Francium

Since Francium (Fr) may be the rares element found on Earth, there are few studies made of this element, some experts believe that no more than 15 grams exist in the Earth's crust, but some scientist in New York found a way to perform measurements in a magnetic field were they can hold the atoms for long enough.

It has no uses, except for reasearch, is a radioactive element.

References:
http://www.scienceclarified.com/A-Al/Alkali-Metals.html
http://www.chemistryexplained.com/elements/C-K/Francium.html