How stable are synthesized atoms?

Question

And why?

Answer 1

That depends on the size of the atom.

When atoms get too large, the protons in the nucleus start to push the atom apart.

Elements above Uranium (92) are radioactive and will decay various half. Some have half-lives under one second.

Answer 2

What do you mean by a synthesized atom?  Molecules are generally synthesized, from other molecules, all of them formed by atoms.  You CAN synthesize an atom by a nuclear reaction that transforms one atom to another. Some are stable, some are not.  Neutron capture on carbon-12 gives carbon-13, which is stable.  Neutron capture on carbon-13 produces carbon-14, which is unstable.  Neutron capture on Uranium-238 causes fission.  There are many other nuclear reactions, not just neutron capture, all of which can produce very stable, or very unstable, products depending on the details.  

Synthesized molecules, if that's what you meant, are similar.  Some products are very stable (Teflon, polyesters), some are not (uh, nitroglycerin).  If you synthesize something that occurs already somewhere in nature (methyl salicylate, oil of wintergreen) it is exactly as stable or unstable as the natural material if they are both purified.