Why does fission/fusion occur instead of alpha/beta/gamma radiation?
That is a very unclear question. I don't understand what you are asking.
Try reading these Wikipedia articles first, then post again with a more specific question.
Sorry if it is a bit confusing but my teacher taught us how atoms emit alpha/beta/gamma radiation in order to become stable. In the next lesson he taught us how atoms undergo fission or fusion to become stable. I was just wondering what makes atoms fission/fusion to become stable rather than emit radiation?
Fission and fusion are two completely different processes.
Fission is an alternative to the decays you mentioned, but only occurs only in certain circumstances involving heavy elements.
Fusion is the result of two light (usually) nuclei undergoing high speed collision. It is not a decay process.
Did you read the links that were suggested as good resources for your learning by @anorlunda they should help you a lot.
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