Well, what do you think? And why do you think what you think?
Approximately the same number as there are hits to the Google query "How many atoms in a sheet of paper thickness".
Yes, really. An atom is a few angstroms across, a sheet paper is maybe a few tenths of a millimeter thick, that works out to something on the order of 106.... and there are 2.3 million Google hits.
This is not a very good question. Commercial paper is made of cellulose (polymerized simple sugars) -- which is in the form of fibers. Usually from pine. These fibers have lots of space between them - from the point of view of an atom.
Note: different atoms have different diameters: ex: Carbon 1.54 x 10^-10 m
And paper comes in different weights (thicknesses). In the US there is 20lb paper, 24lb paper etc.
Care to refine your question? We have too many variables here to give a decent answer.
Also please note: Science deals with provable facts, not what 'you think'. The 'what I think' mentality about Science is the reason the internet is full of non-science, or politically motivated disinformation. We try to limit that here.
My first thoughts too: 'paper' is just too vague. Perhaps with more specifics, the maths would be as simple as @Nugatory shows.
That said, in a watered-down point of view, I fail to see why the answer should be any more than an order or two of magnitude different from @Nugatory's estimate of one million.
The question is "how many atoms thick is a sheet of paper".
Not how many atoms are actually aligned across the thickness of the paper.
So it seems that Nugatory's estimate makes perfect sense for the question asked.
Same as "how many fingers thick is a that brick". There are no fingers in the brick, for sure. And there are different types of fingers. But we can make an estimate.
Science is also about good estimates and order of magnitude calculations.
How long is a piece of string?
About two halves of the same piece of string.
always 2 inches shorter than what you need for your task
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