The name "rare-earths" is a bit of a misnomer, because several aren't rare at all... they're just not commonly understood, and are found in nature at very low concentrations. Additionally, they are often difficult to extract from the ores in which they are found.
One of the most frequent uses of lanthanide metals is in color television sets, because they glow in distinctive colors when bombarded with electrons.
Atomic Symbol: Eu
Atomic Number: 63
Europium is used to coat television picture tubes to give a bright red color. Every time you see the color red on television, it's thanks to the presence of europium. In fact, it was this property which caused early pioneers of television to consider the possibility of developing color.
Europium was found in much higher concentrations than expected in rocks brought back from the surface of the Moon. This unusually high abundance suggests that the Earth and Moon were not formed from the same cosmic material. As yet, there is no generally accepted theory about how the Moon was formed.
Atomic Symbol: Gd
Atomic Number: 64
Like several other rare-earth elements, gadolinium is used in television screens. However, it does not produce a vibrant color when exposed to electrons. It is therefore used to control the picture's brightness and contrast, because it gives off bright light without "quenching" the colors of the other elements.
Gadolinium is unique in two respects: first, it has the greatest neutron-capturing ability of any known element, which is put to use in medical techniques like neutron radiography. Second, it is magnetic, like iron, but loses its magnetism when its temperature rises above 20oC. For this reason it is used in video recording and data storage discs which can be permanent or erasable.
Atomic Symbol: Tb
Atomic Number: 65
This is one of the rarest of the rare-earth elements, being four times more expensive than platinum. It has few commercial uses because it is so costly. There was once a plan to use ceramic containing terbium for false teeth because it resembles the gleam of real teeth, but nothing came of it.
Using terbium has led to greater safety when taking X-rays, because it reduces the time the patient is exposed to this dangerous radiation. Terbium allows the same quality image to be produced in a quarter of the time previously required.
A favorite book of mine which has been invaluable in writing these chemistry posts is Nature's Building Blocks: An A-Z Guide to the Elements, by John Emsley. A great recent addition is The Elements: A Visual Exploration, by Theodore Gray, which includes a lot of nice pictures and is suitable for a coffee table near you.
For my previous posts on the elements, click here.