How would you know if one version is wrong, whereas the other version is right? Normally, I assume, we would use the word 'conversational' in its adjectival function, but how about the word 'conversation' in a noun form? In the phrase 'conversation activity', the use of the noun form --the word 'conversation'-- doesn't seem incorrect since we are not using the word 'conversation' in an odd way. What are the rules on this if there is any?

We will have a conversational (or converesation??) activity.
Why do you need to have a conversation activity? Why can't you just have a conversation? Apart from that, both conversation and conversationalwill do the job just fine. English is very flexible in this respect and in many cases both a noun and an adjective are correct - at least if you ask me.Emotion: smile

an atom/atomic bomb

I am not a native speaker but as per my understanding both conversation activity and conversational activity are correct because the the latter one is adjective and former is not. same as in given example:

conversation book means a book which contains conversations
conversational book means a book which perform conversations