The answer depends on your world. Does your culture shackle this creation for fear of what it could do? Or does it just hand the keys to the LHC over and say "Please don't blow up the universe!".
Practically speaking, the one self sustained and self-aware class of beings has discovered 98 natural elements and then invented 20 more by smashing things together at really high speeds (numbers vary slightly, depending on what you consider to be "natural", but they add up to 118). Those 20 were discovered in the last 100 years. The probability of that being all the elements we discover is basically zip, which makes the probability that such an AI might discover a new one to be 100%.
That is, of course, unless we die in a nuclear war. You did watch the required primers on dangerous AI at the 101 and 202 level that got produced over the last few decades, right? A good solid nuclear war could prevent AIs from discovering much of anything.
The other fun issue is that there's not many elements that are interesting to discover in the short term. Most of them are terribly fleeting things. Oganesson, element 118, has a half life on the order of 1ms, So we're not about to use it as a building material any time soon. However, there is a theory that there might be an island of stability where there's a few long-lasting atoms which might still be discovered.
So that's the physics. The AI side of things is simply bounded by what you feel your AI should be capable of doing. The current prvailing opinions on AI from educated AI experts range from "It will never be able to do more than simple pattern matching" to "It will become a hyper-intelligent being of depths which humans cannot comprehend." So I think anything you choose will fit somewhere in that wide bound.