I know there are tables of decay chain of radioactive elements. Is there a way to predict the whole chain from the first radioactive element?
Use the Evaluated Nuclear Structure Data File; search "by decay" and put the nuclide you'd like to start with in "parent." This will also tell you half-lives and Q-values.
A few nuclides have multiple decay modes; for instance radon-221 usually beta-decays to francium-221, but alpha-decays to polonium-217 about 22% of the time. You may find other "forks in the road" depending on where you start.
You ask in a comment about U-235. You can go a little simpler by looking at the chart of nuclides, which lists decay modes:
- U-235: α
- Th-231: β
- Pa-231: α
- Ac-227: β 99% (neglect α 1%)
- Th-227: α
- Ra-223: α
- Ra-219: α
- Po-215: α
- Pb-211: β
- Bi-211: α 99.3% (neglect β 0.7%)
- Tl-207: β
That takes you to lead-207, which is stable (and makes up 22% of natural lead).