In the standard periodic table, the elements are listed in order of increasing atomic number. A new row (period) is started when a new electron shell has its first electron. Columns (groups) are determined by the electron configuration of the atom; elements with the same number of electrons in a particular subshell fall into the same columns (e.g. oxygen, sulfur, and selenium are in the same column because they all have four electrons in the outermost p-subshell). Elements with similar chemical properties generally fall into the same group in the periodic table, although in the f-block, and to some respect in the d-block, the elements in the same period tend to have similar properties, as well. Thus, it is relatively easy to predict the chemical properties of an element if one knows the properties of the elements around it.
Today, 118 elements are known, the first 94 of which are known to occur naturally on Earth at present. The remaining 24, americium to oganesson (95–118), occur only when synthesized in laboratories. Of the 94 naturally occurring elements, 83 are primordial and 11 occur only in decay chains of primordial elements. A few of the latter are so rare that they were not discovered in nature, but were synthesized in the laboratory before it was determined that they do exist in nature after all: technetium (element 43), promethium (element 61), astatine (element 85), neptunium (element 93), and plutonium (element 94). No element heavier than einsteinium (element 99) has ever been observed in macroscopic quantities in its pure form, nor has astatine; francium (element 87) has been only photographed in the form of light emitted from microscopic quantities (300,000 atoms). Of the 94 natural elements, eighty have a stable isotope and one more (bismuth) has an almost-stable isotope (with a half-life of 2.01×1019 years, over a billion times the age of the universe). Two more, thorium and uranium, 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.
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. Groups can also be named by their first element, e.g. the "scandium group" for group 3. Previously, groups were known by Roman numerals. In the United States, the Roman numerals were followed by either an "A" if the group was in the s- or p-block, or a "B" if the group was in the d-block. 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 group 14 elements were group IVA). In Europe, the lettering was similar, except that "A" was used for groups 1 through 7, and "B" was used for groups 11 through 17. 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 IUPAC (International Union of Pure and Applied Chemistry) naming system (1–18) was put into use, and the old group names (I–VIII) were deprecated.
For reasons of space, the periodic table is commonly presented with the f-block elements cut out and positioned as a distinct part below the main body. This 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. 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.
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 atomic number. Elements are placed in the periodic table according to their electron configurations, the periodic recurrences of which explain the trends in properties across the periodic table.
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 characterized by the quantum numbers. Four numbers describe an orbital in an atom completely: the principal quantum number n, the azimuthal quantum number ℓ (the orbital type), the orbital magnetic quantum number mℓ, and the spin magnetic quantum number ms.
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 hydrogen, 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. Helium adds a second electron, which also goes into 1s, completely filling the first shell and giving the configuration 1s2.
The first 18 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. (Some contemporary authors question even this single exception, preferring to consistently follow the valence configurations and place helium over beryllium.) There are eight columns in this periodic table fragment, corresponding to at most eight outer-shell electrons. 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.
This completes the modern periodic table, with all seven rows completely filled to capacity.
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. Completely filled subshells have been greyed out.
Although the modern periodic table is standard today, the placement of the period 1 elements hydrogen and helium remains an open issue under discussion, and some variation can be found. Following their respective s1 and s2 electron configurations, hydrogen would be placed in group 1, and helium would be placed in group 2. The group 1 placement of hydrogen is common, but helium is almost always placed in group 18 with the other noble gases. The debate has to do with conflicting understandings of the extent to which chemical or electronic properties should decide periodic table placement.
Like the group 1 metals, hydrogen has one electron in its outermost shell and typically loses its only electron in chemical reactions. Hydrogen has some metal-like chemical properties, being able to displace some metals from their salts. But it forms a diatomic nonmetallic gas at standard conditions, unlike the alkali metals which are reactive solid metals. This and hydrogen's formation of hydrides, in which it gains an electron, brings it close to the properties of the halogens which do the same (though it is rarer for hydrogen to form H− than H+). Moreover, the lightest two halogens (fluorine and chlorine) are gaseous like hydrogen at standard conditions. Some properties of hydrogen are not a good fit for either group: hydrogen is neither highly oxidizing 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. This last option has nonetheless been criticized by the chemist and philosopher of science Eric Scerri on the grounds that it appears to imply that hydrogen is above the periodic law altogether, unlike all the other elements.
Helium is the only element that routinely occupies a position in the periodic table that is not consistent with its electronic structure. It 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. However it is unreactive 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. For these reasons helium is nearly universally placed in group 18 which its properties best match; a proposal to move helium to group 2 was rejected by IUPAC in 1988 for these reasons. Nonetheless, helium is still occasionally placed in group 2 today, and some of its physical and chemical properties are closer to the group 2 elements and support the electronic placement. 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. Recent theoretical developments in noble gas chemistry, in which helium is expected to show slightly less inertness than neon and to form (HeO)(LiF)2 with a structure similar to the analogous beryllium compound (but with no expected neon analogue), have resulted in more chemists advocating a placement of helium in group 2. This relates to the electronic argument, as the reason for neon's greater inertness is repulsion from its filled p-shell that helium lacks, though realistically it is unlikely that helium-containing molecules will be stable outside extreme low-temperature conditions (around 10 K).
In many periodic tables, the f-block is shifted one element to the right, so that lanthanum and actinium become d-block elements in group 3, and Ce–Lu and Th–Lr form the f-block. Thus the d-block is split into two very uneven portions. This is a holdover from early mistaken measurements of electron configurations; modern measurements are more consistent with the form with lutetium and lawrencium in group 3, and with La–Yb and Ac–No as the f-block.
A third form can sometimes be encountered in which the spaces below yttrium in group 3 are left empty, such as the table appearing on the IUPAC web site, but this creates an inconsistency with quantum mechanics by making the f-block 15 elements wide (La–Lu and Ac–Lr) even though only 14 electrons can fit in an f-subshell. There is moreover some confusion in the literature on which elements are then implied to be in group 3. While the 2021 IUPAC report noted that 15-element-wide f-blocks are supported by some practitioners of a specialized branch of relativistic quantum mechanics focusing on the properties of superheavy elements, the project'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". Other authors focusing on superheavy elements since clarified that the "15th entry of the f-block represents the first slot of the d-block which is left vacant to indicate the place of the f-block inserts", which would imply that this form still has lutetium and lawrencium (the 15th entries in question) as d-block elements in group 3. Indeed, when IUPAC publications expand the table to 32 columns, they make this clear and place lutetium and lawrencium under yttrium in group 3.
Several arguments in favour of Sc-Y-La-Ac can be encountered in the literature, but they have been challenged as being logically inconsistent. For example, it has been argued that lanthanum and actinium cannot be f-block elements because as individual gas-phase atoms, they have not begun to fill the f-subshells. But the same is true of thorium which is never disputed as an f-block element, and this argument overlooks the problem on the other end: that the f-shells complete filling at ytterbium and nobelium, matching the Sc-Y-Lu-Lr form, and not at lutetium and lawrencium as the Sc-Y-La-Ac form would have it. Not only are such exceptional configurations in the minority, but they have also in any case never been considered as relevant for positioning any other elements on the periodic table: in gaseous atoms, the d-shells complete their filling at copper, palladium, and gold, but it is universally accepted by chemists that these configurations are exceptional and that the d-block really ends in accordance with the Madelung rule at zinc, cadmium, and mercury. The relevant fact for placement is that lanthanum and actinium (like thorium) have valence f orbitals that can become occupied in chemical environments, whereas lutetium and lawrencium do not: their f-shells are in the core, and cannot be used for chemical reactions. Thus the relationship between yttrium and lanthanum is only a secondary relationship between elements with the same number of valence electrons but different kinds of valence orbitals, such as that between chromium and uranium; whereas the relationship between yttrium and lutetium is primary, sharing both valence electron count and valence orbital type.
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. As analogous configurations occur 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.
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 Arthur Haas in 1910 to within an order of magnitude (a factor of 10) of the accepted value, the Bohr radius (~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.
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, 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. A similar situation holds for the d-block, with lutetium through tungsten atoms being slightly smaller than yttrium through molybdenum atoms respectively.
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 stabilized and shrunken (it fills in thallium and lead), but the other two (filling in bismuth through radon) are relativistically destabilized and expanded. Relativistic effects also explain why gold 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 (hassium), and experimental chemistry beyond 108 has only been done for elements 112 (copernicium) through 115 (moscovium), so the chemical characterization of the heaviest elements remains a topic of current research.
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.
Some atoms, like the noble gases, have no electron affinity: they cannot form stable gas-phase anions. (They can form metastable resonances if the incoming electron arrives with enough kinetic energy, but these inevitably and rapidly autodetach: for example, the lifetime of the most long-lived He− level is about 359 microseconds.) 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 (because of extreme interelectronic repulsion for the very small fluorine atom), but is more reactive.
The electron configuration suggests a ready explanation from the number of electrons available for bonding; indeed, the number of valence electrons starts at 1 in group 1, and then increases towards the right side of the periodic table, only resetting at 3 whenever each new block starts. Thus in period 6, Cs–Ba have 1–2 valence electrons; La–Yb have 3–16; Lu–Hg have 3–12; and Tl–Rn have 3–8. However, towards the right side of the d- and f-blocks, the theoretical maximum corresponding to using all valence electrons is not achievable at all; the same situation affects oxygen, fluorine, and the light noble gases up to krypton.
Number of valence electronsA full explanation requires considering the energy that would be released in forming compounds with different valences rather than simply considering electron configurations alone. 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 enthalpy 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 ionizing 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 hybridization can be used for the less electronegative p-block elements.
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 silver), 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. Because ionizing 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 ionize 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. OsO4), and then decrease to +2 at the end. The lanthanides and late actinides usually have high fourth ionisation energies and hence rarely surpass the +3 oxidation state, whereas early actinides have low fourth ionisation energies and so for example neptunium and plutonium can reach +7. The very last actinides go further than the lanthanides towards low oxidation states: mendelevium is more easily reduced to the +2 state than thulium or even europium (the lanthanide with the most stable +2 state, on account of its half-filled f-shell), and nobelium outright favours +2 over +3, in contrast to ytterbium.
As elements in the same group share the same valence configurations, they usually exhibit similar chemical behaviour. For example, the alkali metals 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 heterogeneous. 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 group 14 comprise a nonmetal (carbon), two semiconductors (silicon and germanium), and two metals (tin and lead); they are nonetheless united by having four valence electrons. This often leads to similarities in maximum and minimum oxidation states (e.g. sulfur and selenium in group 16 both have maximum oxidation state +6, as in SO3 and SeO3, and minimum oxidation state −2, as in sulfides and selenides); but not always (e.g. oxygen is not known to form oxidation state +6, despite being in the same group as sulfur and selenium).
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 (fluorine) is given electronegativity 4.0, and the least electronegative atom (caesium) is given electronegativity 0.79. In fact neon is the most electronegative element, but the Pauling scale cannot measure its electronegativity because it does not form covalent bonds with most elements.
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. 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.
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 synchronized 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 metallic bond. Elements forming such bonds are often called metals; those which do not are often called nonmetals. Some elements can form multiple simple substances with different structures: these are called allotropes. For example, diamond and graphite 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 delocalized 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.
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 band gaps and are semiconductors at ambient conditions: electrons can cross the gap when thermally excited. (Boron is also a semiconductor at ambient conditions.) The band gap disappears in tin, so that tin and lead become metals. As the temperature rises, all nonmetals develop some semiconducting properties, to a greater or lesser extent depending on the size of the band gap. Thus metals and nonmetals may be distinguished by the temperature dependence of their electrical conductivity: a metal's conductivity lowers as temperature rises (because thermal motion makes it more difficult for the electrons to flow freely), whereas a nonmetal's conductivity rises (as more electrons may be excited to cross the gap).
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 and yellow arsenic (P4 and As4), sulfur and red selenium (S8 and Se8), 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, antimony, bismuth) that only extend in one or two rather than three dimensions. Both kinds of structures can be found as allotropes of phosphorus, arsenic, and selenium, although the long-chained allotropes are more stable in all three. 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, antimony, and bismuth are semimetals (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 metalloids. 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 network 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 characterized 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.
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 kinetic energy: 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 generalizations: for example, beryllium, chromium, manganese, antimony, bismuth, and uranium are brittle (not an exhaustive list); chromium is extremely hard; gallium, rubidium, caesium, and mercury are liquid at or close to room temperature; and noble metals 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, and tellurium. Selenium has both a semiconducting grey allotrope and an insulating red allotrope; arsenic has a metallic grey allotrope, a semiconducting black allotrope, and an insulating yellow allotrope (though the last is unstable at ambient conditions). 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. For example, unlike all the other elements generally considered metalloids or nonmetals, antimony's only stable form has metallic conductivity. Moreover, the element resembles bismuth and, more generally, the other p-block metals in its physical and chemical behaviour. On this basis some authors have argued that it is better classified as a metal than as a metalloid. On the other hand, selenium has some semiconducting properties in its most stable form (though it also has insulating allotropes) and it has been argued that it should be considered a metalloid – though this situation also holds for phosphorus, which is a much rarer inclusion among the metalloids.
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). 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. Relationships between elements with the same number of valence electrons but different types of valence orbital have been called secondary or isodonor relationships: they usually have the same maximum oxidation states, but not the same minimum oxidation states. For example, chlorine and manganese both have +7 as their maximum oxidation state (e.g. Cl2O7 and Mn2O7), but their respective minimum oxidation states are −1 (e.g. HCl) and −3 (K2[Mn(CO)4]). Elements with the same number of valence vacancies but different numbers of valence electrons are related by a tertiary or isoacceptor relationship: they usually have similar minimum but not maximum oxidation states. For example, hydrogen and chlorine both have −1 as their minimum oxidation state (in hydrides and chlorides), but hydrogen's maximum oxidation state is +1 (e.g. H2O) while chlorine's is +7.
Many other physical properties of the elements exhibit periodic variation in accordance with the periodic law, such as melting points, boiling points, heats of fusion, heats of vaporization, 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 acidic 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.
Many terms have been used in the literature to describe sets of elements that behave similarly. The group names alkali metal, alkaline earth metal, triel, tetrel, 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 and IUPAC does not presently mention it as allowable in its Principles of Chemical Nomenclature.
Many more categorizations 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. A few terms are widely used, but without any very formal definition, such as "heavy metal", which has been given such a wide range of definitions that it has been criticized 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 specialize 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.
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 Bohuslav Brauner 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 asteroid belt instead of a single planet between Mars and Jupiter, so the place below yttrium was thought to be occupied by all the lanthanides instead of just one element.
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 atoms (shown to the right) mostly do not accord with those now known. They were improved further after the work of Arnold Sommerfeld and Edmund Stoner discovered more quantum numbers.
Bohr's electron configurations for light elements
The first one to systematically expand and correct the chemical potentials of Bohr's atomic theory was Walther Kossel 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:
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 Julius Thomsen in 1895, and the Swiss chemist Alfred Werner in 1905. Bohr used Thomsen's form in his 1922 Nobel Lecture; Werner's form is very similar to the modern 32-column form. In particular, this supplanted Brauner's asteroidal hypothesis.
In 1988, IUPAC released a report supporting this composition of group 3, a decision that was reaffirmed in 2021. Variation can still be found in textbooks on the composition of group 3, and some argumentation against this format is still published today, but chemists and physicists who have considered the matter largely agree on group 3 containing scandium, yttrium, lutetium, and lawrencium and challenge the counterarguments as being inconsistent.
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 synthesized artificially via nuclear reactions rather than discovered in nature. It was discovered in 1937 by Italian chemists Emilio Segrè and Carlo Perrier, who named their discovery technetium, after the Greek word for "artificial". Elements 61 (promethium) and 85 (astatine) were likewise produced artificially in 1945 and 1940 respectively; element 87 (francium) became the last element to be discovered in nature, by French chemist Marguerite Perey in 1939. The elements beyond uranium were likewise discovered artificially, starting with Edwin McMillan and Philip Abelson's 1940 discovery of neptunium (via bombardment of uranium with neutrons). Glenn T. Seaborg and his team at the Lawrence Berkeley National Laboratory (LBNL) continued discovering transuranium elements, starting with plutonium in 1941, 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 Charles Janet (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 synthesized up to 1955, 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 Albert Ghiorso) and a team of Soviet scientists at the Joint Institute for Nuclear Research (JINR) led by Georgy Flyorov. 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. IUPAC at first adopted a hands-off approach, preferring to wait and see if a consensus would be forthcoming. But as it was also the height of the Cold War, it became clear 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 (Riken). 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 Yuri Oganessian 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. 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.
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 164"), or by the IUPAC systematic element names adopted in 1978, which directly relate to the atomic numbers (e.g. "unhexquadium" for element 164, derived from Latin unus "one", Greek hexa "six", Latin quadra "four", and the traditional -ium suffix for metallic elements). All attempts to synthesize such elements have failed so far. An attempt to make element 119 has been ongoing since 2018 at the Riken research institute in Japan. The LBNL in the United States, the JINR in Russia, and the Heavy Ion Research Facility in Lanzhou (HIRFL) in China also plan to make their own attempts at synthesizing the first few period 8 elements.
If the eighth period followed the pattern set by the earlier periods, then it would contain fifty elements, filling the 8s, 5g, 6f, 7d, and finally 8p subshells in that order. But by this point, relativistic effects should result in significant deviations from the Madelung rule. Various different models have been suggested for the configurations of eighth-period elements, as well as how to show the results in a periodic table. All agree that the eighth period should begin like the previous ones with two 8s elements, 119 and 120. However, after that the massive energetic overlaps between the 5g, 6f, 7d, and 8p subshells means that they all begin to fill together, and it is not clear how to separate out specific 5g and 6f series. Elements 121 through 156 thus do not fit well as chemical analogues of any previous group in the earlier parts of the table, although they have sometimes been placed as 5g, 6f, and other series to formally reflect their electron configurations. Eric 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.
The situation from elements 157 to 172 should return to normalcy and be more reminiscent of the earlier rows. The heavy p-shells are split by the spin–orbit interaction: one p orbital (p1/2) is more stabilized, and the other two (p3/2) are destabilized. (Such shifts in the quantum numbers happen for all types of shells, but it makes the biggest difference to the order for the p-shells.) It is likely that by element 157, the filled 8s and 8p1/2 shells with four electrons in total have sunk into the core. Beyond the core, the next orbitals are 7d and 9s at similar energies, followed by 9p1/2 and 8p3/2 at similar energies, and then a large gap. Thus, the 9s and 9p1/2 orbitals in essence replace the 8s and 8p1/2 ones, making elements 157–172 probably chemically analogous to groups 3–18: for example, element 164 would appear two places below lead in group 14 under the usual pattern, but is calculated to be very analogous to palladium in group 10 instead. Thus, it takes fifty-four elements rather than fifty to reach the next noble element after 118. However, while these conclusions about elements 157 through 172's chemistry are generally agreed by models, there is disagreement on whether the periodic table should be drawn to reflect chemical analogies, or if it should reflect likely formal electron configurations, which should be quite different from earlier periods and are not agreed between sources. Discussion about the format of the eighth row thus continues.
Beyond element 172, calculation is complicated by the 1s electron energy level becoming imaginary. Such a situation does have a physical interpretation and does not in itself pose an electronic limit to the periodic table, but the correct way to incorporate such states into multi-electron calculations is still an open question needing to be solved to calculate the periodic table's structure beyond this point.
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, probably at around 114–126 protons and 184 neutrons. They are probably close to a predicted island of stability, where superheavy nuclides should be more long-lived than expected: predictions for the longest-lived nuclides on the island range from microseconds to millions of years. It should nonetheless be noted that these are essentially extrapolations into an unknown part of the chart of nuclides, and systematic model uncertainties need to be taken into account.
As the closed shells are passed, the stabilizing effect should vanish. Thus, superheavy nuclides with more than 184 neutrons are expected to have much shorter lifetimes, spontaneously fissioning within 10−15 seconds. If this is so, then it would not make sense to consider them chemical elements: [IUPAC/IUPAP theorizes and recommends] an element to exist only if the nucleus lives longer than 10−14 seconds, the time needed for it to gather an electron cloud. Nonetheless, theoretical estimates of half-lives are very model-dependent, ranging over many orders of magnitude. The extreme repulsion between protons is predicted to result in exotic nuclear topologies, with bubbles, rings, and tori expected: this further complicates extrapolation. 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. As such, it may be that the periodic table practically ends around element 120, as elements become too short-lived to observe, and then too short-lived to have chemistry; the era of discovering new elements would thus be close to its end. If another proton shell closure beyond 126 does exist, then it probably occurs around 164; thus the region where periodicity fails more or less matches the region of instability between the shell closures.
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 119 and 120 are expected to be reachable with present means, the elements beyond that are expected to require new technology, if they can be produced at all. Experimentally characterizing these elements chemically would also pose a great challenge.
The periodic law may be represented in multiple ways, of which the standard periodic table is only one. 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 Charles Janet'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 and triangles.
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. 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 n + ℓ, and regularises atomic number triads and the first-row anomaly trend. While he notes that its placement of helium atop the alkaline earth metals can be seen a disadvantage from a chemical perspective, he 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.
The question of how many natural elements there are is quite complicated and is not fully resolved. The heaviest element that occurs in large quantities on Earth is element 92, uranium. However, uranium can undergo spontaneous fission in nature, and the resulting neutrons can strike other uranium atoms. If neutron capture then occurs, elements 93 and 94, neptunium and plutonium, are formed via beta decay;[10] these are in fact more common than some of the rarest elements in the first 92, such as promethium, astatine, and francium (see Abundance of elements in Earth's crust). Theoretically, neutron capture on the resulting plutonium might produce even higher-numbered elements, but the quantities would be too small to be observed.[10] In the early Solar System, shorter-lived elements had not yet decayed away, and consequently there were more than 94 naturally occurring elements. Curium (element 96) is the longest-lived element beyond the first 94, and is probably still being brought to Earth via cosmic rays, but it has not been found.[10] Elements up to 99 (einsteinium) have been observed in Przybylski's Star.[11] Elements up to 100 (fermium) probably occurred in the natural nuclear fission reactor at Oklo Mine, Gabon, but they have long since decayed away.[12] Even heavier elements may be produced in the r-process via supernovae or neutron star mergers, but this has not been confirmed. It is not clear how far they would extend past 100 and how long they would last: calculations suggest that nuclides of mass number around 280 to 290 are formed in the r-process, but quickly beta decay to nuclides that suffer spontaneous fission, so that 99.9% of the produced superheavy nuclides would decay within a month.[13] If instead they were sufficiently long-lived, they might similarly be brought to Earth via cosmic rays, but again none have been found.[10] /wiki/Uranium
"Periodic Table of Elements". IUPAC | International Union of Pure and Applied Chemistry. Retrieved 11 May 2024. https://iupac.org/what-we-do/periodic-table-of-elements/
Meija, Juris; et al. (2016). "Atomic weights of the elements 2013 (IUPAC Technical Report)". Pure and Applied Chemistry. 88 (3): 265–291. doi:10.1515/pac-2015-0305. https://doi.org/10.1515%2Fpac-2015-0305
Prohaska, Thomas; Irrgeher, Johanna; Benefield, Jacqueline; Böhlke, John K.; Chesson, Lesley A.; Coplen, Tyler B.; Ding, Tiping; Dunn, Philip J. H.; Gröning, Manfred; Holden, Norman E.; Meijer, Harro A. J. (4 May 2022). "Standard atomic weights of the elements 2021 (IUPAC Technical Report)". Pure and Applied Chemistry. doi:10.1515/pac-2019-0603. ISSN 1365-3075. https://www.degruyter.com/document/doi/10.1515/pac-2019-0603/html
An element zero (i.e. a substance composed purely of neutrons), is included in a few alternate presentations, for example, in the Chemical Galaxy. See Labarca, M. (2016). "An element of atomic number zero?". New Journal of Chemistry. 40 (11): 9002–9006. doi:10.1039/C6NJ02076C. hdl:11336/46854. ISSN 1144-0546. /wiki/Neutronium
IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Chemical element". doi:10.1351/goldbook.C01022 /wiki/International_Union_of_Pure_and_Applied_Chemistry
"Periodic Table of Elements". iupac.org. IUPAC. 2021. Archived from the original on 10 April 2016. Retrieved 3 April 2021. https://iupac.org/what-we-do/periodic-table-of-elements/
"Periodic Table of Elements". iupac.org. IUPAC. 2021. Archived from the original on 10 April 2016. Retrieved 3 April 2021. https://iupac.org/what-we-do/periodic-table-of-elements/
"Standard Atomic Weights". Commission on Isotopic Abundances and Atomic Weights. International Union of Pure and Applied Chemistry. 2019. Archived from the original on 8 August 2020. Retrieved 7 February 2021. https://www.ciaaw.org/atomic-weights.htm
Greenwood & Earnshaw, pp. 24–27
Gray, p. 6
Thornton, Brett F.; Burdette, Shawn C. (2019). "Neutron stardust and the elements of Earth". Nature Chemistry. 11 (1): 4–10. Bibcode:2019NatCh..11....4T. doi:10.1038/s41557-018-0190-9. PMID 30552435. S2CID 54632815. Archived from the original on 14 August 2021. Retrieved 19 February 2022. https://www.nature.com/articles/s41557-018-0190-9
The question of how many natural elements there are is quite complicated and is not fully resolved. The heaviest element that occurs in large quantities on Earth is element 92, uranium. However, uranium can undergo spontaneous fission in nature, and the resulting neutrons can strike other uranium atoms. If neutron capture then occurs, elements 93 and 94, neptunium and plutonium, are formed via beta decay;[10] these are in fact more common than some of the rarest elements in the first 92, such as promethium, astatine, and francium (see Abundance of elements in Earth's crust). Theoretically, neutron capture on the resulting plutonium might produce even higher-numbered elements, but the quantities would be too small to be observed.[10] In the early Solar System, shorter-lived elements had not yet decayed away, and consequently there were more than 94 naturally occurring elements. Curium (element 96) is the longest-lived element beyond the first 94, and is probably still being brought to Earth via cosmic rays, but it has not been found.[10] Elements up to 99 (einsteinium) have been observed in Przybylski's Star.[11] Elements up to 100 (fermium) probably occurred in the natural nuclear fission reactor at Oklo Mine, Gabon, but they have long since decayed away.[12] Even heavier elements may be produced in the r-process via supernovae or neutron star mergers, but this has not been confirmed. It is not clear how far they would extend past 100 and how long they would last: calculations suggest that nuclides of mass number around 280 to 290 are formed in the r-process, but quickly beta decay to nuclides that suffer spontaneous fission, so that 99.9% of the produced superheavy nuclides would decay within a month.[13] If instead they were sufficiently long-lived, they might similarly be brought to Earth via cosmic rays, but again none have been found.[10] /wiki/Uranium
Emsley, John (2011). Nature's Building Blocks: An A-Z guide to the elements (New ed.). New York, NY: Oxford University Press. ISBN 978-0-19-960563-7. 978-0-19-960563-7
Silva, Robert J. (2006). "Fermium, Mendelevium, Nobelium and Lawrencium". In Morss, L. R.; Edelstein, N. M.; Fuger, J. (eds.). The Chemistry of the Actinide and Transactinide Elements (3rd ed.). Dordrecht: Springer Science+Business Media. ISBN 978-1-4020-3555-5. 978-1-4020-3555-5
Marcillac, Pierre de; Noël Coron; Gérard Dambier; Jacques Leblanc; Jean-Pierre Moalic (April 2003). "Experimental detection of α-particles from the radioactive decay of natural bismuth". Nature. 422 (6934): 876–878. Bibcode:2003Natur.422..876D. doi:10.1038/nature01541. PMID 12712201. S2CID 4415582. /wiki/Bibcode_(identifier)
Some isotopes currently considered stable are theoretically expected to be radioactive with extremely long half-lives: for instance, all the stable isotopes of elements 62 (samarium), 63 (europium), and all elements from 67 (holmium) onward are expected to undergo alpha decay or double beta decay. However, the predicted half-lives are extremely long (e.g. the alpha decay of 208Pb to the ground state of 204Hg is expected to have a half-life greater than 10120 years), and the decays have never been observed.[16][17] /wiki/Samarium
The half-life of plutonium's most stable isotope is just long enough that it should also be a primordial element. A 1971 study claimed to have detected primordial plutonium,[18] but a more recent study from 2012 could not detect it.[19] Based on its likely initial abundance in the Solar System, present experiments as of 2022 are likely about an order of magnitude away from detecting live primordial 244Pu.[20] /wiki/Plutonium
Tiny traces of plutonium are also continually brought to Earth via cosmic rays.[21]
"Periodic Table of Elements". iupac.org. IUPAC. 2021. Archived from the original on 10 April 2016. Retrieved 3 April 2021. https://iupac.org/what-we-do/periodic-table-of-elements/
Connelly, N. G.; Damhus, T.; Hartshorn, R. M.; Hutton, A. T. (2005). Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005 (PDF). RSC Publishing. p. 51. ISBN 978-0-85404-438-2. Archived (PDF) from the original on 23 November 2018. Retrieved 26 November 2018. 978-0-85404-438-2
Connelly, N. G.; Damhus, T.; Hartshorn, R. M.; Hutton, A. T. (2005). Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005 (PDF). RSC Publishing. p. 51. ISBN 978-0-85404-438-2. Archived (PDF) from the original on 23 November 2018. Retrieved 26 November 2018. 978-0-85404-438-2
Fluck, E. (1988). "New Notations in the Periodic Table" (PDF). Pure Appl. Chem. 60 (3): 431–436. doi:10.1351/pac198860030431. S2CID 96704008. Archived (PDF) from the original on 25 March 2012. Retrieved 24 March 2012. https://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf
Fluck, E. (1988). "New Notations in the Periodic Table" (PDF). Pure Appl. Chem. 60 (3): 431–436. doi:10.1351/pac198860030431. S2CID 96704008. Archived (PDF) from the original on 25 March 2012. Retrieved 24 March 2012. https://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf
Scerri, Eric (18 January 2021). "Provisional Report on Discussions on Group 3 of the Periodic Table" (PDF). Chemistry International. 43 (1): 31–34. doi:10.1515/ci-2021-0115. S2CID 231694898. Archived (PDF) from the original on 13 April 2021. Retrieved 9 April 2021. https://iupac.org/wp-content/uploads/2021/04/ChemInt_Jan2021_PP.pdf
William B. Jensen (1982). "The Positions of Lanthanum (Actinium) and Lutetium (Lawrencium) in the Periodic Table". J. Chem. Educ. 59 (8): 634–636. Bibcode:1982JChEd..59..634J. doi:10.1021/ed059p634. /wiki/Bibcode_(identifier)
L. D. Landau, E. M. Lifshitz (1958). Quantum Mechanics: Non-Relativistic Theory. Vol. 3 (1st ed.). Pergamon Press. pp. 256–7. /wiki/Lev_Landau
Jensen, William B. (2015). "The positions of lanthanum (actinium) and lutetium (lawrencium) in the periodic table: an update". Foundations of Chemistry. 17: 23–31. doi:10.1007/s10698-015-9216-1. S2CID 98624395. Archived from the original on 30 January 2021. Retrieved 28 January 2021. https://link.springer.com/article/10.1007/s10698-015-9216-1
Scerri, Eric (2009). "Which Elements Belong in Group 3?". Journal of Chemical Education. 86 (10): 1188. doi:10.1021/ed086p1188. Retrieved 1 January 2023. https://pubs.acs.org/doi/pdf/10.1021/ed086p1188
Chemey, Alexander T.; Albrecht-Schmitt, Thomas E. (2019). "Evolution of the periodic table through the synthesis of new elements". Radiochimica Acta. 107 (9–11): 1–31. doi:10.1515/ract-2018-3082. /wiki/Doi_(identifier)
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Pfeiffer, Paul (1920). "Die Befruchtung der Chemie durch die Röntgenstrahlenphysik". Naturwissenschaften (in German). 8 (50): 984–991. Bibcode:1920NW......8..984P. doi:10.1007/BF02448807. S2CID 7071495. https://link.springer.com/article/10.1007/BF02448807
Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
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Fluck, E. (1988). "New Notations in the Periodic Table" (PDF). Pure Appl. Chem. 60 (3): 431–436. doi:10.1351/pac198860030431. S2CID 96704008. Archived (PDF) from the original on 25 March 2012. Retrieved 24 March 2012. https://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf
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Thyssen, P.; Binnemans, K. (2011). "Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis". In Gschneidner, K. A. Jr.; Bünzli, J-C.G; Vecharsky, Bünzli (eds.). Handbook on the Physics and Chemistry of Rare Earths. Vol. 41. Amsterdam: Elsevier. pp. 1–93. doi:10.1016/B978-0-444-53590-0.00001-7. ISBN 978-0-444-53590-0. 978-0-444-53590-0
"Periodic Table of Elements". iupac.org. IUPAC. 2021. Archived from the original on 10 April 2016. Retrieved 3 April 2021. https://iupac.org/what-we-do/periodic-table-of-elements/
Thyssen, P.; Binnemans, K. (2011). "Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis". In Gschneidner, K. A. Jr.; Bünzli, J-C.G; Vecharsky, Bünzli (eds.). Handbook on the Physics and Chemistry of Rare Earths. Vol. 41. Amsterdam: Elsevier. pp. 1–93. doi:10.1016/B978-0-444-53590-0.00001-7. ISBN 978-0-444-53590-0. 978-0-444-53590-0
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"The constitution of group 3 of the periodic table". IUPAC. 2015. Archived from the original on 5 July 2016. Retrieved 30 July 2016. https://iupac.org/projects/project-details/?project_nr=2015-039-2-200
See for example the periodic table poster sold by Sigma-Aldrich. https://www.sigmaaldrich.com/SG/en/product/aldrich/z543209
Scerri, p. 17
"periodic law". Merriam-Webster.com Dictionary. Merriam-Webster. Retrieved 29 March 2021. https://www.merriam-webster.com/dictionary/periodic%20law
Jensen, William B. (2009). "Misapplying the Periodic Law". Journal of Chemical Education. 86 (10): 1186. Bibcode:2009JChEd..86.1186J. doi:10.1021/ed086p1186. /wiki/William_B._Jensen
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Petrucci et al., p. 323
Strictly speaking, one cannot draw an orbital such that the electron is guaranteed to be inside it, but it can be drawn to guarantee a 90% probability of this for example.[41]
Petrucci et al., p. 322
Ball, David W.; Key, Jessie A. (2011). Introductory Chemistry (1st Canadian ed.). Vancouver, British Columbia: BC Campus (opentextbc.ca). ISBN 978-1-77420-003-2. Archived from the original on 15 August 2021. Retrieved 15 August 2021. 978-1-77420-003-2
"Electron Configurations". www.chem.fsu.edu. Florida State University. 6 May 2020. Archived from the original on 6 May 2022. Retrieved 17 April 2022. https://www.chem.fsu.edu/chemlab/chm1045/e_config.html
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Goudsmit, S. A.; Richards, Paul I. (1964). "The Order of Electron Shells in Ionized Atoms" (PDF). Proc. Natl. Acad. Sci. 51 (4): 664–671 (with correction on p 906). Bibcode:1964PNAS...51..664G. doi:10.1073/pnas.51.4.664. PMC 300183. PMID 16591167. Archived (PDF) from the original on 10 October 2017. Retrieved 15 August 2021. https://www.pnas.org/content/51/4/664.full.pdf
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jolly, William L. (1984). Modern Inorganic Chemistry (1st ed.). McGraw-Hill. pp. 10–12. ISBN 0-07-032760-2. 0-07-032760-2
Ostrovsky, V. N. (May 2001). "What and How Physics Contributes to Understanding the Periodic Law". Foundations of Chemistry. 3 (2): 145–181. doi:10.1023/A:1011476405933. S2CID 15679915. /wiki/Doi_(identifier)
Ostrovsky, V. N. (1981). "Dynamic symmetry of atomic potential". Journal of Physics B: Atomic and Molecular Physics. 14 (23): 4425–4439. Bibcode:1981JPhB...14.4425O. doi:10.1088/0022-3700/14/23/008. /wiki/Bibcode_(identifier)
Wong, D. Pan (1979). "Theoretical justification of Madelung's rule". J. Chem. Educ. 56 (11): 714–718. Bibcode:1979JChEd..56..714W. doi:10.1021/ed056p714. /wiki/Journal_of_Chemical_Education
Authors differ on whether the n + ℓ rule has yet been derived from quantum mechanics. Scerri claims that it has not,[290][291] despite several attempts to do so.[292] On the other hand, Ostrovsky, who has claimed such justification from 1971, wrote "Some authors insist that 'still nobody has deduced the n+l rule from the principles of quantum
mechanics', while others present quantum justification of the rule that was not ever disputed."[293] Other authors argue that such a derivation is not necessary, because it admits exceptions.[294]
Ostrovsky, V. N. (May 2001). "What and How Physics Contributes to Understanding the Periodic Law". Foundations of Chemistry. 3 (2): 145–181. doi:10.1023/A:1011476405933. S2CID 15679915. /wiki/Doi_(identifier)
Ostrovsky, V. N. (May 2001). "What and How Physics Contributes to Understanding the Periodic Law". Foundations of Chemistry. 3 (2): 145–181. doi:10.1023/A:1011476405933. S2CID 15679915. /wiki/Doi_(identifier)
Goudsmit, S. A.; Richards, Paul I. (1964). "The Order of Electron Shells in Ionized Atoms" (PDF). Proc. Natl. Acad. Sci. 51 (4): 664–671 (with correction on p 906). Bibcode:1964PNAS...51..664G. doi:10.1073/pnas.51.4.664. PMC 300183. PMID 16591167. Archived (PDF) from the original on 10 October 2017. Retrieved 15 August 2021. https://www.pnas.org/content/51/4/664.full.pdf
Wong, D. Pan (1979). "Theoretical justification of Madelung's rule". J. Chem. Educ. 56 (11): 714–718. Bibcode:1979JChEd..56..714W. doi:10.1021/ed056p714. /wiki/Journal_of_Chemical_Education
Ostrovsky, V. N. (May 2001). "What and How Physics Contributes to Understanding the Periodic Law". Foundations of Chemistry. 3 (2): 145–181. doi:10.1023/A:1011476405933. S2CID 15679915. /wiki/Doi_(identifier)
Ostrovsky, V. N. (1981). "Dynamic symmetry of atomic potential". Journal of Physics B: Atomic and Molecular Physics. 14 (23): 4425–4439. Bibcode:1981JPhB...14.4425O. doi:10.1088/0022-3700/14/23/008. /wiki/Bibcode_(identifier)
Petrucci et al., p. 331
Ostrovsky, V. N. (May 2001). "What and How Physics Contributes to Understanding the Periodic Law". Foundations of Chemistry. 3 (2): 145–181. doi:10.1023/A:1011476405933. S2CID 15679915. /wiki/Doi_(identifier)
Petrucci et al., p. 328
Cao, Changsu; Vernon, René E.; Schwarz, W. H. Eugen; Li, Jun (6 January 2021). "Understanding Periodic and Non-periodic Chemistry in Periodic Tables". Frontiers in Chemistry. 8 (813): 813. Bibcode:2021FrCh....8..813S. doi:10.3389/fchem.2020.00813. PMC 7818537. PMID 33490030. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7818537
Jørgensen, Christian (1973). "The Loose Connection between Electron Configuration and the Chemical Behavior of the Heavy Elements (Transuranics)". Angewandte Chemie International Edition. 12 (1): 12–19. doi:10.1002/anie.197300121. /wiki/Doi_(identifier)
Once two to four electrons are removed, the d and f orbitals usually become lower in energy than the s ones:[52]
1s ≪ 2s < 2p ≪ 3s < 3p ≪ 3d < 4s < 4p ≪ 4d < 5s < 5p ≪ 4f < 5d < 6s < 6p ≪ 5f < 6d < 7s < 7p ≪ ...
and in the limit for extremely highly charged ions, orbitals simply fill in the order of increasing n instead. There is a gradual transition between the limiting situations of highly charged ions (increasing n) and neutral atoms (Madelung's rule).[45] Thus for example, the energy order for the 55th electron outside the xenon core proceeds as follows in the isoelectronic series of caesium (55 electrons):[53]
Cs0: 6s < 6p < 5d < 7s < 4f
Ba+: 6s < 5d < 6p < 7s < 4f
La2+: 5d < 4f < 6s < 6p < 7s
Ce3+: 4f < 5d < 6s < 6p < 7s
and in the isoelectronic series of holmium (67 electrons), a Ho0 atom is [Xe]4f116s2, but Er+ is [Xe]4f126s1, Tm2+ through W7+ are [Xe]4f13, and from Re8+ onward the configuration is [Cd]4f145p5 following the hydrogenic order.[54][55]
Also, the ordering of the orbitals between each ≪ changes somewhat throughout each period. For example, the ordering in argon and potassium is 3p ≪ 4s < 4p ≪ 3d; by calcium it has become 3p ≪ 4s < 3d < 4p; from scandium to copper it is 3p ≪ 3d < 4s < 4p; and from zinc to krypton it is 3p < 3d ≪ 4s < 4p[51] as the d orbitals fall into the core at gallium.[56][57] Deeply buried core shells in heavy atoms thus come closer to the hydrogenic order: around osmium (Z = 76) 4f falls below 5p, and around bismuth (Z = 83) 4f falls below 5s as well.[54]
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
In fact, electron configurations represent a first-order approximation: an atom really exists in a superposition of multiple configurations, and electrons in an atom are indistinguishable.[28] The elements in the d- and f-blocks have multiple configurations separated by small energies and can change configuration depending on the chemical environment.[52] In some of the undiscovered g-block elements, mixing of configurations may become so important that the result can no longer be well-described by a single configuration.[59]
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Scerri, p. 17
Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
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Petrucci et al., p. 331
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jørgensen, Christian (1973). "The Loose Connection between Electron Configuration and the Chemical Behavior of the Heavy Elements (Transuranics)". Angewandte Chemie International Edition. 12 (1): 12–19. doi:10.1002/anie.197300121. /wiki/Doi_(identifier)
Wulfsberg, p. 27
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Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jensen, William B. (2009). "Misapplying the Periodic Law". Journal of Chemical Education. 86 (10): 1186. Bibcode:2009JChEd..86.1186J. doi:10.1021/ed086p1186. /wiki/William_B._Jensen
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
Feynman, Richard; Leighton, Robert B.; Sands, Matthew (1964). "19. The Hydrogen Atom and The Periodic Table". The Feynman Lectures on Physics. Vol. 3. Addison–Wesley. ISBN 0-201-02115-3. Archived from the original on 19 October 2021. Retrieved 15 August 2021. {{cite book}}: ISBN / Date incompatibility (help) 0-201-02115-3
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
Keeler, James; Wothers, Peter (2014). Chemical Structure and Reactivity (2nd ed.). Oxford University Press. pp. 257–260. ISBN 978-0-19-9604135. 978-0-19-9604135
Petrucci et al., pp. 326–7
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Wulfsberg, p. 53: "As pointed out by W. B. Jensen, the metallurgical resemblance [to yttrium] is much stronger for lutetium than for lanthanum, so we have adopted the metallurgist's convention of listing Lu (and by extension Lr) below Sc and Y. An important additional advantage of this is that the periodic table becomes more symmetrical, and it becomes easier to predict electron configurations. E. R. Scerri points out that recent determinations of the electron configurations of most of the f-block elements now are more compatible with this placement of Lu and Lr."
William B. Jensen (1982). "The Positions of Lanthanum (Actinium) and Lutetium (Lawrencium) in the Periodic Table". J. Chem. Educ. 59 (8): 634–636. Bibcode:1982JChEd..59..634J. doi:10.1021/ed059p634. /wiki/Bibcode_(identifier)
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Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
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Johnson, David (1984). The Periodic Law (PDF). The Royal Society of Chemistry. ISBN 0-85186-428-7. 0-85186-428-7
There are many lower oxides as well: for example, phosphorus in group 15 forms two oxides, P2O3 and P2O5.[113] /wiki/Phosphorus
Greenwood and Earnshaw, pp. 27–9
Greenwood and Earnshaw, pp. 27–9
Wulfsberg, p. 26
Wulfsberg, p. 28
Wulfsberg, p. 274
Greenwood and Earnshaw, p. 113
Siekierski and Burgess, pp. 45–54
The normally "forbidden" intermediate oxidation states may be stabilized by forming dimers, as in [Cl3Ga–GaCl3]2− (gallium in the +2 oxidation state) or S2F10 (sulfur in the +5 oxidation state).[140] Some compounds that appear to be in such intermediate oxidation states are actually mixed-valence compounds, such as Sb2O4, which contains both Sb(III) and Sb(V).[141] /wiki/Dimer_(chemistry)
Siekierski and Burgess, pp. 134–137
Siekierski and Burgess, pp. 45–54
Siekierski and Burgess, pp. 178–180
Siekierski and Burgess, pp. 134–137
Johnson, David (1984). The Periodic Law (PDF). The Royal Society of Chemistry. ISBN 0-85186-428-7. 0-85186-428-7
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Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
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Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
Greenwood and Earnshaw, pp. 25–6
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Greenwood and Earnshaw, pp. 25–6
Dieter, R. K.; Watson, R. T. (2009). "Transmetalation reactions producing organocopper compounds". In Rappoport, Z.; Marek, I. (eds.). The Chemistry of Organocopper Compounds. Vol. 1. John Wiley & Sons. pp. 443–526. ISBN 978-0-470-77296-6. Archived from the original on 17 October 2022. Retrieved 6 April 2022. 978-0-470-77296-6
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"Intermolecular bonding – van der Waals forces". Archived from the original on 22 January 2022. Retrieved 17 November 2021. https://www.chemguide.co.uk/atoms/bonding/vdw.html
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Clark, Jim (2019). "Metallic Bonding". Chemguide. Archived from the original on 21 April 2021. Retrieved 30 March 2021. https://www.chemguide.co.uk/atoms/bonding/metallic.html
Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
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The boundary between dispersion forces and metallic bonding is gradual, like that between ionic and covalent bonding. Characteristic metallic properties do not appear in small mercury clusters, but do appear in large ones.[151]
Siekierski and Burgess, pp. 60–66
Siekierski and Burgess, pp. 60–66
Steudel, Ralf; Scheschkewitz, David (2020). Chemistry of the Non-Metals. Walter de Gruyter. pp. 154–155, 425, 436. ISBN 978-3-11-057805-8. In Group 15 of the Periodic Table, as in both neighboring groups, the metallic character increases when going down. More specifically, there is a transition from a purely non-metallic element (N) via elements with nonmetallic and metallic modifications to purely metallic elements (Sb, Bi). This chapter addresses the two elements besides nitrogen, which are clearly nonmetallic under standard conditions: phosphorus and arsenic. The chemistry of arsenic, however, is only briefly described as many of the arsenic compounds resemble the corresponding phosphorus species. 978-3-11-057805-8
Siekierski and Burgess, pp. 60–66
Siekierski and Burgess, pp. 60–66
All this describes the situation at standard pressure. Under sufficiently high pressure, the band gaps of any solid drop to zero and metallization occurs. Thus for example at about 170 kbar iodine becomes a metal,[152] and metallic hydrogen should form at pressures of about four million atmospheres.[154] See metallization pressure for values for all nonmetals. /wiki/Bar_(unit)
Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
Hawkes, Stephen J. (2001). "Semimetallicity?". Journal of Chemical Education. 78 (12): 1686. Bibcode:2001JChEd..78.1686H. doi:10.1021/ed078p1686. /wiki/Bibcode_(identifier)
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Mewes, Jan-Michael; Smits, Odile Rosette; Jerabek, Paul; Schwerdtfeger, Peter (25 July 2019). "Oganesson is a Semiconductor: On the Relativistic Band-Gap Narrowing in the Heaviest Noble-Gas Solids". Angewandte Chemie. 58 (40): 14260–14264. doi:10.1002/anie.201908327. PMC 6790653. PMID 31343819. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6790653
Descriptions of the structures formed by the elements can be found throughout Greenwood and Earnshaw. There are two borderline cases. Arsenic's most stable form conducts electricity like a metal, but the bonding is significantly more localized to the nearest neighbours than it is for the similar structures of antimony and bismuth,[157] and unlike normal metals it does not have a long liquid range, but rather sublimes instead. Hence its structure is better treated as network covalent.[158] Carbon as graphite shows metallic conduction parallel to its planes, but is a semiconductor perpendicular to them. Some computations predict copernicium and flerovium to be nonmetallic,[159][160] but the most recent experiments on them suggest that they are metallic.[161][162][163] Astatine is calculated to metallise at standard conditions,[164] so presumably tennessine should as well.[165]
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Rayner-Canham, Geoffrey (2020). The Periodic Table: Past, Present, Future. World Scientific. pp. 53–70, 85–102. ISBN 978-981-12-1850-7. 978-981-12-1850-7
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See melting points of the elements (data page). The same is probably true of francium, but due to its extreme instability, this has never been experimentally confirmed. Copernicium and flerovium are expected to be liquids,[159][160] similar to mercury, and experimental evidence suggests that they are metals.[161][162][163] /wiki/Melting_points_of_the_elements_(data_page)
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Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
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Steudel, Ralf; Scheschkewitz, David (2020). Chemistry of the Non-Metals. Walter de Gruyter. pp. 154–155, 425, 436. ISBN 978-3-11-057805-8. In Group 15 of the Periodic Table, as in both neighboring groups, the metallic character increases when going down. More specifically, there is a transition from a purely non-metallic element (N) via elements with nonmetallic and metallic modifications to purely metallic elements (Sb, Bi). This chapter addresses the two elements besides nitrogen, which are clearly nonmetallic under standard conditions: phosphorus and arsenic. The chemistry of arsenic, however, is only briefly described as many of the arsenic compounds resemble the corresponding phosphorus species. 978-3-11-057805-8
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Gonick, First; Criddle, Craig (2005). The Cartoon Guide to Chemistry. Collins. pp. 17–65. ISBN 0-06-093677-0. 0-06-093677-0
See lists of metalloids. For example, a periodic table used by the American Chemical Society includes polonium as a metalloid,[176] but one used by the Royal Society of Chemistry does not,[177] and that included in the Encyclopædia Britannica does not refer to metalloids or semi-metals at all.[178] Classification can change even within a single work. For example, Sherwin and Weston's Chemistry of the Non-Metallic Elements (1966) has a periodic table on p. 7 classifying antimony as a nonmetal, but on p. 115 it is called a metal.[179] /wiki/Lists_of_metalloids
Rayner-Canham, Geoffrey (2020). The Periodic Table: Past, Present, Future. World Scientific. pp. 53–70, 85–102. ISBN 978-981-12-1850-7. 978-981-12-1850-7
Hawkes, Stephen J. (2001). "Semimetallicity?". Journal of Chemical Education. 78 (12): 1686–1687. Bibcode:2001JChEd..78.1686H. doi:10.1021/ed078p1686. /wiki/Bibcode_(identifier)
Steudel, Ralf; Scheschkewitz, David (2020). Chemistry of the Non-Metals. Walter de Gruyter. pp. 154–155, 425, 436. ISBN 978-3-11-057805-8. In Group 15 of the Periodic Table, as in both neighboring groups, the metallic character increases when going down. More specifically, there is a transition from a purely non-metallic element (N) via elements with nonmetallic and metallic modifications to purely metallic elements (Sb, Bi). This chapter addresses the two elements besides nitrogen, which are clearly nonmetallic under standard conditions: phosphorus and arsenic. The chemistry of arsenic, however, is only briefly described as many of the arsenic compounds resemble the corresponding phosphorus species. 978-3-11-057805-8
Hawkes, Stephen J. (2001). "Semimetallicity?". Journal of Chemical Education. 78 (12): 1686–1687. Bibcode:2001JChEd..78.1686H. doi:10.1021/ed078p1686. /wiki/Bibcode_(identifier)
Steudel, Ralf; Scheschkewitz, David (2020). Chemistry of the Non-Metals. Walter de Gruyter. pp. 154–155, 425, 436. ISBN 978-3-11-057805-8. In Group 15 of the Periodic Table, as in both neighboring groups, the metallic character increases when going down. More specifically, there is a transition from a purely non-metallic element (N) via elements with nonmetallic and metallic modifications to purely metallic elements (Sb, Bi). This chapter addresses the two elements besides nitrogen, which are clearly nonmetallic under standard conditions: phosphorus and arsenic. The chemistry of arsenic, however, is only briefly described as many of the arsenic compounds resemble the corresponding phosphorus species. 978-3-11-057805-8
See lists of metalloids. For example, a periodic table used by the American Chemical Society includes polonium as a metalloid,[176] but one used by the Royal Society of Chemistry does not,[177] and that included in the Encyclopædia Britannica does not refer to metalloids or semi-metals at all.[178] Classification can change even within a single work. For example, Sherwin and Weston's Chemistry of the Non-Metallic Elements (1966) has a periodic table on p. 7 classifying antimony as a nonmetal, but on p. 115 it is called a metal.[179] /wiki/Lists_of_metalloids
Scerri, pp. 407–420
Scerri, pp. 407–420
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Horvitz, L. (2002). Eureka!: Scientific Breakthroughs That Changed The World. New York: John Wiley. p. 43. Bibcode:2001esbt.book.....H. ISBN 978-0-471-23341-1. OCLC 50766822. 978-0-471-23341-1
Scerri, p. 47
Ball, P. (2002). The Ingredients: A Guided Tour of the Elements. Oxford: Oxford University Press. p. 100. ISBN 978-0-19-284100-1. 978-0-19-284100-1
Chisholm, Hugh, ed. (1911). "Newlands, John Alexander Reina" . Encyclopædia Britannica. Vol. 19 (11th ed.). Cambridge University Press. p. 515. /wiki/Hugh_Chisholm
Chisholm, Hugh, ed. (1911). "Newlands, John Alexander Reina" . Encyclopædia Britannica. Vol. 19 (11th ed.). Cambridge University Press. p. 515. /wiki/Hugh_Chisholm
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
Meyer, Julius Lothar; Die modernen Theorien der Chemie (1864); table on page 137 Archived 2 January 2019 at the Wayback Machine https://reader.digitale-sammlungen.de/de/fs1/object/goToPage/bsb10073411.html?pageNo=147
Scerri, pp. 106–108
Scerri, p. 113
Scerri, pp. 117–123
Jensen, William B. (2000). "The Periodic Law and Table" (PDF). Archived from the original (PDF) on 10 November 2020. Retrieved 10 December 2022. /wiki/William_B._Jensen
Scerri, pp. 117–123
Mendeleev, D. (1871). "The natural system of elements and its application to the indication of the properties of undiscovered elements". Journal of the Russian Chemical Society (in Russian). 3: 25–56. Archived from the original on 13 August 2017. Retrieved 23 August 2017. https://web.archive.org/web/20170813142644/https://www.knigafund.ru/books/56718/read#page31
Scerri, p. 149
Scerri, p. 151–2
Rouvray, R. "Dmitri Mendeleev". New Scientist. Archived from the original on 15 August 2021. Retrieved 19 April 2020. https://www.newscientist.com/people/dmitri-mendeleev/
Scerri, pp. 164–169
Thyssen, P.; Binnemans, K. (2011). "Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis". In Gschneidner, K. A. Jr.; Bünzli, J-C.G; Vecharsky, Bünzli (eds.). Handbook on the Physics and Chemistry of Rare Earths. Vol. 41. Amsterdam: Elsevier. pp. 1–93. doi:10.1016/B978-0-444-53590-0.00001-7. ISBN 978-0-444-53590-0. 978-0-444-53590-0
Marshall, J.L.; Marshall, V.R. (2010). "Rediscovery of the Elements: Moseley and Atomic Numbers" (PDF). The Hexagon. Vol. 101, no. 3. Alpha Chi Sigma. pp. 42–47. S2CID 94398490. Archived from the original (PDF) on 16 July 2019. Retrieved 15 August 2021. https://web.archive.org/web/20190716215907/https://pdfs.semanticscholar.org/afe4/8822cd0871e65dc5401166e7df68dc0ecb7f.pdf
A. van den Broek, Physikalische Zeitschrift, 14, (1913), 32–41 /wiki/Physikalische_Zeitschrift
Scerri, p. 185
A. van den Broek, Die Radioelemente, das periodische System und die Konstitution der Atom, Physik. Zeitsch., 14, 32, (1913).
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."
Atkins, P. W. (1995). The Periodic Kingdom. HarperCollins Publishers, Inc. p. 87. ISBN 978-0-465-07265-1. 978-0-465-07265-1
Marshall, J.L.; Marshall, V.R. (2010). "Rediscovery of the Elements: Moseley and Atomic Numbers" (PDF). The Hexagon. Vol. 101, no. 3. Alpha Chi Sigma. pp. 42–47. S2CID 94398490. Archived from the original (PDF) on 16 July 2019. Retrieved 15 August 2021. https://web.archive.org/web/20190716215907/https://pdfs.semanticscholar.org/afe4/8822cd0871e65dc5401166e7df68dc0ecb7f.pdf
Egdell, Russell G.; Bruton, Elizabeth (2020). "Henry Moseley, X-ray spectroscopy and the periodic table". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 378 (2180). doi:10.1002/chem.202004775. PMID 32811359. https://doi.org/10.1002%2Fchem.202004775
Marshall, J.L.; Marshall, V.R. (2010). "Rediscovery of the Elements: Moseley and Atomic Numbers" (PDF). The Hexagon. Vol. 101, no. 3. Alpha Chi Sigma. pp. 42–47. S2CID 94398490. Archived from the original (PDF) on 16 July 2019. Retrieved 15 August 2021. https://web.archive.org/web/20190716215907/https://pdfs.semanticscholar.org/afe4/8822cd0871e65dc5401166e7df68dc0ecb7f.pdf
Hisamatsu, Yoji; Egashira, Kazuhiro; Maeno, Yoshiteru (2022). "Ogawa's nipponium and its re-assignment to rhenium". Foundations of Chemistry. 24: 15–57. doi:10.1007/s10698-021-09410-x. https://doi.org/10.1007%2Fs10698-021-09410-x
Scerri, Eric (2013). A Tale of Seven Elements. Oxford University Press. pp. 47–53, 115. ISBN 978-0-19-539131-2. 978-0-19-539131-2
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.
Scerri, pp. 208–218
Niels Bohr, "On the Constitution of Atoms and Molecules, Part III, Systems containing several nuclei" Philosophical Magazine 26:857--875 (1913)
Kragh, Helge (1 January 1979). "Niels Bohr's Second Atomic Theory". Historical Studies in the Physical Sciences. 10: 123–186. doi:10.2307/27757389. ISSN 0073-2672. JSTOR 27757389. https://online.ucpress.edu/hsns/article/doi/10.2307/27757389/47571/Niels-Bohr-s-Second-Atomic-Theory
Scerri, Eric (2013). A Tale of Seven Elements. Oxford University Press. pp. 47–53, 115. ISBN 978-0-19-539131-2. 978-0-19-539131-2
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.
Langmuir, Irving (June 1919). "The Arrangement of Electrons in Atoms and Molecules". Journal of the American Chemical Society. 41 (6): 868–934. Bibcode:1919JAChS..41..868L. doi:10.1021/ja02227a002. ISSN 0002-7863. Archived from the original on 26 January 2021. Retrieved 22 October 2021. /wiki/Irving_Langmuir
Bury, Charles R. (July 1921). "Langmuir's Theory of the Arrangement of Electrons in Atoms and Molecules". Journal of the American Chemical Society. 43 (7): 1602–1609. Bibcode:1921JAChS..43.1602B. doi:10.1021/ja01440a023. ISSN 0002-7863. Archived from the original on 30 October 2021. Retrieved 22 October 2021. /wiki/Charles_Rugeley_Bury
Jensen, William B. (2003). "The Place of Zinc, Cadmium, and Mercury in the Periodic Table" (PDF). Journal of Chemical Education. 80 (8): 952–961. Bibcode:2003JChEd..80..952J. doi:10.1021/ed080p952. Archived (PDF) from the original on 19 April 2012. Retrieved 18 September 2021. The first use of the term "transition" in its modern electronic sense appears to be due to the British chemist C. R.Bury, who first used the term in his 1921 paper on the electronic structure of atoms and the periodic table https://www.uv.es/~borrasj/ingenieria_web/temas/tema_1/lecturas_comp/p952.pdf
Coster, D.; Hevesy, G. (1923). "On the Missing Element of Atomic Number 72". Nature. 111 (2777): 79. Bibcode:1923Natur.111...79C. doi:10.1038/111079a0. https://doi.org/10.1038%2F111079a0
Fernelius, W. C. (1982). "Hafnium" (PDF). Journal of Chemical Education. 59 (3): 242. Bibcode:1982JChEd..59..242F. doi:10.1021/ed059p242. Archived from the original (PDF) on 15 March 2020. Retrieved 3 September 2009. https://web.archive.org/web/20200315031648/http://www.jce.divched.org/Journal/Issues/1982/Mar/jceSubscriber/JCE1982p0242.pdf
Burdette, Shawn C.; Thornton, Brett F. (2018). "Hafnium the lutécium I used to be". Nature Chemistry. 10 (10): 1074. Bibcode:2018NatCh..10.1074B. doi:10.1038/s41557-018-0140-6. PMID 30237529. Retrieved 8 February 2024. https://www.nature.com/articles/s41557-018-0140-6
Scerri, Eric (2013). A Tale of Seven Elements. Oxford University Press. pp. 47–53, 115. ISBN 978-0-19-539131-2. 978-0-19-539131-2
Scerri, pp. 218–23
Jensen, William B. (2007). "The Origin of the s, p, d, f Orbital Labels" (PDF). Journal of Chemical Education. 84 (5): 757–8. Bibcode:2007JChEd..84..757J. doi:10.1021/ed084p757. Archived from the original (PDF) on 23 November 2018. Retrieved 15 August 2021. https://web.archive.org/web/20181123140649/https://www.che.uc.edu/jensen/w.%20b.%20jensen/reprints/137.%20s,%20p,%20d,%20f.pdf
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Klechkovskii, V.M. (1962). "Justification of the Rule for Successive Filling of (n+l) Groups". Journal of Experimental and Theoretical Physics. 14 (2): 334. Retrieved 23 June 2022. http://jetp.ras.ru/cgi-bin/e/index?t=&au=+Klechkovskii&yf=2022&yt=2022&se=1&a=s
Demkov, Yury N.; Ostrovsky, Valentin N. (1972). "n+l Filling Rule in the Periodic System and Focusing Potentials". Journal of Experimental and Theoretical Physics. 35 (1): 66–69. Bibcode:1972JETP...35...66D. Retrieved 25 November 2022. http://jetp.ras.ru/cgi-bin/e/index/e/35/1/p66?a=list
Demkov and Ostrovsky consider the potential
U
1
/
2
(
r
)
=
−
2
v
r
R
(
r
+
R
)
2
{\displaystyle U_{1/2}(r)=-{\frac {2v}{rR(r+R)^{2}}}}
where
R
{\displaystyle R}
and
v
{\displaystyle v}
are constant parameters; this approaches a Coulomb potential for small
r
{\displaystyle r}
. When
v
{\displaystyle v}
satisfies the condition
v
=
v
N
=
1
4
R
2
N
(
N
+
1
)
{\displaystyle v=v_{N}={\frac {1}{4}}R^{2}N(N+1)}
, where
N
=
n
+
l
{\displaystyle N=n+l}
, the zero-energy solutions to the Schrödinger equation for this potential can be described analytically with Gegenbauer polynomials. As
v
{\displaystyle v}
passes through each of these values, a manifold containing all states with that value of
N
{\displaystyle N}
arises at zero energy and then becomes bound, recovering the Madelung order. Perturbation-theory considerations show that states with smaller
n
{\displaystyle n}
have lower energy, and that the s orbitals (with
l
=
0
{\displaystyle l=0}
) have their energies approaching the next
n
+
l
{\displaystyle n+l}
group.[242][90] /wiki/Coulomb_potential
Thyssen, P.; Binnemans, K. (2011). "Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis". In Gschneidner, K. A. Jr.; Bünzli, J-C.G; Vecharsky, Bünzli (eds.). Handbook on the Physics and Chemistry of Rare Earths. Vol. 41. Amsterdam: Elsevier. pp. 1–93. doi:10.1016/B978-0-444-53590-0.00001-7. ISBN 978-0-444-53590-0. 978-0-444-53590-0
William B. Jensen (1982). "The Positions of Lanthanum (Actinium) and Lutetium (Lawrencium) in the Periodic Table". J. Chem. Educ. 59 (8): 634–636. Bibcode:1982JChEd..59..634J. doi:10.1021/ed059p634. /wiki/Bibcode_(identifier)
Scerri, pp. 392−401
Thyssen, P.; Binnemans, K. (2011). "Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis". In Gschneidner, K. A. Jr.; Bünzli, J-C.G; Vecharsky, Bünzli (eds.). Handbook on the Physics and Chemistry of Rare Earths. Vol. 41. Amsterdam: Elsevier. pp. 1–93. doi:10.1016/B978-0-444-53590-0.00001-7. ISBN 978-0-444-53590-0. 978-0-444-53590-0
Bury, Charles R. (July 1921). "Langmuir's Theory of the Arrangement of Electrons in Atoms and Molecules". Journal of the American Chemical Society. 43 (7): 1602–1609. Bibcode:1921JAChS..43.1602B. doi:10.1021/ja01440a023. ISSN 0002-7863. Archived from the original on 30 October 2021. Retrieved 22 October 2021. /wiki/Charles_Rugeley_Bury
For example, the early actinides continue to behave more like the d-block transition metals in their propensity towards high oxidation states all the way from actinium to uranium, even though it is actually only actinium and thorium that have d-block-like configurations in the gas phase; f-electrons appear already at protactinium.[110] Uranium's actual configuration of [Rn]5f36d17s2 is in fact analogous to that Hund assumed for the lanthanides, but uranium does not favour the trivalent state, preferring to be tetravalent or hexavalent.[54] On the other hand, lanthanide-like configurations for the actinides begin at plutonium, but the shift towards lanthanide-like behaviour is only clear at curium: the elements between uranium and curium form a transition from transition-metal-like behaviour to lanthanide-like behaviour.[110] Thus chemical behaviour and electron configuration do not exactly match each other.[110]
Jørgensen, Christian Klixbüll (1988). "Influence of Rare Earths on Chemical Understanding and Classification". In Gschneidner Jr., Karl A.; Eyring, Leroy (eds.). Handbook on the Physics and Chemistry of Rare Earths. Vol. 11. Elsevier. pp. 197–292. ISBN 978-0-444-87080-3. 978-0-444-87080-3
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L. D. Landau, E. M. Lifshitz (1958). Quantum Mechanics: Non-Relativistic Theory. Vol. 3 (1st ed.). Pergamon Press. pp. 256–7. /wiki/Lev_Landau
Kondō, Jun (January 1963). "Superconductivity in Transition Metals". Progress of Theoretical Physics. 29 (1): 1–9. Bibcode:1963PThPh..29....1K. doi:10.1143/PTP.29.1. https://doi.org/10.1143%2FPTP.29.1
Hamilton, David C. (1965). "Position of Lanthanum in the Periodic Table". American Journal of Physics. 33 (8): 637–640. Bibcode:1965AmJPh..33..637H. doi:10.1119/1.1972042. /wiki/Bibcode_(identifier)
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William B. Jensen (1982). "The Positions of Lanthanum (Actinium) and Lutetium (Lawrencium) in the Periodic Table". J. Chem. Educ. 59 (8): 634–636. Bibcode:1982JChEd..59..634J. doi:10.1021/ed059p634. /wiki/Bibcode_(identifier)
Hamilton, David C. (1965). "Position of Lanthanum in the Periodic Table". American Journal of Physics. 33 (8): 637–640. Bibcode:1965AmJPh..33..637H. doi:10.1119/1.1972042. /wiki/Bibcode_(identifier)
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Fluck, E. (1988). "New Notations in the Periodic Table" (PDF). Pure Appl. Chem. 60 (3): 431–436. doi:10.1351/pac198860030431. S2CID 96704008. Archived (PDF) from the original on 25 March 2012. Retrieved 24 March 2012. https://www.iupac.org/publications/pac/1988/pdf/6003x0431.pdf
Thyssen, P.; Binnemans, K. (2011). "Accommodation of the Rare Earths in the Periodic Table: A Historical Analysis". In Gschneidner, K. A. Jr.; Bünzli, J-C.G; Vecharsky, Bünzli (eds.). Handbook on the Physics and Chemistry of Rare Earths. Vol. 41. Amsterdam: Elsevier. pp. 1–93. doi:10.1016/B978-0-444-53590-0.00001-7. ISBN 978-0-444-53590-0. 978-0-444-53590-0
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Jensen, William B. (2015). "The positions of lanthanum (actinium) and lutetium (lawrencium) in the periodic table: an update". Foundations of Chemistry. 17: 23–31. doi:10.1007/s10698-015-9216-1. S2CID 98624395. Archived from the original on 30 January 2021. Retrieved 28 January 2021. https://link.springer.com/article/10.1007/s10698-015-9216-1
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Scerri, pp. 322–340
Technetium, promethium, astatine, neptunium, and plutonium were eventually discovered to occur in nature as well, albeit in tiny traces. See timeline of chemical element discoveries. /wiki/Timeline_of_chemical_element_discoveries
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Authors differ on whether the n + ℓ rule has yet been derived from quantum mechanics. Scerri claims that it has not,[290][291] despite several attempts to do so.[292] On the other hand, Ostrovsky, who has claimed such justification from 1971, wrote "Some authors insist that 'still nobody has deduced the n+l rule from the principles of quantum
mechanics', while others present quantum justification of the rule that was not ever disputed."[293] Other authors argue that such a derivation is not necessary, because it admits exceptions.[294]
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