Radioactive?

Its been quite a while since my high school science classes, but I still remember learning about man-made elements. Of course, we're all thinking, if they're man-made how can they be elements? Just bear with me. Anyway, scientists take one element and shoot another nucleus of protons into it to form a new element that just doesn't occur in nature - an unnatural union, if you will. The problem with this creation is that it is inherently unstable. You can hold it together for a little while, but inevitably, the combination is too unstable and it will start to break apart. You just hope that it just doesn't do too much damage in the process.