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).

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.

Wednesday, February 19, 2014

History of The Periodic Table Part 5: Rare Earths - A Story of Discovery, Demand and International Intrigue

The discovery of the rare earth elements is an especially interesting story. These elements make up half of an assemblage of thirty elements that are found in Group 3 on the periodic table, shown below. These thirty elements are the lanthanide and actinide series, the two groups that don't fit in and are located in the separate f-block (the single and double asterisked series).

Rare earth elements include all of the lanthanide elements (lanthanum, cerium, praseodymium, neodymium, promethium, samarium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium and lutetium), as well as two Group 3 non-lanthanides (scandium (Z=21) and yttrium (Z=39)) because they are found in the same ores as the lanthanides and share similar chemical properties.

Rare earths routinely make it into the international news because they are at the heart of the burgeoning global high-tech economy. They are used in everything from cellphones to missile systems to hybrid cars.

Examples of How Rare Earths are Used

Neodymium (below right) is used in laser technology but it is better known for its use as a rare earth magnet.;Wikipedia
Neodymium magnets are the most powerful permanent magnets known, Developed in 1982, these magnets, made from an alloy of neodymium, iron and boron (Nd2Fe14B), have replaced many other types of magnet in applications ranging from cordless tools to hard disk drives to missiles. The unique tetragonal crystal structure of Nd2Fe14B gives it very high resistance to being demagnetized and very high saturation magnetization, which means its maximum magnetic energy density makes it a very powerful magnet.

The power of these magnets depends on their alloy composition, their microstructure and how they are made. There are two basic manufacturing processes for neodymium magnets. The most powerful neodymium magnets are sintered. The raw materials are melted and cast into ingot molds. The ingots are then pulverized into tiny particles, which are sintered. The powder is magnetically aligned into blocks and then the blocks are heat treated, cut to shape and magnetized.

Yttrium (below) is used in lasers and superconductors.

Europium is never found in nature as the pure metal shown below because it almost instantly oxidizes in air.

Europium is one of several rare earth metals that are very useful as phosphors in lights and in TV screens. A phosphor is a substance that emits visible light when it is energized, usually by a beam of electrons (in the case of LCD lights and flat panel TV screens) or by ultraviolet light (in the case of fluorescent lights). In a TV, a pattern of red, blue and green phosphors create all the colours we see. In a fluorescent light, a mixture of the three phosphors combine into what we see as white light. Most of europium's uses exploit its fluorescence in one of its two possible (+2 or +3) oxidation states. The fluorescent nature of europium was known for many centuries but people called the substance fluorite (CaF2), shown below left, not knowing that its blue fluorescence came from Europium (Eu3+) impurities within the crystal structure of the mineral rather than from CaF2 itself.

A sample of fluorite from a mine in Durham, England in daylight (A) and under ultraviolet light (B) displays its natural bright blue fluorescence, below left.

Didier Descouens;Wikipedia
This is a natural example of doping - adding an impurity to a crystal structure in order to change its properties. In the 1960's, europium doping was put to its first commercial use as a bright red phosphor as the substance yttrium orthovanadate (YVO4:Eu3+). Red europium phosphors are shown below the mineral sample as part of a CRT (cathode ray tube) screen used in older (fat) TV sets and computer screens.

Until the 1960's, colour TV was impossible because three basic phosphors - red, blue and green - were needed to make all colours and no bright red phosphors were known. It is still one of very few ions known to emit bright red when it is excited.

Light of a specific wavelength is emitted when an electron in an atom drops back down from a higher energy state to a lower energy state. The wavelength of this emission depends on the symmetry of the site of the europium ion inside the crystal matrix it's embedded in, and this depends on different factors including what kind of mineral is doped with europium ions and whether the europium ion is in its +3 oxidation state or +2 oxidation state. For this reason, europium can be used in many different host materials to attain a wide range of phosphor colours. And it is why the Eu3+ ion glows blue in fluorite (CaF2:Eu3+) but bright red in oxides such as YVO4:Eu3+ or Eu2O3.

Terbium (below) is used in lasers, as a bright green phosphor in projection TV's and as an X-ray phosphor, and it is used as well in fuel cells and sonar systems.;Wikipedia
What Makes Rare Earth Elements So Useful and Valuable?

The world mines almost 150,000 metric tons of rare earth elements a year, with China producing 97% of the total. Although rare earth elements have a vast array of very specific as well as more general uses, it is their unique electron configurations, explored in detail in the previous article, History of the Periodic Table Part 4: Lanthanides and Actinides - Elemental Misfits? which gives them their particular value. Electron configuration plus atomic size (most exhibit lanthanide contraction) makes these elements unique physically and chemically. The practical uses of rare earth elements depends on their physical and chemical properties, some of which are shared among all of them, and this makes them difficult to separate from each other in the ore. Other qualities - optical, electric, magnetic, thermal, etc. - are specific to each particular element.

Thanks to their useful and unique properties rare earth elements are increasingly used in electronics, as powerful magnets (neodymium), catalysts (cerium and lanthanum), and in ceramics (all rare earths) and alloys (cerium, lanthanum, neodymium). Thermal properties of some rare earth elements help them stabilize alloys under great stress and varying temperature, such as parts inside jet engines.

Rare earth elements are especially and increasingly important in new low-carbon technologies (dysprosium, neodymium, terbium, etc.), such as electric vehicles, solar energy, fuel cells, wind energy technology and low-energy lighting. Global demand for them is already very high and is set to grow quickly. If you Google "rare earth shortage" or "rare earth demand" you will get many hits, all describing an increasingly critical global situation.

The commerce of these useful elements is as mysterious as the elements themselves, one reason being they are not traded on the global stock exchange like precious metals are. Instead, they are traded on the private market. They are also not usually sold in pure form but in mixtures (usually as very stable oxides) of varying purity. This makes procurement, buying and selling complicated for the burgeoning high-tech industry. There is the perception that these elements are rare (hence the name rare earth) and that their sources are rapidly being depleted. Like the gold rush, prices are pushed up and politics comes into play. They are now so valuable that the recycling of electronics and recovery from mining tailings have become economically viable sources of various rare earth elements.

Surprisingly, rare earths are actually quite abundant in the Earth's crust. Often many rare earth elements are found together in the same deposit. The problem is that they are also found in a dispersed state rather than in pure deposits like gold, copper and silver are, and they tend to be chemically very similar to each other, making separation difficult. These two considerations, along with high demand, are what make the rare earths so expensive. If you are interested in following their prices try It follows, along with other metals, one of the largest global suppliers of rare earths, HEFA Rare Earth, with a parent company in China and a Canadian subdivision. You might be surprised by their incredible price volatility.

Discovery of the Rare Earths

Chemical and physical similarity among the rare earths is what made their discoveries, beginning in 1794, such a long and harrowing process. Most of them were found in black mineral deposits in a Swedish mine. When the first of these elements were discovered, only two methods for extraction and separation were available - repeated precipitation and/or crystallization. These are two processes that you may have performed yourself in either high school or first-year university. Carrying them out divides the black ore into two different precipitates, suggesting the presence of two elements. At the time, the researchers had no idea there were actually far more elements present. It took 30 years to figure out that they could separate each of the two precipitates into different salts (elements) by heating them and dissolving the product in nitric acid.

However, unknown to them at the time, one element they called didymium was especially stubborn. It was actually still a mixture of elements. Not until optical flame spectroscopy was developed in the late 1800's did researchers find several unknown spectral lines in the didymium sample, indicating that a second element must be present. It was found to be a mixture of two elements - praseodymium and neodymium - that could be separated, thanks to a new procedure called fractional crystallization. Didymium is dissolved in nitric acid over heat and then the solution is cooled. The elements will crystallize out and settle but the precipitate will contain more of one element than the other one due to a subtle difference in solubility. This is repeated over and over in a cascade process until the two elements are finally separated.

Rare Earth Supply and Demand

Deposits of rare earth-rich elements are found all over the world - India, Brazil, South Africa and the United States, but production in these places dwindled over the years. In fact, China, which contains only 23% of the world's rare earth supply most of which is in a deposit in inner Mongolia (shown below), supplies almost all of the world's rare earths.

A NASA satellite view of Bayan Obo mine in Mongolia (false colour) is shown below - vegetation appears red, grassland is light brown, rocks are black, and water is green. Two circular open-pit mines are visible, as well as a number of tailings ponds and tailings piles.

Increasing demand is straining this supply and, as you can imagine, China is in an enviable position to restrict and manipulate this supply, an uncomfortable situation for other countries. Interestingly as of 2010, the USGS (U.S. Geological Survey) indicated that the U.S. actually has as much as 13 million metric tons of rare earth elements. Between 1965 and 1995, the Mountain Pass Mine in California supplied most of the world with rare earths, most of the demand at the time being for europium (for TV's). It closed in 2002 because China developed its own supply and undercut US pricing, making mining and purification uneconomical in the US. Since then, China has been flexing its muscle. It banned export of rare earths altogether to Japan in 2010, making the world very nervous. In 2012, the Mountain Pass Mine reopened under new environmental restrictions to resume production of rare earths and secure a supply for the large US market. This will be a story to follow in the next few years as other countries, such as Brazil in particular, begin to take advantage of their own large rare earth deposits and perhaps jump into the lucrative high-tech race themselves.

In the final article in this series we explore the future of the periodic table.

Saturday, February 15, 2014

History of the Periodic Table Part 4: Lanthanides and Actinides - Elemental Misfits?

Two series of elements - lanthanides and actinides - make up a group called the inner transition metals, falling between groups 2 and 4 on the periodic table (see the single and double asterisks below).

The border indicates the natural occurrence of the element and the colour of the atomic number indicates its state of matter.

These are screenshots from Wikipedia's "Periodic Table." For clearer larger graphics go to the page.

The lanthanides and actinides are typical metals, even the radioactive elements in these series. They all have a silvery colour.

All the actinides are unstable, making them radioactive. Some actinides are found naturally and in very low concentrations, such as uranium (92), thorium (90) as well as tiny amounts of plutonium (94). The decay and transmutation of uranium also produces transient amounts of actinium (89) and protactinium (91) as well as occasional atoms of neptunium (93), americium (95), curium (96), berkelium (97) and californium (98). The rest of the actinides (Ensteinium (99), Fermium (100), Mendelevium (101), Nobelium (102) and Lawrencium (103), are purely synthetic and can only be made in colliders.

All the lanthanides are stable, except for one element, promethium (61). This synthetically produced element has no less than 38 different radioisotopes, most of which have half-lives of less of than 30 seconds. The other lanthanides are all found in nature and are often called rare earth elements, a group which also typically includes two non-lanthanides - scandium (21) and yttrium (39). These two elements are grouped in with them because they are often found in the same mineral deposits as the lanthanides and they share similar chemical properties with them.

What makes both actinides and lanthanides unique, and what boots them out into their own section, is their electron configurations.

The Electron Configurations of the Actinides/Lanthanides

In order to understand electron configurations, we must first take a look at electron energy shells, subshells and orbitals. The electron shells are labeled K, L, M, N, O, P and Q (or n=1, n=2, n=3, n=4 etc.) as you go from the innermost shell closest to the nucleus outward. Electrons in outer shells have more energy than those in inner shells. The very outermost electrons are the ones that participate in chemical reactions, so their configuration is an especially important indicator of how the element will act chemically.

Each shell is composed of one or more subshells. Subshells are labeled s, p, d, f and g. The s subshell can hold a maximum of 2 electrons (in one orbital), p can hold 6 electrons (in three orbitals), d can hold 10 electrons (in five orbitals), f can hold 14 electrons (in seven orbitals) and g can hold 18 electrons (in nine orbitals). Each orbital can hold a maximum of two electrons, with opposite electron spins. This allows them to obey the Pauli exclusion principle, which means no two electrons in an atom can have identical quantum numbers.

The table below is another Wikipedia screenshot. I've added it to show you how the increasing number of lobes in orbitals allows them to hold more electrons. Click the "table below" link to see a much larger version.

The K energy shell (n=1) is just a tiny sphere, a 1s subshell (see left), so it can hold only two electrons. The L shell (n=2) consists of a higher energy 2s spherical subshell plus three 2p subshells, each one looking like a barbell that is oriented in a different direction. This means that this energy shell can hold 8 electrons in total. The M shell (n=3) can hold 18 electrons in total and the N shell (n=4) can hold up to 32 electrons in total. Each increasing energy shell adds a new orbital:  p, d, f and so on.

An atom GENERALLY fills up electrons in order, so the K shell fills first, then the L shell starts to fill up and then the M shell fills up and so on.

If you look at the periodic table below, you will see group 3B (same thing as group 3): scandium, yttrium, and then going down this group, you see lanthanum and actinium. These lowest two squares are the first elements that begin filling up the d subshell with electrons, just like scandium and yttrium do, as you expect them to. Lanthanum and actinium are also the first two elements of the f-block. In fact, the whole f-block fits into group 3B.

Adapted from Roshan220195;wikipedia)
Scandium's (Z=21) electron configuration is written as [Ar]3d14s2 or 2,8,9,2. Noble gases such as argon (2,8,8) are simply used as writing shortcuts. These notations take a little practice with reading them. In scandium, this notation means that there are 2 electrons in the 1s K shell, 8 electrons in the L shell (2-2s electrons + 6-2p electrons), 9 electrons in the M shell (2-3s electrons, 6-3p electrons and 1-3d electron) as well as two electrons in the N shell (2-4s electrons). The important thing to note here is that some of the N energy shell begins to fill before the M energy shell is filled. Why would this be?

All the f-block elements have just one electron in their d-subshell. Electrons, instead, are filling up the 4f-subshell in the N energy shell. That's what places them all in Group 3 (or 3B). The number of electrons in the outermost shell determines the group. Notice from the table above that the 4f-subshell can hold a maximum of 14 electrons. Each series in the f-block contains, just as you expect, 14 elements. When the 4f-subshell is completely filled, atoms add electrons to the 4d-subshell. This subshell can hold ten electrons, and that's why the d-block is ten elements across. In Group 4, next door, there are two electrons in the d-subshell. In Group 5, there are three electrons in the d-subshell, and so on.

This periodic table shows electron energy shell diagrams (Bohr diagrams) of the elements. It's really useful to count the electrons and test your predictive skills but it is almost impossible to see, so click here to see a greatly expanded version on Wikipedia. If you scroll down, I've captured a screenshot of the first three elements in each of the two series. If you count the energy shells outward you have electrons in the K, L, M, N, O, P (lanthanides) and Q (actinides) energy shells. The O energy shell can hold up to 50 electrons, the P energy shell can hold up to 72 electrons, and the Q energy shell can theoretically hold up to 98 electrons. The largest atom in the current table contains 118 electrons - a partly filled P energy shell. A theoretical (behemoth!) atom having all shells filled including the Q shell would have the atomic number 260, with 260 electrons.

For the larger f-block atoms we use Xenon (2,8,18,18,8) as a shortcut. Lanthanum, like scandium, has one electron in the d-subshell. Its electron configuration is [Xe]5d16s2 or 2,8,18,18,9,2. Cerium, the next element over IN THE LANTHANIDES, not in group 4, also has just one electron in the d subshell, and it is written as [Xe]4f15d16s2 or 2,8,18,19,9,2. Notice that an electron is added instead to the f subshell. If you look at the diagram below, you can see where the new electron is added to cerium - to the N energy shell - and to the 4d-subshell in this energy shell in particular.

Lanthanum (2,8,18,18,9,2) has 1-5d, 2-5s and 6-5p (a total of 9) electrons in the O shell and 2-6s electrons in the outermost P shell. Cerium has exactly the same numbers of electrons in its outer O and P shells as lanthanum does. Next over, praseodymium has the same outermost shell as the other two do, but one less electron in its O shell and two more electrons in its N shell. You can begin to get a hint about why these elements look and behave so similarly to each other. They all share identical outermost electron shells, the shell that most determines their chemical nature. You can see the same trend in the actinides - they all fill an f-subshell first. The f-subshell contains seven orbitals, with each one holding a maximum of two electrons. The lanthanides fill up the 4f-subshell and the actinides below them fill up the 5f-subshell before the 6d energy shell is filled.

All the lanthanide elements have just one d1 electron until you get to hafnium (72) (which is not a lanthanide). Its electron configuration is [Xe}4f15d26s2 or 2,8,18,32,10,2 where the d2 electron is finally filled.

Americium and Curium Offer First Clues to the Existence of the F-block

The first clue that two series of elements should form rows separate from the rest of the periodic table came from Glenn Seaborg (below left) thanks to his work on the Manhattan Project in 1943.

He had found it unexpectedly difficult to isolate two radioactive actinide elements - americium (Z=95) and curium (Z=96). Most americium, a silvery white metal (a small disc under a microscope is shown below right), is produced by the fission of uranium or plutonium in nuclear reactors. Each tonne of spent nuclear fuel contains 100 grams of highly radioactive americium. It is most commonly used in smoke detectors.

Most curium is produced the same way as americium. 1 tonne of spent nuclear fuel contains 20 grams of it. It is one of the most radioactive elements known, emitting radiation so strong that a sample of curium glows purple in the dark, shown below left.

Its most common use is in X-ray spectrometers. Curium, harder and denser than americium but similar in appearance, was discovered before americium in 1944. The separation of americium from curium took so long (abut a year) and was so painstaking that researchers working on them first called these elements pandemonium (meaning demons or hell in Greek) and delirium (madness), respectively. A 7-minute RSC podcast describes the discovery of americium (and how smoke detectors work as well as americium's connection to the nuclear bomb).

Seaborg was the first to suggest that the f energy shell was filling up before the d shell. Before this, the actinides were thought to be filling up a fourth d-block row. He published his theory despite warnings from his colleagues that this radical departure from the current formulation of the periodic table would ruin his career. In 1951, he received the Nobel prize in Chemistry not for placing the actinide/lanthanide series as a separate group called the f block, but for discovering or co-discovering ten radioactive elements, some of which are actinides and several of which are man-made, including seaborgium (106) (not an actinide) and more than 100 atomic isotopes as well.

How the F-block Works Differently Than the D-block

The reason why these elements act this way is because the energy difference between the 4f and 5d (and between the 5f and 6d) subshells is very small to begin with. After lanthanum, for example, the energy of the 4f sub shell actually falls below that of the 5d sub shell and that's why it's filled first. The evidence for this came from the unique emission line spectra of these elements, revealing unexpected energy differences as electrons shift between these energy shells.

Another electron arrangement unique to the lanthanides series is that the 5s and 5p orbitals penetrate into the 4f-subshell. This has the effect that 4f-subshell electrons are not shielded from the increasing positive nuclear charge and that means that the attractive force makes the radii of their orbitals contract so they nudge closer to the nucleus. This means that the radii (physical size) of the lanthanide atoms actually decreases as atomic number increases. For example, the atomic radius of cerium (second lightest lanthanide, Z=58) is 2.70 angstroms across and the atomic radius of lutetium (heaviest lanthanide, Z=71) is just 2.25 angstroms. As proton number increases and radius decreases, the ionization energy (the energy you need to pull an electron into a higher energy shell or the energy released as it returns to ground state) increases, as you might expect. Increasing ionization energy means that outermost electrons are held more and more tightly to the atom. Density, hardness and melting points are high to start with in the lanthanides and they increase even further as you go left to right in the series as a consequence of this. This makes the lanthanides easier to separate from non-lanthanides, but it makes it more difficult to separate lanthanides from each other. This, and their chemical similarity to one another, is why the rare earths are notoriously hard to purify (we will explore these fascinating rare earths in Periodic Table Part 5: Rare Earths - A Story of Discovery, Demand and International Intrigue.

The unusual progression toward smaller atomic size is called the lanthanide contraction. It is similar to a contraction that occurs in the d-block elements (transition metals), called the scandide contraction, but the mechanisms behind the two contractions are slightly different: The scandide contraction is caused by poor shielding of the nuclear charge by electrons in the d-subshell, whereas the lanthanide contraction is caused by poor nuclear shielding by electrons in the f-subshell.

Next up: History of the Periodic Table Part 5.

Thursday, February 13, 2014

History of the Periodic Table Part 3: Spectroscopy Paves the Way For the Quantum Atom

The early 20th century was the most fruitful time ever for atomic theory. Research from many different angles was refining Rutherford's atomic model into the modern quantum mechanical atom. As the concept of the atomic nucleus came together (explored in detail in History of the Periodic Table Part 2), so did the mysterious workings of the atom's electrons. New technologies such as X-ray spectrometry helped elucidate the electron configurations of the different elements.

The way X-ray spectroscopy works depends on the atom's electrons rather than its protons. The light each element emits when its atoms are excited creates a specific spectrum, filled with special absorption lines called Fraunhofer lines. You can tell a lot from these lines and they are invaluable for studying the compositions of faraway stars simply by examining their light. These lines are present in every spectrum, even the band of colours you see in a prism or a rainbow. You don't usually see them because they are extremely fine. Each line is created by electrons in atoms absorbing photons of a very specific energy, observed as a specific wavelength of electromagnetic radiation, or colour.

Spectral lines had been known as early as around 1800. Fraunhofer, using a very good prism called a spectroscope (a diagram of the setup is shown right), rediscovered them in 1814, and was the first person to carefully measure them in the Sun's spectrum.

The Sun's visual spectrum with Fraunhofer lines is shown below.

Their origin however was a mystery. In 1888, Johannes Rydberg came up with an ingenious formula that described the relationships between spectral lines emitted by alkali metals, but he did not know why his formula worked.

When an atom is excited (has extra energy), one or more electrons jump up to higher energy orbitals. An electron can gain energy by absorbing a photon of a specific energy or by absorbing energy through a collision with another particle such as an electron. The atom's electron then releases the extra energy as a photon of a specific wavelength when it jumps back down to its non-excited state. Absorption and emission give each element an absorption spectrum and an emission spectrum. Simplified spectra of hydrogen are shown below.
The emission/absorption lines in these spectra only represent photons in the visual spectrum, but emitted photons can be photons of visible light (low energy), ultraviolet light (higher energy) or even X-ray photons (much higher energy), depending on the energy difference between the two orbitals in the atom. The smaller an atom is, the fewer electrons it has and more simple its absorption spectrum is, but even hydrogen's absorption spectrum is very complex if shown in finer detail. The visual spectrum of the Sun (almost all just hydrogen and helium) at the top of this article gives you an idea of how complex it can be. Large atoms produce extremely complex spectra but one or two lines are often extra bright. These brightest lines represent the most common lower-energy orbital jumps, and they can be used to identify the presence of that element.

As often happens in science, a breakthrough begins with a problem. In 1913, Niels Bohr (shown below right) proposed a solution to a very disturbing problem with Rutherford's atomic model.

According to classical mechanics (the Larmor formula specifically), an electron should release electromagnetic (EM) radiation while orbiting a nucleus because the electron is in a state of acceleration so it should continuously lose energy and spiral inward, and all the while the frequency of the EM radiation should increase. This means that no atom can be stable. Bohr, thinking about this, proposed that electrons orbit only in stable orbits around the nucleus which are set at specific energies and which don't change. They orbit as different frequencies of standing waves in other words. These waves have resonance so the continuing waves interfere constructively with each other, maintaining the energy of each electron in its orbit.

Below is a typical Bohr model of an atom; this one is an excited hydrogen atom. It has just one electron, which can assume one of many different possible energy levels, some of which are represented below as grey circles. These circles represent electron energy shells. Higher shells represent more energy (hydrogen has more than 11 energy shells, which are increasingly faint in its spectrum because these electron transitions are increasingly rare events).

A previous article, Atoms Part 2: Atoms and Light, explains in detail what energy shells are and how they work. Emission spectra and absorption spectra are also explained in detail in that article.

The Bohr model was not only about to help usher in a huge breakthrough in atomic theory - quantum mechanics - it also had great bonus effects - it explained why Rydberg's formula works and it sparked a way to figure out why atomic number corresponds to proton number in the periodic table.

Henry Moseley, a physicist (shown below), became interested in Bohr's new atomic model. Moseley knew that Rydberg's formula worked very well for hydrogen, but he wanted to know if it also worked for larger atoms as well. He also wanted to know if there was a real physical relationship between atomic number and atomic weight.

Like the Sun's visible light, X-rays are photons of EM radiation. To do X-ray spectroscopy, Moseley bombarded his target element with high-speed electrons. Each of these electrons had enough energy to eject an electron from the innermost energy shell in a target atom. This left a vacancy in that shell so an electron from the next highest energy shell dropped down to fill in the spot. As it did so, it emitted a photon with a sharply defined energy corresponding to the energy difference between its original energy shell and the one it dropped down to.

To explore his questions, Moseley studied the brightest spectral line (called the K-alpha line) of ten elements from calcium (Z=20) to zinc (Z=30). This spectral line is the result of a transition by a single electron from an outer L (also called n=2) electron energy shell to an inner K (also called n=1) shell of the atom.

When an electron jumps down from the L shell to the K shell, it emits photon of a particular X-ray frequency (the K-alpha line). We know today that the wavelength of the K-alpha line depends on the energy of the electron's energy shells. The energy of an electron's energy shell depends on a complex interaction between two opposing forces - electrostatic repulsion between the electron and all other electrons in the atom, which depends on where the electrons are located relative to each other, and second, the electrostatic attraction between the electron and the nucleus, which depends on how much positive charge (how many protons) the nucleus has. Shielding by the nucleus also complicates matters because there is always at least one electron that is opposite the electron in question, with its repulsive charge being shielded by the charge of the nucleus. This complex picture is why the Rydberg formula only works perfectly for hydrogen (a simple arrangement of an electron and a proton) and well for elements that have small nuclei and few electrons, such as the ions He+, Li2+ and Be3+ with reduced numbers of electrons.

Moseley found a way to identify larger elements by developing a formula (Moseley's law) from his work with larger (calcium to zinc) atoms. This formula can be used to predict the strongest spectral line, the K-alpha (n=2 to n=1emission) line, for larger atoms. These atoms, despite their complexity, have one trend in common that makes Moseley's law work. As the charge of the nucleus increases, the attractive pull on electrons in the closest energy shell increases in a fairly simple linear way. A photographic recording of his results is shown below left.

In general, from left to right each element's spectrum shows strong Ka (the line he was particularly interested in) and Kb X-ray emission lines. Brass (shown at the bottom above), an alloy of copper and zinc, shows the spectra of both these elements.

As nuclear size increases, more energy is required to move electrons up from the n=1 shell to the n=2 energy shell farther away from the positive charge, and therefore more energy (a shorter X-ray wavelength) is emitted when that electron falls back down to n=1.

Moseley found a systematic relationship between wavelength and the element's atomic number, providing a physical basis for a number that, before this, was considered to be more or less an arbitrary place setting for elements listed according to their increasing atomic weights. An example of how Moseley's work is useful comes from comparing cobalt (top) and nickel (bottom) shown below right.

Cobalt, Alchemist-hp;Wikipedia
Based on their atomic mass alone, nickel (58.69 u) should come before cobalt (58.93 u) in the periodic table, and Mendeleev placed them in this order to reflect that. But X-ray spectroscopy tells us that nickel actually has a higher positive electric nuclear charge than cobalt does, placing nickel before cobalt. Today we know that nickel has 28 protons in its nucleus (atomic number 28) and cobalt has 27 (atomic number 27 or Z = 27). Potassium (Z=19) and argon (Z=20) are two other examples of elements flipped to their correct places in the periodic table based on X-ray spectroscopy.
Nickel, Materialscientist;Wikipedia

X-ray spectroscopy is also a very useful tool for distinguishing elements that are almost identical chemically and physically. For example, its use proved the existence of a missing element predicted at atomic number 72, hafnium. This element is chemically virtually indistinguishable from zirconium, Z=40) and they are often found in the same mineral. Hafnium (top) and zirconium (bottom) are shown below left.

In 1913, Moseley concluded not only that atomic number was the most important factor in ordering the periodic table, but that this ordering was more consistent with the chemical and physical properties of elements than atomic weight was.

He deduced that atomic number is based on the number of protons (he called them positive units of charge because the proton was not named until 1920) in the periodic table. The stage was set to take Bohr's still fairly simple energy shell model of the atom to the modern quantum mechanical model, which is based on complex mathematical calculations and interpretations.

In this model, the energy and position of electrons inside an atom are determined by a set of numbers called quantum numbers, and it changed our mental picture of an electron from a particle/wave to a fuzzy cloud. The numbers are solutions to complex quantum equations. They not only define the electron's energy state but also the shape of its trajectory, or orbital, when it is in that energy state.

Around 1925, Erwin Schrodinger applied the principles of wave mechanics to the atom. His solutions resulted in various orbital shapes for electrons based on their energies. In the same year, Werner Heisenberg applied his quantum uncertainty principle to the electron, defining orbitals further as probability densities, and refining the electron itself into a fuzzy cloud of charge rather than a particle/wave.

An online chemistry lecture called Atomic Theory: The Quantum Model of the Atom from the University of Vermont provides an excellent review of the evolution of atomic theory described in this article.

Next up: History of the Periodic Table Part 4.

Tuesday, February 11, 2014

History of the Periodic Table Part 2: What is Atomic Mass?

In the early 1800's, as Johan Wolfgang Dobereiner's triadic version of the periodic table was being developed, John Dalton, Thomas Thomson and Jons Jakob Berzelius were beginning to figure out the relative atomic masses of the elements. At the time, each element's mass was taken as a number relative to the lightest known element, hydrogen, which they called number 1. The logic behind this is that scientists believed that each element was built up of atoms of hydrogen. And at this time, knowing nothing about subatomic particles, they considered each atom to be an indivisible unit.

This relative mass idea is known as Prout's hypothesis. Scientists thought that the atomic mass of any element would always be an exact whole-number multiple of hydrogen's mass (1), but soon, to the shock of the scientists involved, this was proved to be wrong. Some measured masses weren't even close. In 1826, Berzelius (shown below right), a man devoted to careful measurement and fastidious lab work, developed a precise way to measure atomic mass through experiment.

He discovered that the atomic mass of chlorine, in particular, fell in between two whole numbers (its mass is approximately 35.45 u). In his Treatise on Chemistry, Berzelius described his procedure for measuring the atomic mass of chlorine:

"I established its [chlorine's] atomic weight by the following experiments: (1) From the dry distillation of 100 parts of anhydrous potassium chlorate, 38.15 parts of oxygen are given off and 60.85 parts of potassium chloride remain behind. (Good agreement between the results of four measurements.) (2) From 100 parts of potassium chloride 192.4 parts of silver chloride can be obtained. (3) From 100 parts of silver 132.175 parts of silver chloride can be obtained. If we assume that chloric acid is composed of 2 Cl and 5 O, then according to these data 1 atom of chlorine is 221.36. If we calculate from the density obtained by Lussac, the chlorine atom is 220 [relative to the atomic weight of oxygen]. If it is calculated on the basis of hydrogen then it is 17.735."

Notice that his measurement is almost exactly half of the modern measurement. The reason is that at the time scientists didn't know hydrogen existed as a diatomic gas so his hydrogen standard was off by half.

Atomic mass can be a confusing concept. Measured in unified atomic mass units, amu or just u, it is sometimes called atomic weight instead - the two terms are often used interchangeably, and most of the time that's fine. However, these are two of several terms in chemistry that create a lot of problems for students and wreak havoc on their teachers. Chemwiki has an excellent definition chart you can use to clear up the chaos. Strictly speaking, atomic mass is the mass of an individual atom at the microscopic scale, whereas atomic weight is the average atomic mass of an element. Isotopes are the reason why there is a subtle difference between the two definitions.

The Discovery of Isotopes: The Modern Atom Begins to Take Shape

Berzelius didn't know this, and in fact most high school chemistry students don't know this (yet), but you can measure the atomic mass of one sample of pure chlorine to fantastic precision and measure another sample of pure chlorine taken from somewhere else in the world and get a different number. Why?

Almost a century after Berzelius's work, around 1910, isotopes were discovered, and the unexpected discrepancies between measurements like the chlorine example I just mentioned, were shown to be due to an isotope effect, where the masses of elements may reflect a mixture of stable isotopes of those elements. This means that atoms of the same element (same number of protons) can have different numbers of neutrons in the nucleus, and that variation affects the atom's mass.

Most people credit the discovery of radioactivity to Henri Becquerel in 1896. He noticed that uranium salts blackened photographic plates, due to some kind of radiation, thought at first to be X-rays. It was not long until researchers such as Ernest Rutherford, Paul Villard and Pierre and Marie Curie realized that the radiation that Becquerel detected was more complex than first thought. And the implications were unsettling.

Around this time, researchers working with thorium, a radioactive element found in naturally occurring thorite minerals, discovered that the naturally found thorium in the mineral emits beta particles (electrons). A thin sheet of thorium in argon is shown below. Pure thorium is a silvery white lustrous metal but when some thorium oxide is present, as it usually is, it eventually tarnishes to black.

They found that thorium isolated from decaying uranium emitted an entirely different particle - the alpha particle. Thorium has over 30 (all radioactive) isotopes, most of which decay by emitting an alpha particle but some isotopes decay through beta decay.

They didn't know what alpha and beta particles were but they could detect that they moved in opposite directions when placed in an electric or magnetic field, and they could detect that one kind (beta) always traveled a lot further than the other kind (alpha). It only took a few years for Becquerel to realize that the beta particle was an electron based on its mass to charge ratio, which was the same as Thomson's results. Otherwise, the two thorium samples were identical. These results flew directly in face of Dalton's atomic theory: If two atoms have the same number of electrons they must also have the same number of protons in their nuclei, and therefore they should behave identically. And yet, these researchers knew that something had to be different between these two thorium samples.

There are many different kinds of radioactive decay and some of them change or transmute one kind of atom into another kind by changing a neutron into a proton or vice versa. Protons were discovered in 1917 when Rutherford expanded on Prout's idea that hydrogen was a standard building block of all heavier elements. Hydrogen contained only one of the newly discovered positively charged particles  emitted through some kinds of radiation (proton emission), while other atoms contained more of these particles. Rutherford named these positive particles protons in 1920.

Along with the isotope mystery, something about atoms was way off. Scientists, looking at the various elements, knew that the relative atomic mass of an atom always seemed to be a bit more than double the atomic number, Z. They also knew that almost all the mass of an atom was concentrated in a tiny volume in the centre (thanks to Rutherford). The atom, as far as they knew,  consisted only of protons and electrons and the atomic mass data meant there had to be twice as many protons as electrons. This was a mystery because they also knew that atoms are electrically neutral. They thought that perhaps half the electrons were bound up in with the protons, cancelling their positive charge somehow. It wasn't a very satisfactory explanation, and the newly formulated uncertainty principle implied that there wasn't nearly enough energy in the atom to confine the (electrically repulsive) electrons inside the positive nucleus.

Neutrons were discovered in 1932 by James Chadwick. It's a bit of a story and the link explains how he did it. His discovery of the neutron finally put the lingering isotope mystery on firm conceptual ground. Isotopes have the same number of protons but different numbers of neutrons in their nuclei. The alpha particle was finally found to be a helium nucleus, consisting of two protons and two neutrons.

Relative atomic mass, which used to be called standard atomic weight, is now calculated as 1/12 the mass of carbon-12. Carbon-12 has an exact isotopic mass of 12 u. This exact value is what makes it useful as a standard atomic mass. Carbon as looked up on Wikipedia has a mass of 12.0107 u and this difference reflects the fact the it is the average mass of carbon-12 and carbon-13, two stable isotopes, according to their average natural abundance.

However, the isotopic makeup of samples from different sources on Earth can vary quite a bit, and this turns out to be both a little problem and a very useful scientific tool. On the plus side, you can pinpoint the original location of archeological samples of bone, teeth, iron tools, glass and lead-based pigments based on their isotopic profile. On the minus side, this can lead to inaccuracy when relying on the relative or average value for mass. Calculating the geographical variance of the isotopic profile for various elements is still a work in progress, as scientists work out with increasing precision the relative isotopic abundance of elements not just at various locations on Earth, but in the universe as a whole.

As a result, in 2010 the International Union of Pure and Applied Chemistry (IUPAC) changed the formal definition of atomic mass. The atomic masses of hydrogen, lithium, boron, carbon, nitrogen, oxygen, silicon, sulfur, chlorine and thallium are now written as intervals rather than as single numbers. Some modern applications require very precise atomic mass, so this change is necessary for accuracy. *Carbon is now listed as 12.0107 +/- 0.0008 u, a reflection of the varying abundance of two stable isotopes - carbon-12 and carbon-13 depending on the geographical origin of the sample. Only ten elements have so far been updated either because others only exist as a single stable isotope or because the upper and lower mass limits of the element haven't been measured yet. The IUPAC also regularly updates atomic masses as measuring precision improves.

Below is a screenshot from Wikipedia showing the average relative atomic masses of the elements. It doesn't reflect the new mass intervals of ten elements.

Lead (Pb, Z=82, atomic weight = 207.2) is the heaviest stable element. All elements with atomic numbers over 82 have no stable isotopes. The atomic mass of these elements is taken as the mass of the longest-lived isotope, and for some very short-lived elements it is an estimate only.

Mass Defect

When isotopes were discovered, scientists figured that a pure isotope (no mixture) should still have a relative atomic mass that is an exact multiple of 1 to within 1%. In other words, it should have a mass equal to adding up the individual masses of its protons, neutrons and electrons (proton and neutron masses are almost identical). However, this too is now known to be incorrect, and we will use the element helium as an example to explain why.

Helium exists almost entirely as helium-4 on Earth. Based on what we now know about relative atomic mass, we expect its mass to be almost exactly 4.000 - 2 neutrons + 2 protons = 4 (plus a small mass contribution made by electrons). We find by Googling helium that its average measured atomic mass (standard atomic weight) is 4.003.

However, helium-3 is also present in trace amounts on Earth (it is the only other stable isotope of helium). Looking up helium-3, we find it has an isotope mass of 3.016. Wait a minute. We expect it to be almost exactly 3.000 because it is a pure isotope. Why so much off?

This leaves us with two questions: (1) why isn't helium-3, a single isotope, almost exactly 3.000 and (2) why is the average atomic mass of helium slightly HIGHER than 4.000 (4.003) rather than lower, since helium-3 (smaller mass) makes an, albeit, small contribution?

The answer is called mass defect. To illustrate what mass defect is, let's add up the known masses of all the subatomic particles in an atom of helium-4. It has two electrons, two protons and two neutrons. The masses of these particles (in amu) are all known to at least six significant digits so:

2 X proton (1.007276) = 2.014552
2 X neutron (1.008665) = 2.017330
2 X electron (0.000549 = 0.001098

Total = 4.032980

Why isn't this value 4.003, the measured mass of helium? First, let's recap what we know: 4.000 is helium's relative atomic mass (relative to carbon) but it is not its unified atomic mass, the value that reflects its actual average measured atomic mass as it is found on Earth. If we look up helium-4's unified atomic mass, it is 4.002603 amu (or just u), rounded up to 4.003 as shown above. This number is quite a bit different from both its relative atomic mass (4.000) and the value we got by adding up its components (4.032980).

The difference between the sum of the components and the measured amu value is called the mass defect. Energy is released when the helium nucleus is assembled from its protons, neutrons and electrons, so the helium atom has lower potential energy (reflected by 4.003 rather than 4.033). The mass difference, 0.030377 u, is the mass equivalent of the energy that is released. This released energy is called the binding energy. The helium nucleus has lower potential energy than it's separate nucleons but it has higher binding energy, and this is what makes the formation of helium atoms thermodynamically favourable. If we wanted to split a helium-4 atom, we would have to add that energy back.

You might wonder why we have to add energy to helium to get it to break apart. After all, doesn't the fission going on in nuclear plants release energy? The answer is in the size of the atom. Iron is the most stable atom of all atoms. It has the highest binding energy and therefore it doesn't fuse or split. Atoms smaller than iron release energy when they fuse into larger atoms. The larger atom will have higher binding energy and lower potential energy. Atoms larger than iron (including those used in nuclear fission reactions, such as uranium) release energy when they are split apart.

If we add up the components of helium-3, we get:

2 X proton (1.007276) = 2.014552
1 X neutron (1.008665) = 1.008665
2 X electron (0.000549 = 0.001098

Total = 3.024315

Helium-3's isotopic mass is 3.0160293 u, so 3.024315 - 3.0160293 gives it a binging energy of 0.0082854 u, about a quarter of helium 4's binding energy of 0.030377 u.

ALL atoms, including those with radioactive unstable nuclei, have at least some positive binding energy. However, the binding energy in some atoms is not strong enough to hold the nucleus together indefinitely. These atoms will lose neutrons or protons (decay) until they reach a product that is stable. Very unstable nuclei may decay in microseconds while almost stable nuclei may take up to billions of years to decay.

The real measured atomic mass of an element therefore depends not only on its isotopic makeup but on its mass defect as well, and that depends on the particular atom's binding energy. An atom's binding energy consists of its nuclear binding energy (huge contribution since the strong force is involved) as well as its electron binding energy, better called ionization energy (a much smaller contribution since the far weaker electromagnetic force is involved). Ionization energy is the energy required to strip the atom of its electrons, to ionize it in other words.

Atoms with especially stable arrangements of neutrons and protons have especially high mass defects, especially low potential energy, and especially high binding energy. Atoms with unstable nuclear arrangements are radioactive. Calculating stability compared to decay rate is a bit complicated; it is an example of a many-body problem in physics. Physics Stack Exchange provides a really good explanation of it, if you are curious. Radioactive nuclei will go through a decay process. There are three basic decay possibilities: A nucleus will change a proton into a neutron or the reverse (beta decay), it will eject either an alpha particle (helium nucleus) or a proton, or, third, it will eject an even larger element nucleus. These decays either result in a new isotope of the element (if only the number of neutrons is altered) or a whole new element (if the number of protons changes). The latter process is called transmutation and it is the only real way, along with fusion, to change one kind of element into another kind. This is the real-life version of the philosopher's stone mentioned in the previous article.

Helium, with its two neutrons, two protons and two electrons, forms an unusually stable atomic arrangement. The graph below compares binding energy with nuclear size.

Iron (Fe), mentioned earlier, has the highest binding energy (graph peak) while helium-4's binding energy forms an unusually sharp upward spike at the left end of the graph. Helium-4 has a remarkably stable nucleus giving it a significantly lowered atomic mass. If you look at helium-3 above you see that it's right in line of where it's supposed to be. It's nuclear arrangement of two protons and just one neutron gives it an average binding energy.

Helium is extremely inert, which means it is chemically unreactive under all normal conditions so it won't form any compounds. It is also almost always a monatomic gas, condensing to a liquid only at the very cold temperature of 4.22 K, or -269°C, that's very close to the temperature of the vacuum of outer space (2.73 K). Like all elements, these chemical properties of helium come from its electron configuration, which is influenced by the electron's interactions with each other and with the nucleus. Helium's unusually stable nucleus and high binding energy is why element formation in the early universe pretty much stopped after helium nuclei formed (all larger atomic nuclei have been created in stars).

Why isn't hydrogen chemically inert too? Iron, even though it has an extremely stable nucleus, is fairly chemically reactive. Because of its particular electron configuration, it can either lose or accept electrons (usually from water or oxygen) to form various ionic compounds, such as iron oxide (rust). It is the electron configuration, not nuclear stability, which influences the physical and chemical properties of the elements, aside from their radioactivity of course. Chemical bonds between atoms was explained by Gilbert Newton Lewis in 1916, as an interaction between the electrons of the atoms involved.

Between 1800 and the early 1900's, the idea of what an atom is evolved at an explosive rate because there were so many great minds at work on the concept of the atom. Around the same time as the proton and neutron were discovered, the electron configuration of the atom was being sorted out. Bohr's model of the atom hinted that electrons have specific energies within the atom. They can gain or lose only discrete packets or quanta of energy. In the 1920's the quantum mechanical model of the atom was formulated. The evolution from Rutherford's atomic model to the modern quantum mechanical model marks one of the greatest breakthroughs ever in both chemistry and physics, with spin-off progress in biology, engineering, geology, practically every other scientific discipline there is.

In 1817, when Johan Wolfgang Dobereiner was putting together his law of triads, none of these things were known - isotopes, nuclear binding energy and ionization energy. No one knew that mass and energy were equivalent. No one knew exactly how atoms interact with each other, why they give off light and other radiation and how they transmit heat. No one knew how the fundamental forces make atoms what they are. All they knew was that the Earth seemed to be composed of a growing list of various simple substances, substances that seemed at the time to be fundamental, meaning they can't be broken down into anything smaller, and that some substances reacted with other substances to make yet different substances and others did not react at all. Unknown to researchers of this time, they were taking the first steps toward an amazing new era of science.

Next up: History of the Periodic Table Part 3.