 3
13
6
Carbon
2, 4
14
7
Nitrogen
2, 5
15
8
Oxygen
2, 6
16
9
Fluorine
2, 7
17
10
Neon
2, 8
18
11
Sodium
2, 8, 1
1
12
Magnesium
2, 8, 2
2
13
Aluminium
2, 8, 3
13
14
Silicon
2, 8, 4
14
15
Phosphorus
2, 8, 5
15
16
Sulfur
2, 8, 6
16
17
Chlorine
2, 8, 7
17
18
Argon
2, 8, 8
18
19
Potassium
2, 8, 8, 1
1
20
Calcium
2, 8, 8, 2
2
21
Scandium
2, 8, 9, 2
3
22
Titanium
2, 8, 10, 2
4
23
Vanadium
2, 8, 11, 2
5
24
Chromium
2, 8, 13, 1
6
25
Manganese
2, 8, 13, 2
7
26
Iron
2, 8, 14, 2
8
27
Cobalt
2, 8, 15, 2
9
28
Nickel
2, 8, 16, 2
10
29
Copper
2, 8, 18, 1
11
30
Zinc
2, 8, 18, 2
12
31
Gallium
2, 8, 18, 3
13
32
Germanium
2, 8, 18, 4
14
33
Arsenic
2, 8, 18, 5
15
34
Selenium
2, 8, 18, 6
16
35
Bromine
2, 8, 18, 7
17
36
Krypton
2, 8, 18, 8
18
37
Rubidium
2, 8, 18, 8, 1
1
38
Strontium
2, 8, 18, 8, 2
2
39
Yttrium
2, 8, 18, 9, 2
3
40
Zirconium
2, 8, 18, 10, 2
4
41
Niobium
2, 8, 18, 12, 1
5
42
Molybdenum
2, 8, 18, 13, 1
6
43
Technetium
2, 8, 18, 13, 2
7
44
Ruthenium
2, 8, 18, 15, 1
8
45
Rhodium
2, 8, 18, 16, 1
9
46
Palladium
2, 8, 18, 18
10
47
Silver
2, 8, 18, 18, 1
11
48
Cadmium
2, 8, 18, 18, 2
12
49
Indium
2, 8, 18, 18, 3
13
50
Tin
2, 8, 18, 18, 4
14
51
Antimony
2, 8, 18, 18, 5
15
52
Tellurium
2, 8, 18, 18, 6
16
53
Iodine
2, 8, 18, 18, 7
17
54
Xenon
2, 8, 18, 18, 8
18
55
Caesium
2, 8, 18, 18, 8, 1
1
56
Barium
2, 8, 18, 18, 8, 2
2
57
Lanthanum
2, 8, 18, 18, 9, 2
58
Cerium
2, 8, 18, 19, 9, 2
59
Praseodymium
2, 8, 18, 21, 8, 2
60
Neodymium
2, 8, 18, 22, 8, 2
61
Promethium
2, 8, 18, 23, 8, 2
62
Samarium
2, 8, 18, 24, 8, 2
63
Europium
2, 8, 18, 25, 8, 2
64
Gadolinium
2, 8, 18, 25, 9, 2
65
Terbium
2, 8, 18, 27, 8, 2
66
Dysprosium
2, 8, 18, 28, 8, 2
67
Holmium
2, 8, 18, 29, 8, 2
68
Erbium
2, 8, 18, 30, 8, 2
69
Thulium
2, 8, 18, 31, 8, 2
70
Ytterbium
2, 8, 18, 32, 8, 2
71
Lutetium
2, 8, 18, 32, 9, 2
3
72
Hafnium
2, 8, 18, 32, 10, 2
4
73
Tantalum
2, 8, 18, 32, 11, 2
5
74
Tungsten
2, 8, 18, 32, 12, 2
6
75
Rhenium
2, 8, 18, 32, 13, 2
7
76
Osmium
2, 8, 18, 32, 14, 2
8
77
Iridium
2, 8, 18, 32, 15, 2
9
78
Platinum
2, 8, 18, 32, 17, 1
10
79
Gold
2, 8, 18, 32, 18, 1
11
80
Mercury
2, 8, 18, 32, 18, 2
12
81
Thallium
2, 8, 18, 32, 18, 3
13
82
Lead
2, 8, 18, 32, 18, 4
14
83
Bismuth
2, 8, 18, 32, 18, 5
15
84
Polonium
2, 8, 18, 32, 18, 6
16
85
Astatine
2, 8, 18, 32, 18, 7
17
86
Radon
2, 8, 18, 32, 18, 8
18
87
Francium
2, 8, 18, 32, 18, 8, 1
1
88
Radium
2, 8, 18, 32, 18, 8, 2
2
89
Actinium
2, 8, 18, 32, 18, 9, 2
90
Thorium
2, 8, 18, 32, 18, 10, 2
91
Protactinium
2, 8, 18, 32, 20, 9, 2
92
Uranium
2, 8, 18, 32, 21, 9, 2
93
Neptunium
2, 8, 18, 32, 22, 9, 2
94
Plutonium
2, 8, 18, 32, 24, 8, 2
95
Americium
2, 8, 18, 32, 25, 8, 2
96
Curium
2, 8, 18, 32, 25, 9, 2
97
Berkelium
2, 8, 18, 32, 27, 8, 2
98
Californium
2, 8, 18, 32, 28, 8, 2
99
Einsteinium
2, 8, 18, 32, 29, 8, 2
100
Fermium
2, 8, 18, 32, 30, 8, 2
101
Mendelevium
2, 8, 18, 32, 31, 8, 2
102
Nobelium
2, 8, 18, 32, 32, 8, 2
103
Lawrencium
2, 8, 18, 32, 32, 8, 3
3
104
Rutherfordium
2, 8, 18, 32, 32, 10, 2
4
105
Dubnium
2, 8, 18, 32, 32, 11, 2
5
106
Seaborgium
2, 8, 18, 32, 32, 12, 2
6
107
Bohrium
2, 8, 18, 32, 32, 13, 2
7
108
Hassium
2, 8, 18, 32, 32, 14, 2
8
109
Meitnerium
2, 8, 18, 32, 32, 15, 2 (?)
9
110
Darmstadtium
2, 8, 18, 32, 32, 16, 2 (?)
10
111
Roentgenium
2, 8, 18, 32, 32, 17, 2 (?)
11
112
Copernicium
2, 8, 18, 32, 32, 18, 2 (?)
12
113
Nihonium
2, 8, 18, 32, 32, 18, 3 (?)
13
114
Flerovium
2, 8, 18, 32, 32, 18, 4 (?)
14
115
Moscovium
2, 8, 18, 32, 32, 18, 5 (?)
15
116
Livermorium
2, 8, 18, 32, 32, 18, 6 (?)
16
117
Tennessine
2, 8, 18, 32, 32, 18, 7 (?)
17
118
Oganesson
2, 8, 18, 32, 32, 18, 8 (?)
18

See also

Wikimedia Commons has media related to Electron shell diagrams.Periodic table (electron configurations)
Electron counting
18-electron rule
Core charge

References

^ a b Re: Why do electron shells have set limits ? madsci.org, 17 March 1999, Dan Berger, Faculty Chemistry/Science, Bluffton College

^ a b Electron Subshells. Corrosion Source.

^ Donald Sadoway, Introduction to Solid State Chemistry, Lecture 5

^ .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:”\”””\”””‘””‘”}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg”)right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}Barkla, Charles G. (1911). “XXXIX.The spectra of the fluorescent Röntgen radiations”. Philosophical Magazine. Series 6. 22 (129): 396–412. doi:10.1080/14786440908637137. Previously denoted by letters B and A (…). The letters K and L are, however, preferable, as it is highly probable that series of radiations both more absorbable and more penetrating exist.

^ Jue, T. (2009). “Quantum Mechanic Basic to Biophysical Methods”. Fundamental Concepts in Biophysics. Berlin: Springer. p. 33. ISBN 978-1-58829-973-4.

^ Orbitals. Chem4Kids. Retrieved on 1 December 2011.

^ Electron & Shell Configuration Archived 28 December 2018 at the Wayback Machine. Chemistry.patent-invent.com. Retrieved on 1 December 2011.

vteElectron configuration
Electron shell
Atomic orbital
Quantum mechanics
Introduction to quantum mechanicsQuantum numbers
Principal quantum number (n)
Azimuthal quantum number (ℓ)
Magnetic quantum number (m)
Spin quantum number (s)Ground-state configurations
Periodic table (electron configurations)
Electron configurations of the elements (data page)Electron filling
Pauli exclusion principle
Hund’s rule
Aufbau principleElectron pairing
Electron pair
Unpaired electronBonding participation
Valence electron
Core electronElectron counting rules
Octet rule
18-electron rule
Authority control
GND: 4127528-7
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The movement of electrons around the nucleus and the energy levels

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Two of the energy levels can hold eight electrons each.

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