Rhodium is a precious metal produced by nuclear fussion, it is possible to extract rhodium from used nuclear fuel. It holds the distinction of being the world's most expensive precious metal. It has an atomic number of 45 and is about as nonreactive as gold. The only way to dissolve rhodium is with sulfuric acid. Part of rhodium's appeal comes from its high reflectance, almost unique among the metals. It is sometimes used as an expensive and flashy alternative to silver in jewelry, on which it is sometimes plated. Some of the most expensive consumer items in the world are made from rhodium.

It was discovered in 1803 by William Hyde Wollaston, from platinum, he named it Rhodium from the latin Rhodon meaning "rose". Rhodium costs about six times as much as gold by weight. It is never found in mineral form, only being found in trace amounts within platinum or nickel ores. Most of it comes from South Africa and world production of the metal is only about 20 ton per year.

Applications (wikipedia)

The primary use of this element is in automobiles as a catalytic converter, which changes harmful emissions from the engine into less polluting gases.   

Catalyst
In 2007, 81% of the world production of rhodium was consumed to produce three-way catalytic converters. Rhodium shows some advantages over the other platinum metals in the reduction of nitrogen oxides to nitrogen and oxygen:

2 NOx → x O2 + N2
The recycling of catalytic converters also became a valuable source for rhodium. In 2007, 5.7 t were extracted from this source. Compared to the 22 t which had been mined, this is a relatively high recycling rate.

Rhodium-based catalysts are used in a number of industrial processes; notably, in the automobile catalytic converters and for catalytic carbonylation of methanol to produce acetic acid by the Monsanto process. It is also used to catalyze addition of hydrosilanes to molecular double bonds, a process important in manufacture of certain silicone rubbers.Rhodium catalysts are also used to reduce benzene to cyclohexane.

The complex of a rhodium ion with BINAP gives a widely used chiral catalyst for chiral synthesis, as in the synthesis of menthol.
Ornamental uses

Rhodium-plated white gold wedding ring
Rhodium finds use in jewelry and for decorations. It is electroplated on white gold and platinum to give it a reflective white surface. This is known as rhodium flashing in the jewelry business. It may also be used in coating sterling silver to protect against tarnish, which is silver sulfide (Ag2S) produced from the atmospheric hydrogen sulfide (H2S). Solid (pure) rhodium jewelry is very rare, because the metal has both high melting point and poor malleability (making such jewelry very hard to fabricate) rather than due to its high price. Additionally, its high cost assures that most of its jewelry usage is in the form of tiny amounts of powder (commonly called rhodium sponge) dissolved intoelectroplating solutions.

Rhodium has also been used for honors or to symbolize wealth, when more commonly used metals such as silver, gold, or platinum are deemed insufficient. In 1979, theGuinness Book of World Records gave Paul McCartney a rhodium-plated disc for being history's all-time best-selling songwriter and recording artist.

Other uses
Rhodium is used as an alloying agent for hardening and improving the corrosion resistance of platinum and palladium. These alloys are used in furnace windings, bushings for glass fiber production, thermocouple elements, electrodes for aircraft spark plugs, and laboratory crucibles. Other uses include:

An electrical contact material due to its low electrical resistance, low and stable contact resistance, and high corrosion resistance.
Plated rhodium, made by electroplating or evaporation, is extremely hard and is used for optical instruments.
It is also used as a filter in mammography systems because of the characteristic X-rays it produces.

Rhodium neutron detectors are used in combustion engineering nuclear reactors to measure neutron flux levels – a method that requires a digital filter to determine the current neutron flux level, as there are three signals generated: immediate, a few seconds later, and a minute later, each with its own signal level, and all three are combined in the rhodium detector signals. The three Palo Verde nuclear reactors each have 305 rhodium neutron detectors, 61 detectors on each of 5 vertical levels, providing an accurate 3-D "picture" of reactivity and allowing fine tuning to most economically burn the nuclear fuel.

Rhodium Price

source: http://www.kitco.com

Rhodium became famous in 1979 when the Guinness Book of World Records awarded Paul McCartney a rhodium-plated disc to celebrate his status as history's all-time best-selling songwriter and recording artist.

Rhodium is used when other precious metals such as silver, gold, or platinum are considered not enough.

*Cost of Rhodium