Hello CoP, I'm sorry but this opening post (OP) isn't comprehensible to me.
It maybe a combination of language difficulties and a limited understanding of the physics but it is hard to guess what you are asking.
I'm guessing that you are asking about the expansion of spacetime between distant object like galaxies. Yes?
The "atoms" part seems to have nothing at all to do with it. You should take that out.
10 000 billion years is a bad number to pick. There hasn't been nearly that much time since the big bang (13.7 billion years).
If you mean to use a light-year in there then you could pick something like the distance to the Andromeda galaxy (2 million light years).
So is your question something like:
There are 2 million light years between us and the Andromdea galaxy. How fst is the space expanding between us and it?
If another galaxy is 1 billion light-years away how fast is the spacetime between it and us expanding?
If this is what you meant please edit your OP to fix it.