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The periodic table, also known as the periodic table of the ( chemical) elements, is a rows and columns arrangement of the . It is widely used in , , and other sciences, and is generally seen as an of chemistry. It is a graphic formulation of the , which states that the properties of the chemical elements exhibit an approximate periodic dependence on their . The table is divided into four roughly rectangular areas called blocks. The rows of the table are called periods, and the columns are called groups. Elements from the same group of the periodic table show similar chemical characteristics. run through the periodic table, with character (keeping their own electrons) increasing from left to right across a period, and from down to up across a group, and character (surrendering electrons to other atoms) increasing in the opposite direction. The underlying reason for these trends is electron configurations of atoms. The periodic table exclusively lists electrically neutral atoms that have an equal number of positively charged protons and negatively charged electrons and puts (atoms with the same number of protons but different numbers of neutrons) at the same place. Other atoms, like and , are graphically collected in other tables like the tables of nuclides (often called Segrè charts).

The first periodic table to become generally accepted was that of the Russian chemist in 1869: he formulated the periodic law as a dependence of chemical properties on atomic mass. Because not all elements were then known, there were gaps in his periodic table, and Mendeleev successfully used the periodic law to predict properties of some of the missing elements. The periodic law was recognized as a fundamental discovery in the late 19th century, and it was explained with the discovery of the atomic number and pioneering work in quantum mechanics of the early 20th century that illuminated the internal structure of the atom. With Glenn T. Seaborg's 1945 discovery that the were in fact f-block rather than d-block elements, a recognisably modern form of the table was reached. The periodic table and law are now a central and indispensable part of modern chemistry.

The periodic table continues to evolve with the progress of science. In nature, only elements up to atomic number 94 exist; to go further, it was necessary to synthesise new elements in the laboratory. Today, all the first 118 elements are known, completing the first seven rows of the table, but chemical characterisation is still needed for the heaviest elements to confirm that their properties match their positions. It is not yet known how far the table will stretch beyond these seven rows and whether the patterns of the known part of the table will continue into this unknown region. Some scientific discussion also continues regarding whether some elements are correctly positioned in today's table. Many alternative representations of the periodic law exist, and there is some discussion as to whether there is an optimal form of the periodic table.


Overview
The periodic table is a 2-dimensional structured table. The elements are placed in table cells, in reading order of ascending . The table columns are called groups, the rows are called periods. The breaks at the end of each period occur according to a repetition (or periodicity) of physical and chemical properties of the elements.


Atomic structure
The smallest constituents of all normal matter are known as . Atoms are extremely small, being about one ten-billionth of a meter across; thus their internal structure is governed by quantum mechanics.
(1964). 9780201021158, Addison–Wesley. .
Atoms consist of a small positively charged , made of positively charged and uncharged , surrounded by a cloud of negatively charged electrons; the charges cancel out, so atoms are neutral.
(1964). 9780201021158, Addison–Wesley. .
Electrons participate in chemical reactions, but the nucleus does not. When atoms participate in chemical reactions, they either gain or lose electrons to form positively- or negatively-charged ; or share electrons with each other.

Atoms can be subdivided into different types based on the number of protons (and thus also electrons) they have. This is called the , often symbolised Z (for "Zahl" — German for "number"). Each distinct atomic number therefore corresponds to a class of atom: these classes are called the . The chemical elements are what the periodic table classifies and organises. is the element with atomic number 1; , atomic number 2; , atomic number 3; and so on. Each of these names can be further abbreviated by a one- or two-letter ; those for hydrogen, helium, and lithium are respectively H, He, and Li. Neutrons do not affect the atom's chemical identity, but do affect its weight. Atoms with the same number of protons but different numbers of neutrons are called of the same chemical element. Naturally occurring elements usually occur as mixes of different isotopes; since each isotope usually occurs with a characteristic abundance, naturally occurring elements have well-defined , defined as the average mass of a naturally occurring atom of that element.

Today, 118 elements are known, the first 94 of which are known to occur naturally on Earth at present. Of the 94 natural elements, eighty have a stable isotope and one more () has an almost-stable isotope (with a half-life over a billion times the age of the universe). Two more, and , have isotopes undergoing radioactive decay with a half-life comparable to the age of the Earth. The stable elements plus bismuth, thorium, and uranium make up the 83 primordial elements that survived from the Earth's formation. The remaining eleven natural elements decay quickly enough that their continued trace occurrence rests primarily on being constantly regenerated as intermediate products of the decay of thorium and uranium. All 24 known artificial elements are radioactive.


Electron configuration
The periodic table is a graphic description of the periodic law, which states that the properties and atomic structures of the chemical elements are a periodic function of their . Elements are placed in the periodic table by their electron configurations, which exhibit periodic recurrences that explain the of properties across the periodic table.

An electron can be thought of as inhabiting an , which characterises the probability it can be found in any particular region of the atom. Their energies are quantised, which is to say that they can only take discrete values. Furthermore, electrons obey the Pauli exclusion principle: different electrons must always be in different states. This allows classification of the possible states an electron can take in various energy levels known as shells, divided into individual subshells, which each contain one or more orbitals. Each orbital can contain up to two electrons: they are distinguished by a quantity known as spin, conventionally labeled "up" or "down".Petrucci et al., p. 323 In a cold atom (one in its ground state), electrons arrange themselves in such a way that the total energy they have is minimised by occupying the lowest-energy orbitals available.Petrucci et al., p. 322 Only the outermost electrons (so-called ) have enough energy to break free of the nucleus and participate in chemical reactions with other atoms. The others are called .

(2022). 9781774200032, BC Campus (opentextbc.ca). .

Elements are known with up to the first seven shells occupied. The first shell contains only one orbital, a spherical s orbital. As it is in the first shell, this is called the 1s orbital. This can hold up to two electrons. The second shell similarly contains a 2s orbital, and it also contains three dumbbell-shaped 2p orbitals, and can thus fill up to eight electrons (2×1 + 2×3 = 8). The third shell contains one 3s orbital, three 3p orbitals, and five 3d orbitals, and thus has a capacity of 2×1 + 2×3 + 2×5 = 18. The fourth shell contains one 4s orbital, three 4p orbitals, five 4d orbitals, and seven 4f orbitals, thus leading to a capacity of 2×1 + 2×3 + 2×5 + 2×7 = 32. Higher shells contain more types of orbitals that continue the pattern, but such types of orbitals are not filled in the ground states of known elements. The subshell types are characterised by the . Four numbers describe an orbital in an atom completely: the principal quantum number n, the azimuthal quantum number ℓ (the orbital type), the magnetic quantum number m, and the spin quantum number s.


The order of subshell filling
The sequence in which the subshells are filled is given in most cases by the , also known as the Madelung or Klechkovsky rule (after and Vsevolod Klechkovsky respectively). This rule was first observed empirically by Madelung, and Klechkovsky and later authors gave it theoretical justification.
(1984). 9780070327603, McGraw-Hill. .
The shells overlap in energies, and the Madelung rule specifies the sequence of filling according to:
1s ≪ 2s < 2p ≪ 3s < 3p ≪ 4s < 3d < 4p ≪ 5s < 4d < 5p ≪ 6s < 4f < 5d < 6p ≪ 7s < 5f < 6d < 7p ≪ ...
Here the sign ≪ means "much less than" as opposed to < meaning just "less than". Phrased differently, electrons enter orbitals in order of increasing n + ℓ, and if two orbitals are available with the same value of n + ℓ, the one with lower n is occupied first. In general, orbitals with the same value of n + ℓ are similar in energy, but in the case of the s-orbitals (with ℓ = 0), quantum effects raise their energy to approach that of the next n + ℓ group. Hence the periodic table is usually drawn to begin each row (often called a period) with the filling of a new s-orbital, which corresponds to the beginning of a new shell. Thus, with the exception of the first row, each period length appears twice:
2, 8, 8, 18, 18, 32, 32, ...

The overlaps get quite close at the point where the d-orbitals enter the picture, and the order can shift slightly with atomic number and atomic charge.

Starting from the simplest atom, this lets us build up the periodic table one at a time in order of atomic number, by considering the cases of single atoms. In , there is only one electron, which must go in the lowest-energy orbital 1s. This electron configuration is written 1s1, where the superscript indicates the number of electrons in the subshell. adds a second electron, which also goes into 1s, completely filling the first shell and giving the configuration 1s2.

(1964). 9780201021158, Addison–Wesley. .

Starting from the third element, , the first shell is full, so its third electron occupies a 2s orbital, giving a 1s2 2s1 configuration. The 2s electron is lithium's only valence electron, as the 1s subshell is now too tightly bound to the nucleus to participate in chemical bonding to other atoms. Thus the filled first shell is called a "" for this and all heavier elements. The 2s subshell is completed by the next element (1s2 2s2). The following elements then proceed to fill the 2p subshell. (1s2 2s2 2p1) puts its new electron in a 2p orbital; (1s2 2s2 2p2) fills a second 2p orbital; and with (1s2 2s2 2p3) all three 2p orbitals become singly occupied. This is consistent with Hund's rule, which states that atoms usually prefer to singly occupy each orbital of the same type before filling them with the second electron. (1s2 2s2 2p4), (1s2 2s2 2p5), and (1s2 2s2 2p6) then complete the already singly filled 2p orbitals; the last of these fills the second shell completely.

Starting from element 11, , the second shell is full, making the second shell a for this and all heavier elements. The eleventh electron begins the filling of the third shell by occupying a 3s orbital, giving a configuratin of 1s2 2s2 2p6 3s1 for sodium. This configuration is abbreviated Ne 3s1, where Ne represents neon's configuration. (Ne 3s2) finishes this 3s orbital, and the following the six elements , , , , , and fill the three 3p orbitals (Ne 3s2 3p1 through Ne 3s2 3p6). This creates an analogous series in which the outer shell structures of sodium through argon are analogous to those of lithium through neon, and is the basis for the periodicity of chemical properties that the periodic table illustrates: at regular but changing intervals of atomic numbers, the properties of the chemical elements approximately repeat.Scerri, p. 17

The first eighteen elements can thus be arranged as the start of a periodic table. Elements in the same column have the same number of valence electrons and have analogous valence electron configurations: these columns are called groups. The single exception is helium, which has two valence electrons like beryllium and magnesium, but is typically placed in the column of neon and argon to emphasise that its outer shell is full. There are eight columns in this periodic table fragment, corresponding to at most eight outer-shell electrons.

(2022). 9780060936778, Collins.
A period begins when a new shell starts filling. Finally, the colouring illustrates the blocks: the elements in the s-block (coloured red) are filling s-orbitals, while those in the p-block (coloured yellow) are filling p-orbitals.

1
2×1 = 2 elements
3
4
5
6
7
8
9
10

11
12
13
14
15
16
17
18
2×(1+3) = 8 elements

Starting the next row, for and the 4s subshell is the lowest in energy, and therefore they fill it. Potassium adds one electron to the 4s shell (Ar 4s1), and calcium then completes it (Ar 4s2). However, starting from (Ar 3d1 4s2) the 3d subshell becomes the next highest in energy. The 4s and 3d subshells have approximately the same energy and they compete for filling the electrons, and so the occupation is not quite consistently filling the 3d orbitals one at a time. The precise energy ordering of 3d and 4s changes along the row, and also changes depending on how many electrons are removed from the atom. For example, due to the repulsion between the 3d electrons and the 4s ones, at the 4s energy level becomes slightly higher than 3d, and so it becomes more profitable to have a Ar 3d5 4s1 configuration than an Ar 3d4 4s2 one. A similar anomaly occurs at . These are violations of the Madelung rule. Such anomalies however do not have any chemical significance, as the various configurations are so close in energy to each otherPetrucci et al., p. 328 that the presence of a nearby atom can shift the balance. The periodic table therefore ignores these and considers only idealised configurations.

At (Ar 3d10 4s2), the 3d orbitals are completely filled with a total of ten electrons. Next come the 4p orbitals, completing the row, which are filled progressively by (Ar 3d10 4s2 4p1) through (Ar 3d10 4s2 4p6), in a manner analogous to the previous p-block elements. From gallium onwards, the 3d orbitals form part of the electronic core, and no longer participate in chemistry. The s- and p-block elements, which fill their outer shells, are called main-group elements; the d-block elements (coloured blue below), which fill an inner shell, are called transition elements (or transition metals, since they are all metals).Petrucci et al., pp. 326–7

The next eighteen elements fill the 5s orbitals ( and ), then 4d ( through , again with a few anomalies along the way), and then 5p ( through ). Hence the fifth row has the same structure as the fourth.

1
2×1 = 2 elements
3
4
5
6
7
8
9
10
2×(1+3) = 8 elements
11
12
13
14
15
16
17
18
2×(1+3) = 8 elements
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
2×(1+3+5) = 18 elements

The sixth row of the table likewise starts with two s-block elements: and . After this, the first f-block elements (coloured green below) begin to appear, starting with . These are sometimes termed inner transition elements. As there are now not only 4f but also 5d and 6s subshells at similar energies, competition occurs once again with many irregular configurations; this has resulted in some dispute about where exactly the f-block is supposed to begin, but most who study the matter agree that it starts at lanthanum in accordance with the Aufbau principle. Even though lanthanum does not itself fill the 4f subshell as a single atom, because of repulsion between electrons, its 4f orbitals are low enough in energy to participate in chemistry. At , the seven 4f orbitals are completely filled with fourteen electrons; thereafter, a series of ten transition elements ( through mercury) follows, and finally six main-group elements ( through ) complete the period.

The seventh row is analogous to the sixth row: 7s fills ( and ), then 5f ( to ), then 6d ( to ), and finally 7p ( to ). Again there are a few anomalies along the way:Petrucci et al., p. 331 for example, as single atoms neither actinium nor actually fills the 5f subshell, and lawrencium does not fill the 6d shell, but all these subshells can still become filled in chemical environments. For a very long time, the seventh row was incomplete as most of its elements do not occur in nature. The missing elements beyond uranium started to be synthesised in the laboratory in 1940, when neptunium was made. The row was completed with the synthesis of in 2010 (the last element had already been made in 2002), and the last elements in this seventh row were given names in 2016.

1
2×1 = 2 elements
3
4
5
6
7
8
9
10
2×(1+3) = 8 elements
11
12
13
14
15
16
17
18
2×(1+3) = 8 elements
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
2×(1+3+5) = 18 elements
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
2×(1+3+5) = 18 elements
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
Hg
81
82
83
84
85
86

87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
2×(1+3+5+7) = 32 elements

This completes the modern periodic table, with all seven rows completely filled to capacity.


Electron configuration table
The following table shows the electron configuration of a neutral gas-phase atom of each element. Different configurations can be favoured in different chemical environments. The main-group elements have entirely regular electron configurations; the transition and inner transition elements show twenty irregularities due to the aforementioned competition between subshells close in energy level. For the last ten elements (109–118), experimental data is lacking and therefore calculated configurations have been shown instead.
(1975). 9783540071099, Springer-Verlag.
Completely filled subshells have been greyed out.


Group names and numbers
Under an international naming convention, the groups are numbered numerically from 1 to 18 from the leftmost column (the alkali metals) to the rightmost column (the noble gases). The f-block groups are ignored in this numbering.
(2022). 9780854044382, RSC Publishing. .
Groups can also be named by their first element, e.g. the "scandium group" for group 3. Previously, groups were known by . In America, the Roman numerals were followed by either an "A" if the group was in the or , or a "B" if the group was in the . The Roman numerals used correspond to the last digit of today's naming convention (e.g. the group 4 elements were group IVB, and the were group IVA). In Europe, the lettering was similar, except that "A" was used if the group was before group 10, and "B" was used for groups including and after group 10. In addition, groups 8, 9 and 10 used to be treated as one triple-sized group, known collectively in both notations as group VIII. In 1988, the new (International Union of Pure and Applied Chemistry) naming system (1–18) was put into use, and the old group names (I–VIII) were deprecated.


Presentation forms

32 columns

18 columns

For reasons of space, the periodic table is commonly presented with the f-block elements cut out and positioned placed as a distinct part below the main body. It reduces the number of element columns from 32 to 18.

Both forms represent the same periodic table. The form with the f-block included in the main body is sometimes called the 32-column or long form; the form with the f-block cut out the 18-column or medium-long form. The 32-column form has the advantage of showing all elements in their correct sequence, but it has the disadvantage of requiring more space.Scerri, p. 375 The form chosen is an editorial choice, and does not imply any change of scientific claim or statement. For example, when discussing the composition of group 3, the options can be shown equally (unprejudiced) in both forms.

Periodic tables usually at least show the elements' symbols; many also provide supplementary information about the elements, either via colour-coding or as data in the cells. The above table shows the names and atomic numbers of the elements, and also their blocks, natural occurrences and standard atomic weights. For the short-lived elements without standard atomic weights, the mass number of the most stable known isotope is used instead. Other tables may include properties such as state of matter, melting and boiling points, densities, as well as provide different classifications of the elements.


Periodic trends
As chemical reactions involve the valence electrons, elements with similar outer electron configurations may be expected to react similarly and form compounds with similar proportions of elements in them. Such elements are placed in the same group, and thus there tend to be clear similarities and trends in chemical behaviour as one proceeds down a group.
(2022). 9780763778330, Jones & Bartlett Publishers.
As analogous configurations return at regular intervals, the properties of the elements thus exhibit periodic recurrences, hence the name of the periodic table and the periodic law. These periodic recurrences were noticed well before the underlying theory that explains them was developed.
(2022). 9780313316647, Greenwood Publishing Group. .
(2022). 9780071120722, McGraw-Hill. .


Atomic radius
Historically, the physical size of atoms was unknown until the early 20th century. The first calculated estimate of the atomic radius of hydrogen was published by physicist Artur Haas in 1910 to within an order of magnitude (a factor of 10) of the accepted value, the (~0.529 Å). In his model, Haas used a single-electron configuration based on the classical atomic model proposed by J. J. Thomson in 1904, often called the plum-pudding model.Haas, Arthur Erich (1884-1941) Uber die elektrodynamische Bedeutung des Planckschen Strahlungsgesetzes und uber eine neue Bestimmung des elektrischen Elementarquantums und der dimension des wasserstoffatoms. Sitzungsberichte der kaiserlichen Akademie der Wissenschaften in Wien. 2a, 119 pp 119-144 (1910). Haas AE. Die Entwicklungsgeschichte des Satzes von der Erhaltung der Kraft. Habilitation Thesis, Vienna, 1909. Hermann, A. Arthur Erich Haas, Der erste Quantenansatz für das Atom. Stuttgart, 1965 contains

(the size of atoms) are dependent on the sizes of their outermost orbitals.Siekierski and Burgess, pp. 23–26 They generally decrease going left to right along the main-group elements, because the nuclear charge increases but the outer electrons are still in the same shell. However, going down a column, the radii generally increase, because the outermost electrons are in higher shells that are thus further away from the nucleus. The first row of each block is abnormally small, due to an effect called or primogenic repulsion: the 1s, 2p, 3d, and 4f subshells have no inner analogues that they would have to be to. Higher s-, p-, d-, and f-subshells experience strong repulsion from their inner analogues, which have approximately the same angular distribution of charge, and must expand to avoid this. This makes significant differences arise between the small 2p elements, which prefer , and the larger 3p and higher p-elements, which do not. Similar anomalies arise for the 1s, 2p, 3d, 4f, and the hypothetical elements: the degree of this first-row anomaly is highest for the s-block, is moderate for the p-block, and is less pronounced for the d- and f-blocks.

In the transition elements, an inner shell is filling, but the size of the atom is still determined by the outer electrons. The increasing nuclear charge across the series and the increased number of inner electrons for shielding somewhat compensate each other, so the decrease in radius is smaller. The 4p and 5d atoms, coming immediately after new types of transition series are first introduced, are smaller than would have been expected,Greenwood and Earnshaw, p. 29 because the added core 3d and 4f subshells provide only incomplete shielding of the nuclear charge for the outer electrons. Hence for example gallium atoms are slightly smaller than aluminium atoms. Together with kainosymmetry, this results in an even-odd difference between the periods (except in the s-block) that is sometimes known as secondary periodicity: elements in even periods have smaller atomic radii and prefer to lose fewer electrons, while elements in odd periods (except the first) differ in the opposite direction. Thus for example many properties in the p-block show a zigzag rather than a smooth trend along the group. For example, phosphorus and antimony in odd periods of group 15 readily reach the +5 oxidation state, whereas nitrogen, arsenic, and bismuth in even periods prefer to stay at +3.

Thallium and lead atoms are about the same size as indium and tin atoms respectively, but from bismuth to radon the 6p atoms are larger than the analogous 5p atoms. This happens because when atomic nuclei become highly charged, special relativity becomes needed to gauge the effect of the nucleus on the electron cloud. These relativistic effects result in heavy elements increasingly having differing properties compared to their lighter homologues in the periodic table. Spin–orbit interaction splits the p-subshell: one p-orbital is relativistically stabilised and shrunken (it fills in thallium and lead), but the other two (filling in bismuth through radon) are relativistically destabilised and expanded. Relativistic effects also explain why is golden and mercury is a liquid at room temperature. They are expected to become very strong in the late seventh period, potentially leading to a collapse of periodicity. Electron configurations are only clearly known until element 108 (), and experimental chemistry beyond 108 has only been done for 112 (), 113 (), and 114 (), so the chemical characterisation of the heaviest elements remains a topic of current research.

(2022). 9781402012501, Kluwer Academic Publishers.


Ionisation energy
The first ionisation energy of an atom is the energy required to remove an electron from it. This varies with the atomic radius: ionisation energy increases left to right and down to up, because electrons that are closer to the nucleus are held more tightly and are more difficult to remove. Ionisation energy thus is minimised at the first element of each period – hydrogen and the – and then generally rises until it reaches the at the right edge of the period. There are some exceptions to this trend, such as oxygen, where the electron being removed is paired and thus interelectronic repulsion makes it easier to remove than expected.Greenwood and Earnshaw, pp. 24–5

In the transition series, the outer electrons are preferentially lost even though the inner orbitals are filling. For example, in the 3d series, the 4s electrons are lost first even though the 3d orbitals are being filled. The shielding effect of adding an extra 3d electron approximately compensates the rise in nuclear charge, and therefore the ionisation energies stay mostly constant, though there is a small increase especially at the end of each transition series.

As metal atoms tend to lose electrons in chemical reactions, ionisation energy is generally correlated with chemical reactivity, although there are other factors involved as well.


Electron affinity
The opposite property to ionisation energy is the electron affinity, which is the energy released when adding an electron to the atom. A passing electron will be more readily attracted to an atom if it feels the pull of the nucleus more strongly, and especially if there is an available partially filled outer orbital that can accommodate it. Therefore, electron affinity tends to increase down to up and left to right. The exception is the last column, the noble gases, which have a full shell and have no room for another electron. This gives the in the next-to-last column the highest electron affinities.

Some atoms, like the noble gases, have no electron affinity: they cannot form stable gas-phase anions. The noble gases, having high ionisation energies and no electron affinity, have little inclination towards gaining or losing electrons and are generally unreactive.

Some exceptions to the trends occur: oxygen and fluorine have lower electron affinities than their heavier homologues sulfur and chlorine, because they are small atoms and hence the newly added electron would experience significant repulsion from the already present ones. For the nonmetallic elements, electron affinity likewise somewhat correlates with reactivity, but not perfectly since other factors are involved. For example, fluorine has a lower electron affinity than chlorine, but is more reactive.


Valence and oxidation states
The valence of an element can be defined either as the number of hydrogen atoms that can combine with it to form a simple binary hydride, or as twice the number of oxygen atoms that can combine with it to form a simple binary oxide (that is, not a or a ). The valences of the main-group elements are directly related to the group number: the hydrides in the main groups 1–2 and 13–17 follow the formulae MH, MH2, MH3, MH4, MH3, MH2, and finally MH. The highest oxides instead increase in valence, following the formulae M2O, MO, M2O3, MO2, M2O5, MO3, M2O7. Today the notion of valence has been extended by that of the , which is the formal charge left on an element when all other elements in a compound have been removed as their ions.

The electron configuration suggests a ready explanation from the number of electrons available for bonding, although a full explanation requires considering the energy that would be released in forming compounds with different valences rather than simply considering electron configurations alone.Greenwood and Earnshaw, p. 113 For example, magnesium forms Mg2+ rather than Mg+ cations when dissolved in water, because the latter would spontaneously disproportionate into Mg0 and Mg2+ cations. This is because the of hydration (surrounding the cation with water molecules) increases in magnitude with the charge and radius of the ion. In Mg+, the outermost orbital (which determines ionic radius) is still 3s, so the hydration enthalpy is small and insufficient to compensate the energy required to remove the electron; but ionising again to Mg2+ uncovers the core 2p subshell, making the hydration enthalpy large enough to allow magnesium(II) compounds to form. For similar reasons, the common oxidation states of the heavier p-block elements (where the ns electrons become lower in energy than the np) tend to vary by steps of 2, because that is necessary to uncover an inner subshell and decrease the ionic radius (e.g. Tl+ uncovers 6s, and Tl3+ uncovers 5d, so once thallium loses two electrons it tends to lose the third one as well). Analogous arguments based on orbital hybridisation can be used for the less electronegative p-block elements. For example, GaCl requires gallium's 4s orbital to mix with only one 4p orbital, whereas GaCl2 and GaCl3 would both require it to mix with two. Hence no extra energy is needed between these last two steps to involve more orbitals, so gallium(II) is unstable while gallium(III) is stable.Siekierski and Burgess, pp. 45–54

For transition metals, common oxidation states are nearly always at least +2 for similar reasons (uncovering the next subshell); this holds even for the metals with anomalous dx+1s1 or dx+2s0 configurations (except for ), because repulsion between d-electrons means that the movement of the second electron from the s- to the d-subshell does not appreciably change its ionisation energy.Siekierski and Burgess, pp. 134–137 Because ionising the transition metals further does not uncover any new inner subshells, their oxidation states tend to vary by steps of 1 instead. The lanthanides and late actinides generally show a stable +3 oxidation state, removing the outer s-electrons and then (usually) one electron from the (n−2)f-orbitals, that are similar in energy to ns. The common and maximum oxidation states of the d- and f-block elements tend to depend on the ionisation energies. As the energy difference between the (n−1)d and ns orbitals rises along each transition series, it becomes less energetically favourable to ionise further electrons. Thus, the early transition metal groups tend to prefer higher oxidation states, but the +2 oxidation state becomes more stable for the late transition metal groups. The highest formal oxidation state thus increases from +3 at the beginning of each d-block row, to +7 or +8 in the middle (e.g. ), and then to +2 at the end. The lanthanides and late actinides usually have high fourth ionisation energies and hence rarely surpass the +3 oxidation states, whereas early actinides have low fourth ionisation energies and so for example neptunium and plutonium can reach +7.Siekierski and Burgess, pp. 178–180

As elements in the same group share the same valence configurations, they usually exhibit similar chemical behaviour. For example, the in the first group all have one valence electron, and form a very homogeneous class of elements: they are all soft and reactive metals. However, there are many factors involved, and groups can often be rather hetereogeneous. For instance, hydrogen also has one valence electron and is in the same group as the alkali metals, but its chemical behaviour is quite different. The stable elements of comprise a nonmetal (), two semiconductors ( and ), and two metals ( and ); they are nonetheless united by having four valence electrons.Scerri, pp. 14–15


Electronegativity
Another important property of elements is their electronegativity. Atoms can form to each other by sharing electrons in pairs, creating an overlap of valence orbitals. The degree to which each atom attracts the shared electron pair depends on the atom's electronegativity – the tendency of an atom towards gaining or losing electrons. The more electronegative atom will tend to attract the electron pair more, and the less electronegative (or more electropositive) one will attract it less. In extreme cases, the electron can be thought of as having been passed completely from the more electropositive atom to the more electronegative one, though this is a simplification. The bond then binds two ions, one positive (having given up the electron) and one negative (having accepted it), and is termed an .

Electronegativity depends on how strongly the nucleus can attract an electron pair, and so it exhibits a similar variation to the other properties already discussed: electronegativity tends to fall going up to down, and rise going left to right. The alkali and alkaline earth metals are among the most electropositive elements, while the chalcogens, halogens, and noble gases are among the most electronegative ones.

Electronegativity is generally measured on the Pauling scale, on which the most electronegative reactive atom () is given electronegativity 4.0, and the least electronegative atom () is given electronegativity 0.79. (Theoretically would be more electronegative than fluorine, but the Pauling scale cannot measure its electronegativity because it does not form covalent bonds.)

An element's electronegativity varies with the identity and number of the atoms it is bonded to, as well as how many electrons it has already lost: an atom becomes more electronegative when it has lost more electrons.Greenwood and Earnshaw, pp. 25–6 This sometimes makes a large difference: lead in the +2 oxidation state has electronegativity 1.87 on the Pauling scale, while lead in the +4 oxidation state has electronegativity 2.33.

(2022). 9780470772966, John Wiley & Sons.


Metallicity
A simple substance is a substance formed from atoms of one chemical element. The simple substances of the more electronegative atoms tend to share electrons (form covalent bonds) with each other. They form either small molecules (like hydrogen or oxygen, whose atoms bond in pairs) or giant structures stretching indefinitely (like carbon or silicon). The noble gases simply stay as single atoms, as they already have a full shell. Substances composed of discrete molecules or single atoms are held together by weaker attractive forces between the molecules, such as the London dispersion force: as electrons move within the molecules, they create momentary imbalances of electrical charge, which induce similar imbalances on nearby molecules and create synchronised movements of electrons across many neighbouring molecules.

The more electropositive atoms, however, tend to instead lose electrons, creating a "sea" of electrons engulfing cations. The outer orbitals of one atom overlap to share electrons with all its neighbours, creating a giant structure of molecular orbitals extending over all the atoms. This negatively charged "sea" pulls on all the ions and keeps them together in a . Elements forming such bonds are often called ; those which do not are often called . Some elements can form multiple simple substances with different structures: these are called . For example, and are two allotropes of carbon.

The metallicity of an element can be predicted from electronic properties. When atomic orbitals overlap during metallic or covalent bonding, they create both bonding and antibonding molecular orbitals of equal capacity, with the antibonding orbitals of higher energy. Net bonding character occurs when there are more electrons in the bonding orbitals than there are in the antibonding orbitals. Metallic bonding is thus possible when the number of electrons delocalised by each atom is less than twice the number of orbitals contributing to the overlap. This is the situation for elements in groups 1 through 13; they also have too few valence electrons to form giant covalent structures where all atoms take equivalent positions, and so almost all of them metallise. The exceptions are hydrogen and boron, which have too high an ionisation energy. Hydrogen thus forms a covalent H2 molecule, and boron forms a giant covalent structure based on icosahedral B12 clusters. In a metal, the bonding and antibonding orbitals have overlapping energies, creating a single band that electrons can freely flow through, allowing for electrical conduction.Siekierski and Burgess, pp. 60–66

In group 14, both metallic and covalent bonding become possible. In a diamond crystal, covalent bonds between carbon atoms are strong, because they have a small atomic radius and thus the nucleus has more of a hold on the electrons. Therefore, the bonding orbitals that result are much lower in energy than the antibonding orbitals, and there is no overlap, so electrical conduction becomes impossible: carbon is a nonmetal. However, covalent bonding becomes weaker for larger atoms and the energy gap between the bonding and antibonding orbitals decreases. Therefore, silicon and germanium have smaller and are : electrons can cross the gap when thermally excited. The band gap disappears in tin, so that tin and lead become metals.

Elements in groups 15 through 17 have too many electrons to form giant covalent molecules that stretch in all three dimensions. For the lighter elements, the bonds in small diatomic molecules are so strong that a condensed phase is disfavoured: thus nitrogen (N2), oxygen (O2), white phosphorus (P4), sulfur (S8), and the stable halogens (F2, Cl2, Br2, and I2) readily form covalent molecules with few atoms. The heavier ones tend to form long chains (e.g. red phosphorus, grey selenium, tellurium) or layered structures (e.g. carbon as graphite, black phosphorus, grey arsenic, grey antimony, bismuth) that only extend in one or two rather than three dimensions. As these structures do not use all their orbitals for bonding, they end up with bonding, nonbonding, and antibonding bands in order of increasing energy. Similarly to group 14, the band gaps shrink for the heavier elements and free movement of electrons between the chains or layers becomes possible. Thus for example black phosphorus, black arsenic, grey selenium, tellurium, and iodine are semiconductors; grey arsenic, grey antimony, and bismuth are (exhibiting quasi-metallic conduction, with a very small band overlap); and polonium and probably astatine are true metals. Finally, the natural group 18 elements all stay as individual atoms.

The dividing line between metals and nonmetals is roughly diagonal from top left to bottom right, with the transition series appearing to the left of this diagonal (as they have many available orbitals for overlap). This is expected, as metallicity tends to be correlated with electropositivity and the willingness to lose electrons, which increases right to left and up to down. Thus the metals greatly outnumber the nonmetals. Elements near the borderline are difficult to classify: they tend to have properties that are intermediate between those of metals and nonmetals, and may have some properties characteristic of both. They are often termed semimetals or . The term "semimetal" used in this sense should not be confused with its strict physical sense having to do with band structure: bismuth is physically a semimetal, but is generally considered a metal by chemists.

The following table considers the most stable allotropes at standard conditions. The elements coloured yellow form simple substances that are well-characterised by metallic bonding. Elements coloured light blue form giant covalent structures, whereas those coloured dark blue form small covalently bonded molecules that are held together by weaker van der Waals forces. The noble gases are coloured in violet: their molecules are single atoms and no covalent bonding occurs. Greyed-out cells are for elements which have not been prepared in sufficient quantities for their most stable allotropes to have been characterised in this way. Theoretical considerations and current experimental evidence suggest that all of those elements would metallise if they could form condensed phases, except perhaps for oganesson.

File:Iron electrolytic and 1cm3 cube.jpg|Iron, a metal Sulfur - El Desierto mine, San Pablo de Napa, Daniel Campos Province, Potosí, Bolivia.jpg|Sulfur, a nonmetal Arsen 1a.jpg|Arsenic, an element often called a semi-metal or metalloid

Generally, metals are shiny and dense. They usually have high melting and boiling points due to the strength of the metallic bond, and are often malleable and ductile (easily stretched and shaped) because the atoms can move relative to each other without breaking the metallic bond. They conduct electricity because their electrons are free to move in all three dimensions. Similarly, they conduct heat, which is transferred by the electrons as extra : they move faster. These properties persist in the liquid state, as although the crystal structure is destroyed on melting, the atoms still touch and the metallic bond persists, though it is weakened. Metals tend to be reactive towards nonmetals. Some exceptions can be found to these generalisations: for example, manganese,

(1985). 9783110075113, Walter de Gruyter.
arsenic, antimony,
(2022). 9780123526519, Academic Press.
and bismuth are brittle;
(2022). 9780849304859, CRC press. .
chromium is extremely hard;
(1968). 9781468460667, IFI-Plenum. .
gallium, rubidium, caesium, and mercury are liquid at or close to room temperature; and such as gold are chemically very inert.

Nonmetals exhibit different properties. Those forming giant covalent crystals exhibit high melting and boiling points, as it takes considerable energy to overcome the strong covalent bonds. Those forming discrete molecules are held together mostly by dispersion forces, which are more easily overcome; thus they tend to have lower melting and boiling points, and many are liquids or gases at room temperature. Nonmetals are often dull-looking. They tend to be reactive towards metals, except for the noble gases, which are inert towards most substances. They are brittle when solid as their atoms are held tightly in place. They are less dense and conduct electricity poorly, because there are no mobile electrons. Near the borderline, band gaps are small and thus many elements in that region are semiconductors, such as silicon, germanium, selenium, and tellurium. Again there are exceptions; for example, diamond has the highest thermal conductivity of all known materials, greater than any metal.

It is common to designate a class of metalloids straddling the boundary between metals and nonmetals, as elements in that region are intermediate in both physical and chemical properties. However, no consensus exists in the literature for precisely which elements should be so designated. When such a category is used, silicon, germanium, arsenic, and tellurium are almost always included, and boron and antimony usually are; but most sources include other elements as well, without agreement on which extra elements should be added, and some others subtract from this list instead.


Further manifestations of periodicity
There are some other relationships throughout the periodic table between elements that are not in the same group, such as the diagonal relationships between elements that are diagonally adjacent (e.g. lithium and magnesium).Scerri, pp. 407–420 Some similarities can also be found between the main groups and the transition metal groups, or between the early actinides and early transition metals, when the elements have the same number of valence electrons. Thus uranium somewhat resembles chromium and tungsten in group 6, as all three have six valence electrons.

Many other physical properties of the elements exhibit periodic variation in accordance with the periodic law, such as , , heats of fusion, heats of vaporisation, atomisation energy, and so on. Similar periodic variations appear for the compounds of the elements, which can be observed by comparing hydrides, oxides, sulfides, halides, and so on. Chemical properties are more difficult to describe quantitatively, but likewise exhibit their own periodicities. Examples include the variation in the and basic properties of the elements and their compounds, the stabilities of compounds, and methods of isolating the elements. Periodicity is and has been used very widely to predict the properties of unknown new elements and new compounds, and is central to modern chemistry.Greenwood and Earnshaw, pp. 29–31


Classification of elements
Many terms have been used in the literature to describe sets of elements that behave similarly. The group names alkali metal, alkaline earth metal, pnictogen, chalcogen, halogen, and noble gas are acknowledged by IUPAC; the other groups can be referred to by their number, or by their first element (e.g., group 6 is the chromium group). Some divide the p-block elements from groups 13 to 16 by metallicity, although there is neither an IUPAC definition nor a precise consensus on exactly which elements should be considered metals, nonmetals, or semi-metals (sometimes called metalloids). Neither is there a consensus on what the metals succeeding the transition metals ought to be called, with post-transition metal and poor metal being among the possibilities having been used. Some advanced monographs exclude the elements of group 12 from the transition metals on the grounds of their sometimes quite different chemical properties, but this is not a universal practice.

The lanthanides are considered to be the elements La–Lu, which are all very similar to each other: historically they included only Ce–Lu, but lanthanum became included by common usage. The rare earth elements (or rare earth metals) add scandium and yttrium to the lanthanides. Analogously, the actinides are considered to be the elements Ac–Lr (historically Th–Lr), although variation of properties in this set is much greater than within the lanthanides. IUPAC recommends the names lanthanoids and actinoids to avoid ambiguity, as the -ide suffix typically denotes a negative ion; however lanthanides and actinides remain common. Some authors who consider lutetium and lawrencium to be group 3 elements prefer to define the lanthanides as La–Yb and the actinides as Ac–No, matching the f-block.

(1981). 9780520906150, University of California Press.

Many more categorisations exist and are used according to certain disciplines. In astrophysics, a metal is defined as any element with atomic number greater than 2, i.e. anything except hydrogen and helium. The term "semimetal" has a different definition in physics than it does in chemistry: bismuth is a semimetal by physical definitions, but chemists generally consider it a metal.

(1985). 9780121460709, Academic Press, Inc..
A few terms are widely used, but without any very formal definition, such as "", which has been given such a wide range of definitions that it has been criticised as "effectively meaningless".

The scope of terms varies significantly between authors. For example, according to IUPAC, the noble gases extend to include the whole group, including the very radioactive superheavy element oganesson. However, among those who specialise in the superheavy elements, this is not often done: in this case "noble gas" is typically taken to imply the unreactive behaviour of the lighter elements of the group. Since calculations generally predict that oganesson should not be particularly inert due to relativistic effects, and may not even be a gas at room temperature if it could be produced in bulk, its status as a noble gas is often questioned in this context. Furthermore, national variations are sometimes encountered: in Japan, alkaline earth metals often do not include beryllium and magnesium as their behaviour is different from the heavier group 2 metals.


History

Early history
In 1817, German physicist Johann Wolfgang Döbereiner began to formulate one of the earliest attempts to classify the elements. Here, Döbereiner found that strontium's properties were intermediate to those of calcium and barium. In 1829, he found that he could form some of the elements into groups of three, with the members of each group having related properties. He termed these groups triads. For an English translation of this article, see: Johann Wolfgang Döbereiner: "An Attempt to Group Elementary Substances according to Their Analogies" (Lemoyne College (Syracuse, New York, USA))
(2022). 9780471233411, John Wiley.
Chlorine, bromine, and iodine formed a triad; as did calcium, strontium, and barium; lithium, sodium, and potassium; and sulfur, selenium, and tellurium. Today, all these triads form part of modern-day groups.Scerri, p. 47 Various chemists continued his work and were able to identify more and more relationships between small groups of elements. However, they could not build one scheme that encompassed them all.
(2022). 9780192841001, Oxford University Press.

German chemist noted the sequences of similar chemical and physical properties repeated at periodic intervals. According to him, if the atomic weights were plotted as ordinates (i.e. vertically) and the atomic volumes as abscissas (i.e. horizontally)—the curve obtained a series of maximums and minimums—the most elements would appear at the peaks of the curve in the order of their atomic weights. In 1864, a book of his was published; it contained an early version of the periodic table containing 28 elements, and classified elements into six families by their valence—for the first time, elements had been grouped according to their valence. Works on organizing the elements by atomic weight had until then been stymied by inaccurate measurements of the atomic weights.Meyer, Julius Lothar; Die modernen Theorien der Chemie (1864); table on page 137 In 1868, he revised his table, but this revision was published as a draft only after his death.Scerri, pp. 106–108


Mendeleev
The definitive breakthrough came from the Russian chemist . Although other chemists (including Meyer) had found some other versions of the periodic system at about the same time, Mendeleev was the most dedicated to developing and defending his system, and it was his system that most impacted the scientific community.Scerri, p. 113 On 17 February 1869 (1 March 1869 in the Gregorian calendar), Mendeleev began arranging the elements and comparing them by their atomic weights. He began with a few elements, and over the course of the day his system grew until it encompassed most of the known elements. After finding a consistent arrangement, his printed table appeared in May 1869 in the journal of the Russian Chemical Society.Scerri, pp. 117–123 In some cases, there appeared to be an element missing from the system, and he boldly predicted that that meant that the element had yet to be discovered. In 1871, Mendeleev published a long article, including an updated form of his table, that made his predictions for unknown elements explicit. Mendeleev predicted the properties of three of these unknown elements in detail: as they would be missing heavier homologues of boron, aluminium, and silicon, he named them eka-boron, eka-aluminium, and eka-silicon ("eka" being Sanskrit for "one").

In 1875, the French chemist Paul-Émile Lecoq de Boisbaudran, working without knowledge of Mendeleev's prediction, discovered a new element in a sample of the mineral , and named it gallium. He isolated the element and began determining its properties. Mendeleev, reading de Boisbaudran's publication, sent a letter claiming that gallium was his predicted eka-aluminium. Although Lecoq de Boisbaudran was initially sceptical, and suspected that Mendeleev was trying to take credit for his discovery, he later admitted that Mendeleev was correct.Scerri, p. 149 In 1879, the Swedish chemist Lars Fredrik Nilson discovered a new element, which he named scandium: it turned out to be eka-boron. Eka-silicon was found in 1886 by German chemist , who named it germanium. The properties of gallium, scandium, and germanium matched what Mendeleev had predicted.Scerri, p. 151–2 In 1889, Mendeleev noted at the Faraday Lecture to the Royal Institution in London that he had not expected to live long enough "to mention their discovery to the Chemical Society of Great Britain as a confirmation of the exactitude and generality of the periodic law". Even the discovery of the noble gases at the close of the 19th century, which Mendeleev had not predicted, fitted neatly into his scheme as an eighth main group.Scerri, pp. 164–169

Mendeleev nevertheless had some trouble fitting the known lanthanides into his scheme, as they did not exhibit the periodic change in valencies that the other elements did. After much investigation, the Czech chemist suggested in 1902 that the lanthanides could all be placed together in one group on the periodic table. He named this the "asteroid hypothesis" as an astronomical analogy: just as there is an instead of a single planet between Mars and Jupiter, so the place below yttrium was occupied by all the lanthanides instead of just one element.


Atomic number
After the internal structure of the atom was probed, amateur Dutch physicist Antonius van den Broek proposed in 1913 that the nuclear charge determined the placement of elements in the periodic table.A. van der Broek, Physikalische Zeitschrift, 14, (1913), 32-41 The New Zealand physicist Ernest Rutherford coined the word "atomic number" for this nuclear charge.Scerri, p. 185 In van der Broek's published article he illustrated the first electronic periodic table showing the elements arranged according to the number of their electrons.A. van der Broek, Die Radioelemente, das periodische System und die Konstitution der Atom, Physik. Zeitsch., 14, 32, (1913). Rutherford confirmed in his 1914 paper that Bohr had accepted the view of van der Broek.E. Rutherford, Phil. Mag., 27, 488-499 (Mar. 1914). "This has led to an interesting suggestion by van Broek that the number of units of charge on the nucleus, and consequently the number of external electrons, may be equal to the number of the elements when arranged in order of increasing atomic weight. On this view, the nucleus charges of hydrogen, helium, and carbon are 1, 2, 6 respectively, and so on for the other elements, provided there is no gap due to a missing element. This view has been taken by Bohr in his theory of the constitution of simple atoms and molecules."

The same year, English physicist using X-ray spectroscopy confirmed van den Broek's proposal experimentally. Moseley determined the value of the nuclear charge of each element from to and showed that Mendeleev's ordering actually places the elements in sequential order by nuclear charge.

(1995). 9780465072651, HarperCollins Publishers, Inc.. .
Nuclear charge is identical to count and determines the value of the ( Z) of each element. Using atomic number gives a definitive, integer-based sequence for the elements. Moseley's research immediately resolved discrepancies between atomic weight and chemical properties; these were cases such as tellurium and iodine, where atomic number increases but atomic weight decreases. Although Moseley was soon killed in World War I, the Swedish physicist continued his work up to , and established that it was the element with the highest atomic number then known (92). Based on Moseley and Siegbahn's research, it was also known which atomic numbers corresponded to missing elements yet to be found.


Electron shells
The Danish physicist applied 's idea of quantisation to the atom. He concluded that the energy levels of electrons were quantised: only a discrete set of stable energy states were allowed. Bohr then attempted to understand periodicity through electron configurations, surmising in 1913 that the inner electrons should be responsible for the chemical properties of the element.See Bohr table from 1913 paper below.Helge Kragh, Aarhus, LARS VEGARD, ATOMIC STRUCTURE, AND THE PERIODIC SYSTEM, Bull. Hist. Chem., VOLUME 37, Number 1 (2012), p.43. In 1913, he produced the first electronic periodic table based on a quantum atom.Scerri, pp. 208–218

Bohr called his electron shells "rings" in 1913: atomic orbitals within shells did not exist at the time of his planetary model. Bohr explains in Part 3 of his famous 1913 paper that the maximum electrons in a shell is eight, writing, "We see, further, that a ring of n electrons cannot rotate in a single ring round a nucleus of charge ne unless n < 8." For smaller atoms, the electron shells would be filled as follows: "rings of electrons will only join if they contain equal numbers of electrons; and that accordingly the numbers of electrons on inner rings will only be 2, 4, 8." However, in larger atoms the innermost shell would contain eight electrons: "on the other hand, the periodic system of the elements strongly suggests that already in neon N = 10 an inner ring of eight electrons will occur." His proposed electron configurations for the light atoms (shown to the right) do not always accord with those now known.Niels Bohr, "On the Constitution of Atoms and Molecules, Part III, Systems containing several nuclei" Philosophical Magazine 26:857--875 (1913)Kragh, Helge. "Niels Bohr's Second Atomic Theory." Https://doi.org/10.2307/27757389 .

+ Bohr's electron configurations for light elements
2,2
2,4
4,3
4,2,2
4,4,1
8,2
8,2,1
8,4,2,2
8,8,2

The first one to systematically expand and correct the chemical potentials of Bohr's atomic theory was in 1914 and in 1916. Kossel explained that in the periodic table new elements would be created as electrons were added to the outer shell. In Kossel's paper, he writes: "This leads to the conclusion that the electrons, which are added further, should be put into concentric rings or shells, on each of which ... only a certain number of electrons—namely, eight in our case—should be arranged. As soon as one ring or shell is completed, a new one has to be started for the next element; the number of electrons, which are most easily accessible, and lie at the outermost periphery, increases again from element to element and, therefore, in the formation of each new shell the chemical periodicity is repeated."W. Kossel, "Über Molekülbildung als Folge des Atom- baues," Ann. Phys., 1916, 49, 229-362 (237).Translated in Helge Kragh, Aarhus, LARS VEGARD, ATOMIC STRUCTURE, AND THE PERIODIC SYSTEM, Bull. Hist. Chem., VOLUME 37, Number 1 (2012), p.43.

In a 1919 paper, postulated the existence of "cells" which we now call orbitals, which could each only contain two electrons each, and these were arranged in "equidistant layers" which we now call shells. He made an exception for the first shell to only contain two electrons. The chemist Charles Rugeley Bury suggested in 1921 that eight and eighteen electrons in a shell form stable configurations. Bury proposed that the electron configurations in transitional elements depended upon the valence electrons in their outer shell. He introduced the word transition to describe the elements now known as or transition elements.

Prompted by Bohr, took up the problem of electron configurations in 1923. Pauli extended Bohr's scheme to use four , and formulated his exclusion principle which stated that no two electrons could have the same four quantum numbers. This explained the lengths of the periods in the periodic table (2, 8, 18, and 32), which corresponded to the number of electrons that each shell could occupy.Scerri, pp. 218–23 In 1925, arrived at configurations close to the modern ones. The that describes the electron configurations of the elements was first empirically observed by in 1926 and published in 1936. In 1961, Vsevolod Klechkovsky derived the first part of the Madelung rule (that orbitals fill in order of increasing n + ℓ) from the Thomas–Fermi model; the second part (that if two orbitals have the same value of n + ℓ, the one with smaller n fills first) was derived from a similar potential in 1971 by Yury N. Demkov and Valentin N. Ostrovsky.

The quantum theory clarified the transition metals and lanthanides as forming their own separate groups, transitional between the main groups, although some chemists had already proposed tables showing them this way before then: the English chemist Henry Bassett did so in 1892, the Danish chemist in 1895, and the Swiss chemist in 1905. Bohr used Thomsen's form in his 1922 Nobel Lecture; Werner's form is very similar to the modern 32-column form.

(2022). 9780444535900, Elsevier.
The exact position of the lanthanides, and thus the composition of group 3, remained under dispute for decades longer because their electron configurations were initially measured incorrectly.Scerri, pp. 392−401 In 2021 IUPAC released a provisional report suggesting that group 3 should contain scandium, yttrium, lutetium, and lawrencium. This matches the classification Bassett and Werner adopted over a century earlier.


Synthetic elements
By 1936, the pool of missing elements from hydrogen to uranium had shrunk to four: elements 43, 61, 85, and 87 remained missing. Element 43 eventually became the first element to be synthesised artificially via nuclear reactions rather than discovered in nature. It was discovered in 1937 by Italian chemists Emilio Segrè and , who named their discovery , after the Greek word for "artificial".Scerri, pp. 313–321 Elements 61 () and 85 () were likewise produced artificially; element 87 () became the last element to be discovered in nature, by French chemist .Scerri, pp. 322–340 The elements beyond uranium were likewise discovered artificially, starting with and 's 1940 discovery of (via bombardment of uranium with neutrons).Scerri, p. 354–6 Glenn T. Seaborg and his team at the Lawrence Berkeley National Laboratory (LBNL) continued discovering transuranium elements, starting with , and discovered that contrary to previous thinking, the elements from actinium onwards were congeners of the lanthanides rather than transition metals. Bassett (1892), Werner (1905), and the French engineer (1928) had previously suggested this, but their ideas did not then receive general acceptance. Seaborg thus called them the actinides. Elements up to 101 (named mendelevium in honour of Mendeleev) were synthesised either through neutron or alpha-particle irradiation, or in nuclear explosions in the cases of 99 (einsteinium) and 100 (fermium).

A significant controversy arose with elements 102 through 106 in the 1960s and 1970s, as competition arose between the LBNL team (now led by ) and a team of Soviet scientists at the Joint Institute for Nuclear Research (JINR) led by . Each team claimed discovery, and in some cases each proposed their own name for the element, creating an element naming controversy that lasted decades. These elements were made by bombardment of actinides with light ions.Scerri, pp. 356–9 IUPAC at first adopted a hands-off approach, preferring to wait and see if a consensus would be forthcoming. Unfortunately, it was also the height of the , and it became clear after some time that this would not happen. As such, IUPAC and the International Union of Pure and Applied Physics (IUPAP) created a Transfermium Working Group (TWG, fermium being element 100) in 1985 to set out criteria for discovery, which were published in 1991. After some further controversy, these elements received their final names in 1997, including seaborgium (106) in honour of Seaborg.

The TWG's criteria were used to arbitrate later element discovery claims from LBNL and JINR, as well as from research institutes in Germany (GSI) and Japan (). Currently, consideration of discovery claims is performed by a IUPAC/IUPAP Joint Working Party. After priority was assigned, the elements were officially added to the periodic table, and the discoverers were invited to propose their names. By 2016, this had occurred for all elements up to 118, therefore completing the periodic table's first seven rows. The discoveries of elements beyond 106 were made possible by techniques devised by at the JINR: cold fusion (bombardment of lead and bismuth by heavy ions) made possible the 1981–2004 discoveries of elements 107 through 112 at GSI and 113 at Riken, and he led the JINR team (in collaboration with American scientists) to discover elements 114 through 118 using hot fusion (bombardment of actinides by calcium ions) in 1998–2010.Scerri, pp. 356–363() The heaviest known element, oganesson (118), is named in Oganessian's honour. Element 114 is named flerovium in honour of his predecessor and mentor Flyorov.

In celebration of the periodic table's 150th anniversary, the declared the year 2019 as the International Year of the Periodic Table, celebrating "one of the most significant achievements in science". The discovery criteria set down by the TWG were updated in 2020 in response to experimental and theoretical progress that had not been foreseen in 1991. Today, the periodic table is among the most recognisable icons of chemistry. IUPAC is involved today with many processes relating to the periodic table: the recognition and naming of new elements, recommending group numbers and collective names, determining which elements belong to group 3, and the updating of atomic weights.


Current questions
Although the modern periodic table is standard today, some variation can be found in period 1 and group 3. Discussion is ongoing about the placements of the relevant elements.


Period 1
Some variation can be found on the placements of the period 1 elements hydrogen and helium. Following electron configurations, hydrogen would be placed in group 1, and helium would be placed in group 2. The group 1 placement of hydrogen is the most common one, but helium is almost always placed in group 18 with the other noble gases. The debate has to do with conflicting understandings of whether chemical or electronic properties should primarily decide periodic table placement, and conflicting views of how the evidence should be used.

Like the group 1 metals, hydrogen has one electron in its outermost shellGray, p. 12 and typically loses its only electron in chemical reactions. It has some metal-like chemical properties, being able to displace some metals from their salts.

(1970). 9780828550673, Mir Publishers.
But hydrogen forms a diatomic nonmetallic gas at standard conditions, unlike the alkali metals which are reactive solid metals. This and hydrogen's formation of , in which it gains an electron, brings it close to the properties of the which do the same (though it is rarer for hydrogen to form H than H+).
(2022). 9789811218507, World Scientific.
Moreover, the lightest two halogens ( and ) are gaseous like hydrogen at standard conditions. Some properties of hydrogen are not a good fit for either group: hydrogen is neither highly oxidising nor highly reducing and is not reactive with water. Hydrogen thus has properties corresponding to both those of the alkali metals and the halogens, but matches neither group perfectly, and is thus difficult to place by its chemistry. Therefore, while the electronic placement of hydrogen in group 1 predominates, some rarer arrangements show either hydrogen in group 17, duplicate hydrogen in both groups 1 and 17, or float it separately from all groups.Greenwood & Earnshaw, throughout the book

Helium is an unreactive noble gas at standard conditions, and has a full outer shell: these properties are like the noble gases in group 18, but not at all like the reactive alkaline earth metals of group 2. Therefore, helium is nearly universally placed in group 18 which its properties best match. However, helium only has two electrons in its outermost shell, whereas the other noble gases have eight; and it is an s-block element, whereas all other noble gases are p-block elements. Also, solid helium crystallises in a hexagonal close-packed structure, which matches beryllium and magnesium in group 2, but not the other noble gases in group 18. In these ways helium better matches the alkaline earth metals.

(2022). 9780199289301, Oxford University Press.
Therefore, tables with both hydrogen and helium floating outside all groups may rarely be encountered. A few chemists have advocated that the electronic placement in group 2 be adopted for helium. Arguments for this often rest on the first-row anomaly trend, as helium as the first s2 element before the alkaline earth metals stands out as anomalous in a way that helium as the first noble gas does not. Thus for example a large difference in atomic radii between the first and second members of each main group is seen in groups 1 and 13–17: it exists between neon and argon, and between helium and beryllium, but not between helium and neon. Moving helium to group 2 makes this trend consistent in groups 2 and 18 as well.Siekierski and Burgess, p. 128


Group 3
Published periodic tables show variation regarding the heavier members of group 3, which begins with scandium and yttrium. They are commonly lanthanum and actinium, but many physicists and chemists have argued that they should be lutetium and lawrencium. The spaces below yttrium are sometimes left blank as a third option, but there is confusion in the literature on whether this format implies that group 3 contains only scandium and yttrium, or if it also contains all the lanthanides and actinides. The dispute arose because the electron configurations of the lanthanides were first measured incorrectly. The incorrect configurations first measured suggested that Sc-Y-La-Ac was better, but the correct ones now known suggest instead Sc-Y-Lu-Lr. While it has been argued that atoms of lanthanum and actinium lack f-electrons and hence that they cannot be f-block elements, the same is true of thorium which is never disputed as an f-block element. The Sc-Y-Lu-Lr table is in accordance with the Madelung rule, and as no other exceptions to the Madelung rule have ever been used to argue for changes to the periodic table, it has been argued that lanthanum and actinium should be treated likewise.

In 2015, a IUPAC project chaired by Scerri was set up to decide the question, giving only Sc-Y-La-Ac and Sc-Y-Lu-Lr as possible resolutions. In 2021, it decided on Sc-Y-Lu-Lr on the basis of three desiderata: displaying all elements in order of increasing atomic number, avoiding a split of the d-block into "two highly uneven portions", and having the blocks follow the widths quantum mechanics demands of them (2, 6, 10, and 14). The Sc-Y-La-Ac form forces a split in the d-block between lanthanum and hafnium (and between actinium and rutherfordium), and the form with blank spaces under yttrium makes the f-block 15 elements wide even though quantum mechanics requires it to be 14 elements wide. While it was noted that 15-element-wide f-blocks are supported by some practitioners of a specialised branch of relativistic quantum mechanics focusing on the properties of superheavy elements, the report's opinion was that such interest-dependent concerns should not have any bearing on how the periodic table is presented to "the general chemical and scientific community".


Future extension beyond the seventh period
The most recently named elements – nihonium (113), moscovium (115), tennessine (117), and oganesson (118) – completed the seventh row of the periodic table. Future elements would have to begin an eighth row. These elements may be referred to either by their atomic numbers (e.g. "element 119"), or by the IUPAC systematic element names which directly relate to the atomic numbers (e.g. "ununennium" for element 119, derived from Latin unus "one", Greek ennea "nine", and the traditional -ium suffix for metallic elements). All attempts to synthesise such elements have failed so far. An attempt to make element 119 has been ongoing since 2018 at the research institute in Japan. The Joint Institute for Nuclear Research in Russia also plans to make its own attempts at synthesising the first few period 8 elements.

Currently, discussion continues regarding whether this future eighth period should follow the pattern set by the earlier periods or not, as calculations predict that by this point relativistic effects should result in significant deviations from the Madelung rule. Various different models have been suggested. All agree that the eighth period should begin like the previous ones with two 8s elements, and that there should then follow a new series of g-block elements filling up the orbitals, but the precise configurations calculated for these elements vary widely between sources. Beyond this series, calculations do not agree on what exactly should follow. Filling of the , 6f, 7d, and 8p shells is expected to occur in approximately that order, but they are likely to be intermingled with each other and with the 9s and 9p subshells, so that it is not clear which elements should go in which groups anymore. Scerri has raised the question of whether an extended periodic table should take into account the failure of the Madelung rule in this region, or if such exceptions should be ignored. The shell structure may also be fairly formal at this point: already the electron distribution in an oganesson atom is expected to be rather uniform, with no discernible shell structure.

Nuclear stability will likely prove a decisive factor constraining the number of possible elements. It depends on the balance between the electric repulsion between protons and the strong force binding protons and neutrons together. Protons and neutrons are arranged in shells, just like electrons, and so a closed shell can significantly increase stability: the known superheavy nuclei exist because of such a shell closure. They are probably close to a predicted island of stability, where superheavy nuclides should have significantly longer half-lives: predictions range from minutes or days, to millions or billions of years. However, as the number of protons increases beyond about 126, this stabilising effect should vanish as a closed shell is passed. It is not clear if any further-out shell closures exist, due to an expected smearing out of distinct nuclear shells (as is already expected for the electron shells at oganesson). Furthermore, even if later shell closures exist, it is not clear if they would allow such heavy elements to exist.Scerri, p. 386 As such, it may be that the periodic table practically ends around element 120, as elements become too short-lived to observe; the era of discovering new elements would thus be close to its end.

Alternatively, may become stable at high mass numbers, in which the nucleus is composed of freely flowing and instead of binding them into protons and neutrons; this would create a continent of stability instead of an island. Other effects may come into play: for example, in very heavy elements the 1s electrons are likely to spend a significant amount of time so close to the nucleus that they are actually inside it, which would make them vulnerable to .

Even if eighth-row elements can exist, producing them is likely to be difficult, and it should become even more difficult as atomic number rises. Although the 8s elements are expected to be reachable with present means, the first few elements are expected to require new technology, if they can be produced at all. Experimentally characterising these elements chemically would also pose a great challenge.


Alternative periodic tables
The periodic law may be represented in multiple ways, of which the standard periodic table is only one.Scerri, p. 20 Within 100 years of the appearance of Mendeleev's table in 1869, Edward G. Mazurs had collected an estimated 700 different published versions of the periodic table. Many forms retain the rectangular structure, including 's left-step periodic table (pictured below), and the modernised form of Mendeleev's original 8-column layout that is still common in Russia. Other periodic table formats have been shaped much more exotically, such as spirals (Otto Theodor Benfey's pictured to the right), circles, triangles, and even elephants.

Alternative periodic tables are often developed to highlight or emphasize chemical or physical properties of the elements that are not as apparent in traditional periodic tables, with different ones skewed more towards emphasizing chemistry or physics at either end.Scerri, pp. 402–3 The standard form, which remains by far the most common, is somewhere in the middle.

The many different forms of the periodic table have prompted the questions of whether there is an optimal or definitive form of the periodic table, and if so, what it might be. There are no current consensus answers to either question. Janet's left-step table is being increasingly discussed as a candidate for being the optimal or most fundamental form; Scerri has written in support of it, as it clarifies helium's nature as an s-block element, increases regularity by having all period lengths repeated, faithfully follows Madelung's rule by making each period correspond to one value of + , and regularises atomic number triads and the first-row anomaly trend. He notes that its placement of helium atop the alkaline earth metals can be seen a disadvantage from a chemical perspective, but counters this by appealing to the first-row anomaly, pointing out that the periodic table "fundamentally reduces to quantum mechanics", and that it is concerned with "abstract elements" and hence atomic properties rather than macroscopic properties.


Notes

Bibliography


Further reading


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