Electron shell

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 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 labelMax electronsShells containing itHistorical name
s02Every shell sharp
p162nd shell and higher principal
d2103rd shell and higher diffuse
f3144th shell and higher fundamental
g4185th 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 4 + 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]

Shell
name
Subshell
name
Subshell
max
electrons
Shell
max
electrons
K1s22
L2s22 + 6 = 8
2p6
M3s22 + 6 + 10
= 18
3p6
3d10
N4s22 + 6 +
10 + 14
= 32
4p6
4d10
4f14
O5s22 + 6 +
10 + 14 +
18 = 50
5p6
5d10
5f14
5g18

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

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 ${\displaystyle n+\ell }$ 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.)

ZElementNo. of electrons/shellGroup
1Hydrogen11
2Helium218
3Lithium2, 11
4Beryllium2, 22
5Boron2, 313
6Carbon2, 414
7Nitrogen2, 515
8Oxygen2, 616
9Fluorine2, 717
10Neon2, 818
11Sodium2, 8, 11
12Magnesium2, 8, 22
13Aluminium2, 8, 313
14Silicon2, 8, 414
15Phosphorus2, 8, 515
16Sulfur2, 8, 616
17Chlorine2, 8, 717
18Argon2, 8, 818
19Potassium2, 8, 8, 11
20Calcium2, 8, 8, 22
21Scandium2, 8, 9, 23
22Titanium2, 8, 10, 24
24Chromium2, 8, 13, 16
25Manganese2, 8, 13, 27
26Iron2, 8, 14, 28
27Cobalt2, 8, 15, 29
28Nickel2, 8, 16, 210
29Copper2, 8, 18, 111
30Zinc2, 8, 18, 212
31Gallium2, 8, 18, 313
32Germanium2, 8, 18, 414
33Arsenic2, 8, 18, 515
34Selenium2, 8, 18, 616
35Bromine2, 8, 18, 717
36Krypton2, 8, 18, 818
37Rubidium2, 8, 18, 8, 11
38Strontium2, 8, 18, 8, 22
39Yttrium2, 8, 18, 9, 23
40Zirconium2, 8, 18, 10, 24
41Niobium2, 8, 18, 12, 15
42Molybdenum2, 8, 18, 13, 16
43Technetium2, 8, 18, 13, 27
44Ruthenium2, 8, 18, 15, 18
45Rhodium2, 8, 18, 16, 19
47Silver2, 8, 18, 18, 111
49Indium2, 8, 18, 18, 313
50Tin2, 8, 18, 18, 414
51Antimony2, 8, 18, 18, 515
52Tellurium2, 8, 18, 18, 616
53Iodine2, 8, 18, 18, 717
54Xenon2, 8, 18, 18, 818
55Caesium2, 8, 18, 18, 8, 11
56Barium2, 8, 18, 18, 8, 22
57Lanthanum2, 8, 18, 18, 9, 2
58Cerium2, 8, 18, 19, 9, 2
59Praseodymium2, 8, 18, 21, 8, 2
60Neodymium2, 8, 18, 22, 8, 2
61Promethium2, 8, 18, 23, 8, 2
62Samarium2, 8, 18, 24, 8, 2
63Europium2, 8, 18, 25, 8, 2
64Gadolinium2, 8, 18, 25, 9, 2
65Terbium2, 8, 18, 27, 8, 2
66Dysprosium2, 8, 18, 28, 8, 2
67Holmium2, 8, 18, 29, 8, 2
68Erbium2, 8, 18, 30, 8, 2
69Thulium2, 8, 18, 31, 8, 2
70Ytterbium2, 8, 18, 32, 8, 2
71Lutetium2, 8, 18, 32, 9, 23
72Hafnium2, 8, 18, 32, 10, 24
73Tantalum2, 8, 18, 32, 11, 25
74Tungsten2, 8, 18, 32, 12, 26
75Rhenium2, 8, 18, 32, 13, 27
76Osmium2, 8, 18, 32, 14, 28
77Iridium2, 8, 18, 32, 15, 29
78Platinum2, 8, 18, 32, 17, 110
79Gold2, 8, 18, 32, 18, 111
80Mercury2, 8, 18, 32, 18, 212
81Thallium2, 8, 18, 32, 18, 313
82Lead2, 8, 18, 32, 18, 414
83Bismuth2, 8, 18, 32, 18, 515
84Polonium2, 8, 18, 32, 18, 616
85Astatine2, 8, 18, 32, 18, 717
86Radon2, 8, 18, 32, 18, 818
87Francium2, 8, 18, 32, 18, 8, 11
88Radium2, 8, 18, 32, 18, 8, 22
89Actinium2, 8, 18, 32, 18, 9, 2
90Thorium2, 8, 18, 32, 18, 10, 2
91Protactinium2, 8, 18, 32, 20, 9, 2
92Uranium2, 8, 18, 32, 21, 9, 2
93Neptunium2, 8, 18, 32, 22, 9, 2
94Plutonium2, 8, 18, 32, 24, 8, 2
95Americium2, 8, 18, 32, 25, 8, 2
96Curium2, 8, 18, 32, 25, 9, 2
97Berkelium2, 8, 18, 32, 27, 8, 2
98Californium2, 8, 18, 32, 28, 8, 2
99Einsteinium2, 8, 18, 32, 29, 8, 2
100Fermium2, 8, 18, 32, 30, 8, 2
101Mendelevium2, 8, 18, 32, 31, 8, 2
102Nobelium2, 8, 18, 32, 32, 8, 2
103Lawrencium2, 8, 18, 32, 32, 8, 33
104Rutherfordium2, 8, 18, 32, 32, 10, 24
105Dubnium2, 8, 18, 32, 32, 11, 25
106Seaborgium2, 8, 18, 32, 32, 12, 26
107Bohrium2, 8, 18, 32, 32, 13, 27
108Hassium2, 8, 18, 32, 32, 14, 28
109Meitnerium2, 8, 18, 32, 32, 15, 2 (?)9
110Darmstadtium2, 8, 18, 32, 32, 16, 2 (?)10
111Roentgenium2, 8, 18, 32, 32, 17, 2 (?)11
112Copernicium2, 8, 18, 32, 32, 18, 2 (?)12
113Nihonium2, 8, 18, 32, 32, 18, 3 (?)13
114Flerovium2, 8, 18, 32, 32, 18, 4 (?)14
115Moscovium2, 8, 18, 32, 32, 18, 5 (?)15
116Livermorium2, 8, 18, 32, 32, 18, 6 (?)16
117Tennessine2, 8, 18, 32, 32, 18, 7 (?)17
118Oganesson2, 8, 18, 32, 32, 18, 8 (?)18

• Periodic table (electron configurations)
• Electron counting
• 18-electron rule
• Core charge

References

1. Re: Why do electron shells have set limits ? madsci.org, 17 March 1999, Dan Berger, Faculty Chemistry/Science, Bluffton College
2. Electron Subshells. Corrosion Source.
3. Donald Sadoway, Introduction to Solid State Chemistry, Lecture 5
4. 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.
5. Jue, T. (2009). "Quantum Mechanic Basic to Biophysical Methods". Fundamental Concepts in Biophysics. Berlin: Springer. p. 33. ISBN 978-1-58829-973-4.
6. Orbitals. Chem4Kids. Retrieved on 1 December 2011.
7. Electron & Shell Configuration Archived 28 December 2018 at the Wayback Machine. Chemistry.patent-invent.com. Retrieved on 1 December 2011.