On 30 December 2015, the science of chemistry officially got four new subjects. The International Union of Pure and Applied Chemistry (IUPAC) confirmed the discovery of four new chemical elements, all of which had been created in labs.

Some reports have suggested that these elements "complete" the periodic table of elements. This is wrong. You can confidently expect further new elements after the latest batch. But it might take a while, because they are getting harder to make.

What the new elements do complete is the seventh row of the periodic table. If and when elements 119 or 120 are made, they will start a whole new row.

No one knows how much longer the table can be extended by the creation of new elements. Some suspect there is no limit. Others say there may be a point beyond which atoms cannot get any heavier: such enormous atoms would be completely unstable, instantly disintegrating in a flurry of radioactivity.

But one thing is clear. If we do manage to build ever-heavier elements, we will find that they behave in truly peculiar ways.

Elements are the fundamental building blocks of chemistry. An element is essentially a substance that only contains one kind of atom. So making a new element means making a new kind of atom.

Each element is assigned a number: for instance, carbon is number 6. These numbers are not arbitrary labels, but have a fundamental significance. They specify how many protons, a kind of elementary particle, the atom contains.

It sounds outlandish but is actually happening all the time, even in some of the atoms in your body

Protons have a positive electrical charge, and they are clumped in a blob in the centre of the atom. The much lighter electrons, with negative charges that balance the protons', "orbit" the nucleus in a diffuse cloud.

With the exception of hydrogen atoms, atomic nuclei also contain a second kind of particle: the neutron, with a mass almost exactly the same as that of a proton but with no electrical charge. Atoms of an element can have different numbers of neutrons, and these variants are called "isotopes".

Neutrons serve as a kind of glue that helps bind protons together. Without them, the protons' positive electric charges would push them apart.

All the same, the nuclei of very heavy atoms like uranium are so packed with mutually-repelling protons that not even a preponderance of neutrons can hold them together. These atoms undergo "radioactive decay": they shed particles and energy.

Bigger stars can generate heavier elements like mercury

When an atom decays, the total number of protons in the nucleus changes, and so the radioactive decay process turns one element into another. It sounds outlandish but is actually happening all the time, even in some of the atoms in your body.

Each type of nucleus has an optimal ratio of protons to neutrons. So atoms will decay if they have too many or too few neutrons, even if they have small nuclei.

For light elements like carbon and oxygen, the stable ratio is pretty much 1:1. Heavier elements need a slight excess of neutrons.

The universe's natural processes can only produce elements up to a certain weight.

The lightest five elements, from hydrogen to boron, were mostly created in the Big Bang that started the universe.

Anything heavier had to be made inside stars. There, the intense temperatures and pressures force the nuclei of light elements to fuse together. This is called nuclear fusion. Bigger stars can generate heavier elements like mercury, which has 80 protons in its nucleus.

The discovery of plutonium remained a military secret until after World War Two

But many of the elements in the periodic table are instead made in the intense environment of an exploding star or "supernova". The enormous energies released can produce new kinds of fusion as atoms crash into one another, producing elements as heavy as uranium, with its 92 protons.

Lots of energy is needed for these nuclear fusion reactions to occur, because the positively-charged atomic nuclei repel one another. A nucleus must be moving really fast to punch through this barrier and merge with another.

As a result, uranium is the heaviest element found in significant quantities in nature. No natural process has been found that makes much of anything heavier.

So when scientists want to make new elements, they have to use particle accelerators to boost colliding atoms to enormous speeds, perhaps a tenth of the speed of light.

This was first done in 1939. Scientists working at the University of California at Berkeley created element 93, which is now called neptunium.

Once the war was over, physicists set to finding new elements in earnest

Two years later, the team bombarded uranium with "heavy hydrogen" nuclei, each of which contained one proton and one neutron. The result was element 94: plutonium.

They soon realized that plutonium, like uranium, would decay spontaneously in a dramatic process called nuclear fission. Its massive nucleus split almost in half, releasing a tremendous amount of energy.

This finding was quickly put to use: plutonium made in particle accelerators was used in the Fat Man atom bomb dropped on Nagasaki in August 1945. The discovery of plutonium remained a military secret until after World War Two.

Once the war was over, physicists set to finding new elements in earnest.

For decades, the key US centre for this research was at Berkeley, but nowadays, much of the activity has shifted to the Lawrence Livermore National Laboratory about 40 km away. The Russian work is based at the Joint Institute of Nuclear Research (JINR) in Dubna, Moscow, founded in 1956.

The US-Soviet rivalry produced some bitter disputes about priority

Initially, the Americans were ahead of the game. As a result, elements 95, 97 and 98 are called americium, berkelium and californium.

But other new elements were found in a completely different way. They were identified in debris from the US's hydrogen-bomb tests of the 1950s. The elements had been created from uranium in the bombs' "fuses" during the intense blasts.

As a result, rather than crowing about their place of origin, elements 99 and 100 are named after two pioneers of nuclear science: einsteinium for Albert Einstein and fermium for Enrico Fermi.

As the Cold War deepened, the US-Soviet rivalry produced some bitter disputes about priority.

Between the late 1950s and the early 1970s, the Berkeley and JINR teams argued over who first made elements 102, 104, 105 and 106. IUPAC adjudicates such arguments, but it took until 1997 to award 104 (rutherfordium) to Berkeley and 105 (dubnium) to JINR.

The Russians are unhappy that element 113 has been awarded to a Japanese group

Meanwhile, element 107 was contested between JINR and a new kid on the block: Germany's Laboratory for Heavy Ion Research, known by the German abbreviation GSI, in Darmstadt. Credit for the discovery was eventually split between the two groups.

While earlier artificial elements were made by bombarding heavy atoms with much lighter ones, the GSI researchers found ways to merge two medium-sized nuclei: for example, firing zinc, nickel and chromium ions at targets of lead and bismuth. By such means, element 108 was first made at GSI, and named hassium.

These days element-making is a little more collaborative. When it came to making the four new elements, the Americans, Russians and Germans pooled their resources.

The IUPAC says the first convincing syntheses of both 117 and 115 were due to a joint effort between JINR, Oak Ridge National Laboratory in Tennessee and Livermore in experiments conducted between 2010 and 2012. A separate JINR-Livermore collaboration starting in 2006 has been awarded element 118.

All is still not entirely rosy, however. The Russians are unhappy that element 113 has been awarded to a Japanese group at the RIKEN Nishina Center for Accelerator-Based Science in Saitama, and might now be named "japonicium".

It might seem that we are reaching the upper limit for atomic size

They say they made it first in 2003 at JINR by smashing calcium into americium. The Japanese experiment was done a year later by shooting zinc ions into bismuth.

The issue in all these disputes is what counts as a convincing result. IUPAC experts decide this, but it is still rather subjective.

The new elements are detected, generally one atom at a time, by the characteristic way they undergo radioactive decay. Each isotope has a different decay process. Each also decays at its own rate, measured as the half-life: the time taken for half of a sample to decay.

These subtle signals have to be spotted amidst a welter of other nuclear processes, so it is not easy to decide whether a claim is persuasive or not.

Given these difficulties, it might seem that we are reaching the upper limit for atomic size. But there is good reason to press on into the eighth row of the periodic table.

The prospect of starting a new row of the table is enticing, because it will mean creating atoms unlike any we have ever seen before.

The electrons in atoms are organized into groups called shells. Each shell has a particular capacity, and it is these shells that determine both how the atoms behave and the shape of the periodic table.

The issue in all these disputes is what counts as a convincing result

The first shell can accommodate only two electrons: hydrogen atoms have one, helium has two. The second shell may house up to eight electrons: this is why the second row of the periodic table has eight members. Higher shells can take even more electrons.

The four new elements are the last remaining members of the seventh row. If we could make element 119 it would be the first member of the eighth row and therefore the first known element with an electron in the eighth shell.

Such extreme elements may break the rules that govern the periodic table.

Elements in the same column of the table have similar properties. This is because their outermost shells are laid out in the same way.

"Relativistic" effects can mean a super-heavy element does not behave as we would expect it to

For example, the elements in the far-left column are all reactive metals. They all have a single electron in their outer shell, which is an unstable setup: the atoms are prone to lose this lone electron.

In contrast, the elements in the far-right column all have full sets of electrons, and this means they are extremely unreactive: hence their name, the "inert gases".

But these rules may not hold for all the super-heavy elements.

In their atoms, the electrons near the nucleus are so tightly bound by the positively-charged nucleus that they travel at immense speeds. They are so fast that they feel the effects of Einstein's theory of special relativity, which states that objects moving close to the speed of light gain mass.

As a result, the inner electrons become heavier. This has a knock-on effect on the outer electrons that determine an element's chemical behaviour, because the electrons "feel" each other's movements thanks to their electrical charges.

There may be some super-heavy elements whose nuclei are relatively long-lived

The upshot is that "relativistic" effects can mean a super-heavy element does not behave as we would expect it to. That seems to be the case for rutherfordium (element 104) and dubnium (105), but not for seaborgium (106) or hassium (108).

Even examining such effects is a staggering technical feat. It requires studying the chemical behaviour of a handful of atoms that only exist for a few seconds.

What's more, super-heavy elements tend to decay ever faster the heavier they get. That means it is going to be increasingly difficult not only to study their chemistry, but even to make them – or at least, to detect them once we have done so.

All the same, it is possible to estimate how stable these larger nuclei will be, and it looks like they will last long enough to study if we make them. So there seems to be no reason in principle why we should not march on into the eighth row of the periodic table.

In fact, super-heavy elements may not always get less stable the heavier they are. There may be some whose nuclei are relatively long-lived, existing in "islands of stability". This will depend on the numbers of neutrons as well as the numbers of protons.

It now seems that this particular island of stability might not materialise until element 122

Nuclear physicists have found that the protons and neutrons in nuclei are, like the orbiting electrons, organized into shells. Filled shells correspond to "magic numbers", and lead to particularly stable nuclei.

The nuclei of helium, oxygen, calcium, tin and lead all have a filled shell of protons, making them especially stable. Filled neutron shells may also confer stability. The isotope lead-208 is "doubly magic", with filled shells of both protons and neutrons.

For super-heavy nuclei, the calculations that reveal the magic numbers are harder to do, so it is less clear what those numbers are.

It was once thought that two isotopes of element 114, named flerovium after the Russian nuclear scientist Georgy Flerov, would be doubly magic and therefore relatively stable. These isotopes had 184 and 196 neutrons, and are dubbed flerovium-298 and flerovium-310.

The best we can realistically hope for is that a few atoms will stick around for a few days

However, it now seems that this particular island of stability might not materialise until element 122.

Still, flerovium might gain some stability from nuclear-shell effects. Flerovium-298 is predicted to have a half-life of around 17 days, which is immense by the standards of super-heavy elements. The longest lived isotope seen so far, flerovium-289, has a half-life of just 2.6 seconds.

It is not clear whether any super-heavy elements will last long enough to be accumulated in appreciable lumps, atom by atom. But it seems unlikely. The best we can realistically hope for is that a few atoms will stick around for a few days.

Beyond that, does there come a point when atoms are so heavy that they simply cannot exist?

The American physicist Richard Feynman thought so. He performed a back-of-the-envelope calculation that suggested that it was impossible to make an atom with 137 protons in the nucleus.

Pairs of particles can sometimes pop into existence out of nothingness

The reason was that the innermost electrons, those in the first shell, had no stable orbit. In other words, the nucleus of element 137 could no longer hold on to them.

However, Feynman's calculation made the approximation that the nucleus has zero size, which of course it doesn't. When the calculations are done more accurately, it seems that nothing untoward happens to the energies of the innermost electrons until atomic number 173.

Even then the atoms can remain stable, but all the same something weird happens.

Like everything else at these tiny scales, it all comes down to quantum mechanics.

Even if there is no end to the periodic table, there may be strange stuff awaiting us in its furthest reaches

This tells us, among other strange things, that pairs of particles can sometimes pop into existence out of nothingness. One of the particles will be made of matter and the other out of antimatter: for example, one might be an electron and the other its antimatter counterpart, a positron. Normally, the two immediately collide and annihilate each other.

It turns out that the innermost electrons of element 173 might be in an unusual, unstable state that can evoke these "virtual" particles.

If one of these electrons gets kicked out of its shell, for example by zapping it with an X-ray, it will leave a hole behind. This hole will be filled by an electron that appears out of nothing. But for this electron to form, a positron must also form, and this will be emitted by the atom.

In other words, the electron clouds of these really huge elements might occasionally burp out particles of antimatter.

So even if there is no end to the periodic table, there may be strange stuff awaiting us in its furthest reaches. Whether we will ever explore these extreme elements is another matter entirely.