Sunday, February 23, 2014

History of The Periodic Table Part 6: The Future of the Periodic Table

The classic periodic table as shown below is now complete, or is it?

Super-Heavy Elements Finally Fill In the Classic Periodic Table

All the elements from Z=1 to Z=118 have been discovered and verified through at least one second experiment. The light grey elements above, 109 to 111 and 113 to 118, were unknown when this table from Wikipedia was drawn up, but all of them have since been discovered in the last few years, including a few atoms of the latest element to be observed (117). The discovery of this last element, ununseptium, was announced in 2010. Fittingly, it was a Russian team of scientists who discovered it by fusing berkelium (Z=97) with calcium (Z=20) in a series of reactions as shown below:

The two numbers before each element symbol is called isotope notation. There are three options for naming an isotope. We've seen one way already in this article series when we compared two isotopes of helium. Helium-3 has two protons and 1 neutron for a total of 3 nucleons, while helium-4 has two protons and two neutrons for a total of 4 nucleons. They can also be written asand respectively. The top number is the total number of nucleons and the bottom number is the number of protons, or they can simply be written as 3He and 4He, because you can look up helium (Z=2) to find it has two protons.

It wasn't an easy process to discover element 117 because only the United States is able to produce the particular isotope of berkelium required. In 2008, they produced just 22 milligrams, enough for the Russian team to run their experiment. Another problem was that it has a half-life of just 330 days and it had to be cooled for 90 days and then purified for an additional 90 days and then it had to get through several layers of red tape (as you can imagine) to be shipped from the US to Russia. Dimitri Mendeleev would be proud.

Just when it seems we can switch the periodic table from "work in progress" to "completed work," recent research on the chemistry of these and other unstable super-heavy elements tells us we do not yet know all there is to know about the elements. This development has to do with the ability to predict the chemical and physical properties of an element based on its atomic number, something Mendeleev himself was able to do with the missing spaces in his then much simpler table, and which convinced the scientific community of its power.

The Janet Left-Step Periodic Table

But first, the periodic table, according to an increasing number of scientists, has some catching up to do. The table arranged by atomic number and according to the, then well known, periodicity of eight is the classic Mendeleev-inspired table shown above. Chemists recognized that the chemical and physical properties of elements seemed to follow a rule of eight. For example, lithium (Z=3) in Group 1 is a soft metal that you can cut with a knife and it reacts vigorously with water. If you move up eight numbers to sodium (Z=11), you again have a metal that is soft and reacts with water. Continuing up, potassium (Z=19) is also a soft metal that reacts with water. There is an eight-space trend of physical and chemical properties: lithium, sodium and potassium all have one valence (chemistry-doing) electron.

However, the periodicity of eight (exploited by the octave rule in chemistry) is not the only periodicity in the table. The reason that some elements tend to have similar chemical properties in sequences of eight is because of quantum mechanics and in particular the physics of how electrons orbit the nucleus, something physicists began to realize in the early 1900's.

Electrons in atoms organize themselves into various kinds of orbitals - s, p, d, f (their shapes are shown below) and possibly theoretical g orbitals (not shown).

(Dhatfield F4M1 png; Wikipedia)
Atoms that tend to most faithfully display a periodicity of eight have a filled s orbital (two electrons) and are filling up the p electron orbital, which contains a total of six electrons in three sub-orbitals (see p1 through p6 - going from right to left in the blue squares - in the Janet table below). This isn't the only periodicity in the periodic table, however. There are other periodicities that are evident in heavier elements, such as within the transition metals. Here a periodicity of ten occurs thanks to the d orbital, which contains up to 10 electrons divided among five sub-orbitals (see d1 through d10 in the lime squares in the Janet table below). The f orbital contains up to 14 electrons in seven sub-orbitals (turquoise), so it displays a periodicity of 14 (the actinides and lanthanides).

In 1928, Charles Janet revised the periodic table to base it on, what was then recently discovered, quantum mechanics rather than on electron valence. The Janet left-step periodic table (shown below) organizes elements according to the order in which electrons fill up atomic orbitals and it is the version most widely used by physicists.

This is a screenshot from Wikipedia (click the link to see a larger easier to read version).

Still, the revised Janet table does not reflect all that is going on in atoms, especially in very heavy elements with lots of electrons and a very large positive charge on the nucleus. In these atoms, another factor comes into play that complicates matters further and makes the physical and chemical properties of some of these elements very difficult to predict.

Relativity and the Large Atom

The orbitals of electrons in an atom are described as solutions to the Schrodinger equation. These solutions are what give the orbitals their shapes and sizes. The Schrodinger equation, however, is a nonrelativistic equation. It does not quite describe electrons that are moving so fast they are approaching a significant fraction of light speed. For smaller atoms, this is no problem. No electrons are orbiting the nucleus that fast. But in larger atoms, some electrons do. They attain what physicists call relativistic speed.

As you move toward atoms with higher atomic numbers, the nuclear charge increases as proton number increases. This has a powerful effect on electrons in orbitals closest to the nucleus, one that asks us to understand the deepest nature of the atom.

An atom has a concentrated positive charge surrounded by more diffuse negative charge. Although certain measurements reduce an electron in an atom to a point charge, an electron in reality is thought to exist as a negative charge and mass that are smeared throughout a cloud, which is in the shape of an orbital. This view of the electron is thanks to Heisenberg's uncertainty principle, which also states that one cannot know both the position and velocity of an electron at the same time. Therefore, when physicists talk about electron velocity inside an atom, they mean an average velocity, and they come to it through a fairly complex set of calculations. The size or spread of the electron cloud is related to the spread of all possible velocities (or momentum) of the electron. As the electron moves away from the nucleus its potential energy increases, in a way that is analogous to someone climbing up a set of stairs. At the top, the person's gravitational potential energy is higher. An electron can lower its potential energy by squishing in closer to the nucleus but it must pay for it by increasing its kinetic energy, or velocity in other words, because total energy in the atom "system" has to be conserved. Atomic size tends to settle at a happy medium where the potential energies and kinetic energies of its electrons settle in at a total minimal energy.

However, when there are many electrons orbiting a large nucleus, things get complicated. Relativistic quantum chemistry must be taken into account. The wave function of the electron allows for a much sharper increase in velocity than classical mechanics allows. First of all, it is very difficult to calculate the various electron trajectories because orbitals interact with each other in often complex ways. Electrons repulse each other and that force ultimately pushes inner electrons closer to the nucleus. As they are squished closer, their velocities increase greatly. In the case of large atoms, innermost electrons can approach relativistic speeds. In a complex mathematical relationship, the wave function of an electron allows the kinetic energy of the squished electron orbital to increase faster than the potential energy decreases. This is why relativistic speeds occur.

The quantum nature of the wave function, however, usually prevents electrons from squishing right down into the nucleus despite the increasing attractive force as they move closer. An electron (generally) must possess a specific minimum total quantum energy, and that keeps it away from the nucleus and gives it a minimum Bohr radius.

Interestingly, this minimum distance itself can change. As a particle approaches light speed, its relativistic mass increases. The mass of an electron at non-relativistic velocities is simply its rest mass but when it (or any object) approaches light speed its mass increases and eventually approaches infinity, as a consequence of the nature of special relativity. The mass of any object (y axis) is plotted against the (relative) velocity of that object (x axis) below right. As velocity approaches c, the speed of light, relativistic mass approaches infinity.

If the relativistic mass of an electron near light speed is plugged into the Bohr radius calculation, the Bohr radius decreases, as shown below left. Ultimately the Bohr radius approaches zero as velocity approaches light speed, and a decay process called electron capture may take place in atoms with very large Z numbers, in which the electron collapses into the nucleus and the atom decays into a new one-proton-smaller atom.

Alternatively you can do a length contraction calculation and apply it to the radius of the electron orbital and you will get the same result as you do with the Bohr radius mass calculation.

All this is called a direct relativistic effect. Inner orbitals contract, and by doing so, they make themselves more stable.

In the other hand, there are indirect relativistic effects on the atom as well. While inner orbitals are stabilized as the nuclear charge goes up, others can be destabilized. In particular, d and f orbitals experience destabilization, an indirect effect of inner orbital contraction, as inner s and p orbitals begin to screen outer electrons from the nucleus' positive charge. The electron clouds of these inner electrons become denser, providing an effective charge screen. Outer electrons, those in the d and f orbitals, feel less electrostatic inward pull than they would otherwise, an effect that partly destabilizes them and extends their radii outward. These are the mechanisms behind transition metal contraction and lanthanide contraction mentioned in previous articles in this series.

Gold and Silver: Two Very Different Relativistic Atoms

Together, these relativistic effects complicate what would otherwise be a fairly straightforward relationship between chemical and physical properties and the periodicity of the elements. A popular example of this complication is gold (Au, Z=79) located in period 6 in Group 11 on the standard table. While almost all the other transition metals (atoms filling up the d orbital), are typically metallic in colour, gold has an intense gold shimmer. Synthetic gold crystals are shown below.

The explanation for its colour comes from how atoms interact with light. When a transition metal is hit by a photon of the right wavelength, it absorbs that photon. The photon's energy is converted into increased potential energy of an electron in the atom. That electron jumps up to the next higher energy orbital. In most transition metals, the gap is pretty large and that means a large energy difference - in the range of ultraviolet photons. This means that visible light photons (all with lower energy and longer wavelength) just bounce off the atoms of these elements. It makes them look characteristically "metallic," like mirrors in other words.

Many of the transition elements have atoms that are large enough to have relativistic properties but complex interactions between electrons and orbitals mean that the effects are very difficult to predict. Gold has a particular arrangement of electrons that makes the relativistic effects on its atoms quite noticeable to us. Relativistic contraction reduces the potential energy of its 6s orbital (it contracts) and raises the potential energy of its 5d orbitals (they extend further). The excited electron jumps from the 5d to the 6s orbital, which in gold is a short enough jump to require the energy of a blue photon in the visible spectrum. Gold therefore reflects all visible photons except blue. The result is that we see white light minus blue light, which looks to us like gold. Gold also has other unique properties due to its relativistic nature, such as its reactivity with the normally inert noble gas, xenon, and it triple bonds with carbon.

If we look at silver (Ag, Z=47), shown below, we would expect silver to have properties similar to gold based on the periodicity of the d-block elements. Silver is in the same group as gold is but in period 5 rather than 6. However, its chemical and physical properties are quite different. It is has the highest electrical conductivity of any element as well as higher thermal conductivity than any other metal. It also reacts with far more elements than gold does (one example is that it tarnishes in air).

A pure synthetically made silver crystal:

In silver, an analogous electron transition from the 4d to 5s orbitals occurs, but the relativistic effects in silver are lower because it is a smaller atom (having 32 less electrons and protons). The 4d orbital experiences some expansion and the 5s orbital experiences some contraction but not as much, and not enough to reduce the photon absorption into the visible range. That is why silver looks much like most other transition metals do - shiny and metallic.

Unexpected physical and chemical properties become even more pronounced in the super-heavy atoms, those with atomic numbers higher than 103. All of these unstable elements are synthetic. They are created in colliders by fusing smaller atoms together. Theoretical calculations predict significant deviations from expected periodic trends due to especially powerful relativistic effects. More research will need to be done on these elements in order to verify those predictions, and it isn't easy to do.

Ordinary wet chemistry can't be done on these unstable elements. They are synthesized in such low quantities in colliders that only a few atoms are often available. You can't put them in nitric acid, for example, to see if they dissolve. Researchers instead are coming up with new and ingenious ways to test the properties of these super-heavy elements, for example, how atoms deposit on various surfaces at specific temperatures. They can synthetically produce samples of smaller elements from the same group to see whether they are similar (periodic trends prevail) or not (relativistic complications prevail).

Even though Mendeleev's periodic table works amazingly well in terms of predicting the chemical and physical properties of lighter elements, such as those involved in organic chemistry for example, it is far from perfect in predicting the behaviours of heavier elements. Even the Janet table, reorganized to reflect the quantum mechanical nature of atoms, does not work consistently well in terms of predicting the behaviours of heavier elements. The relativistic behaviours of electrons in atoms affects orbital size, and therefore, how electrons within them interact with each other and with the nucleus, altering them in ways that are both complex and difficult to predict. It may be possible to work some of these complex configurations out, and in the meantime gather more information about the chemical and physical properties of super-heavy atoms. This could mean that a further refinement of the periodic table might be in store.

It is also possible that the periodic table will continue to grow in size. In 1911, Elliot Adams suggested that atoms larger than Z=100 do not exist. In the late 1960's, Glenn Seaborg proposed an island of stability that suggests that elements around Z=126 might exist due to particularly stable nucleon arrangements. Richard Feynman suggested that element 137 might be the largest atom possible because the Dirac equation, which accounts for relativistic effects, predicts that the wave functions of electrons in atoms this size and larger become oscillatory and unbound. By applying the hyperbolic law to the periodic table, Albert Khazan thinks atoms might be as large as Z=155.

Below, an extended version of the periodic table is shown accommodating elements up to Z=184.

For a larger version, use this link.

The classic periodic table contains seven periods of elements, culminating with Z=118 (ununoctium).  Glenn Seaborg suggested an 8-period table, which includes atoms filling a g orbital in an additional g-block, which would contain at least some additional atoms, according to him up to Z=130. In the Janet table, they would be located in an additional block to the far left. The extended table above contains ten periods rather than seven, accommodating elements up to Z=184, and perhaps beyond. These atoms would be expected to be extremely short-lived although some might exist in a proposed island of stability, explored in The History of the Periodic Table Part 1, and these elements might exhibit slightly, and perhaps even significantly, longer half-lives.

As mentioned in this and previous articles in this series, the orbital filling process of atoms generally follows a particular order - 1s then 2s then 2p then 3s then 3p then 4s and so on.* (This statement, though found in similar form in many textbooks, is actually flawed as pointed out to me by an expert. Please read the comment of Dr. Scerri and my correction of the statement to follow. It points out a fascinating , subtle, and critical flaw in the Aufbau principle). This filling rule is called the Madelung energy-ordering rule, or diagonal rule (shown below right), and it is based on the Aufbau principle. An atom is (theoretically) built up by progressively adding electrons, and as each one is added, they assume their most stable configurations (orbitals) with respect to both other electrons as well as to the nucleus. They fill the lowest available energy levels before adding electrons to higher energy levels.

However, this rule has serious flaws. It tends to weaken as atoms get heavier, as in transition metal contraction, and in the lanthanide contraction, the filling rule is broken, as orbitals increasingly interact with each other in complex ways. Element 118 has all orbitals filled from 1s to 7p. For theoretical atoms larger than this, orbital filling is expected to be very complex thinks to the extremely close proximity of electron energy shells.

An alternative periodic table called the Pyykko model, addresses this problem by using computer modeling to calculate the positions of elements up to Z=172. This modeling suggests the following orbital filling order: 8s, 5g, first 2 spaces of 8p, 6f, 7d, 9s, first 2 spaces of 9p and so on. As you can see, it deviates quite a bit from the diagonal rule. This table is wide and difficult to show in this article. See it in the extended periodic table Wikipedia page here. Some experts believe such heavy atoms to be impossible because at very high nuclear charges, the nucleus would simply capture an orbiting electron and emit a neutrino. This would cause the proton number to go down by one (and neutron number to go up by one). This kind of decay is well known in unstable isotopes that have an overabundance of protons (a note: these atoms don't have to be super-heavy to decay by this mode. Atoms as small as aluminum-26 decay by electron capture. The requirement is too many protons in the nucleus rather than extremely relativistic electrons).

For the reasons explored in this article, the history of the periodic table is not yet complete. It is a work in progress in which the complicated quantum nature of the atom continues to be explored and understood more deeply. In the meantime, physicists are busy attempting to create ever-larger atoms in an effort to find if there really is a limit to size, and to test how these atoms behave.

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