Electron shell
In chemistry and atomic physics, an electron shell may be thought of as an orbit that electrons follow 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, ...). A useful guide when understanding electron shells in atoms is to note that each row on the conventional periodic table of elements represents an electron shell.
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
In 1913, Niels Bohr proposed a model of the atom, giving the arrangement of electrons in their sequential orbits. At that time, Bohr allowed the capacity of the inner orbit of the atom to increase to eight electrons as the atoms got larger, and "in the scheme given below the number of electrons in this [outer] ring is arbitrary put equal to the normal valency of the corresponding element". Using these and other constraints, he proposed configurations that are in accord with those now known only for the first six elements. "From the above we are led to the following possible scheme for the arrangement of the electrons in light atoms:"[3][4]
Element | Electrons per shell | Element | Electrons per shell | Element | Electrons per shell |
---|---|---|---|---|---|
1 | 1 | 9 | 4, 4, 1 | 17 | 8, 4, 4, 1 |
2 | 2 | 10 | 8, 2 | 18 | 8, 8, 2 |
3 | 2, 1 | 11 | 8, 2, 1 | 19 | 8, 8, 2, 1 |
4 | 2, 2 | 12 | 8, 2, 2 | 20 | 8, 8, 2, 2 |
5 | 2, 3 | 13 | 8, 2, 3 | 21 | 8, 8, 2, 3 |
6 | 2, 4 | 14 | 8, 2, 4 | 22 | 8, 8, 2, 4 |
7 | 4, 3 | 15 | 8, 4, 3 | 23 | 8, 8, 4, 3 |
8 | 4, 2, 2 | 16 | 8, 4, 2, 2 | 24 | 8, 8, 4, 2, 2 |
The shell terminology comes from
The existence of electron shells was first observed experimentally in
The work of assigning electrons to shells was continued from 1913 to 1925 by many chemists and a few physicists. Niels Bohr was one of the few physicists who followed the chemist's work
As work continued on the electron shell structure of the Sommerfeld-Bohr Model, Sommerfeld had introduced three "quantum numbers n, k, and m, that described the size of the orbit, the shape of the orbit, and the direction in which the orbit was pointing."[23] Because we use k for the Boltzmann constant, the azimuthal quantum number was changed to ℓ. When the modern quantum mechanics theory was put forward based on Heisenberg's matrix mechanics and Schrödinger's wave equation, these quantum numbers were kept in the current quantum theory but were changed to n being the principal quantum number, and m being the magnetic quantum number.
However, the final form of the electron shell model still in use today for the number of electrons in shells was discovered in 1923 by
Subshells
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 | ℓ | 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)[24] |
- 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. Each of the following subshells (p, d, f, g) can have 4 more electrons than the one preceding 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]
Shell name |
Subshell name |
Subshell max electrons |
Shell max electrons |
---|---|---|---|
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 (in known elements) for the first four shells (K, L, M, N). No known element has more than 32 electrons in any one shell.
Subshell energies and filling order
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.
Because of this, the later shells are filled over vast sections of the periodic table. The K shell fills in the first period (hydrogen and helium), while the L shell fills in the second (lithium to neon). However, the M shell starts filling at sodium (element 11) but does not finish filling till copper (element 29), and the N shell is even slower: it starts filling at potassium (element 19) but does not finish filling till ytterbium (element 70). The O, P, and Q shells begin filling in the known elements, but they are not complete even at the heaviest known element, oganesson (element 118).
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 ( electric blue) before each noble gas (group 18, 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. The elements past 108 have such short half-lives that their electron configurations have not yet been measured, and so predictions have been inserted instead.
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
References
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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.
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