In terms of production costs, the most expensive substance in the world is antimatter. The cost of creating this material has been estimated at about $1,771 trillion US Dollars (USD) per ounce ($62.5 trillion USD per gram), although some authorities think it may eventually come down to a mere $141.75 billion USD per ounce ($5 billion USD per gram). This is the cost of antihydrogen, the simplest form of this type of substance, and the antimatter equivalent of the element hydrogen. Other anti-elements would be even more expensive. As of 2013, only small numbers of antihydrogen atoms have been produced — for research purposes only — and the substance is not available for sale.
Why Antimatter is so Expensive

Antimatter consists of particles that can be considered the opposites of their normal matter counterparts. The matter people are familiar with is made up of atoms, which consist of a nucleus containing heavy, positively charged, particles called protons surrounded by a “cloud” of lightweight, negatively charged electrons. Atoms of antimatter have negatively charged antiprotons in the nucleus, with positively charged anti-electrons — normally called positrons — surrounding them. Although antiprotons have been detected in cosmic rays, and positrons are emitted by some radioactive elements, there is no known natural source of anti-atoms, so antimatter has to be manufactured.
Positrons can be obtained quite easily from materials that emit them, but the much heavier antiprotons have to be created in particle colliders — machines that send subatomic particles crashing into one another, and into other materials, at enormous speeds. These collisions concentrate tremendous amounts of energy into extremely small volumes of space, which results in the creation of matter in the form of particles and antiparticles, including antiprotons. These can be separated magnetically, and combined with positrons to make atoms of antihydrogen.

Since these anti-atoms can only be made at a handful of facilities, and only in tiny quantities, antihydrogen is extremely scarce. Not only is it difficult and costly to make, it is also difficult to trap and store. Anti-atoms are strongly attracted to normal atoms, due to electrons and positrons having opposite electrical charges, and when they meet, they annihilate one another, with all their mass turning into energy. Storage involves vacuum containers that keep the anti-atoms from touching the sides using magnetic fields. These factors combine to make antimatter the world’s most expensive substance.

Uses for Antimatter

Scientists would not go to the trouble of making this substance if it did not have some potential uses. Antimatter has the greatest energy density of any possible fuel, meaning that it has the potential to release more energy per unit weight than any other substance. Since it takes even more energy to produce antimatter than can be obtained from it, it is not a solution to the planet’s energy problems; however, it has been proposed as a possible future rocket fuel, as, in theory, it could accelerate a payload to a substantial fraction of the speed of light. For the moment, though, its main interest to scientists lies in what it can reveal about the laws of physics.

Other Expensive Substances

Still in the realm of exotic physics, nuclear isomers, although falling some way short of the world’s most expensive substance, would carry an extremely high price tag — possibly over $28 billion USD per ounce ($1 billion USD per gram). These are elements in which the atomic nucleus has more than its minimum amount of energy — the minimum being known as the “ground state.” In most cases, a nucleus in this “excited” state will revert to its ground state within a tiny fraction of a second, releasing energy in the form of gamma rays, but some nuclear isomers, such as hafnium-178m2 and tantalum-180m, are relatively stable and long-lived. Under normal circumstances, these isomers release energy slowly, as their nuclei revert randomly over a long period.

Experiments in the 1990s seemed to show that a sample of hafnium-178m2 could be triggered to revert to its ground state all at once, releasing large amounts of energy, by bombarding it with X-rays. This raised the possibility of using the isomer to store energy, or to develop new types of weapon. Attempts to reproduce the effect, however, have so far failed, and many scientists are very skeptical about these possibilities. As with antimatter, these substances need to be manufactured in expensive particle colliders, and are available only in tiny amounts.

Hmmm