You are free to look up the physical dimensions of the planet Earth, math formulas, physical constants etc using books, tables, Google etc. You are precluded to ask (i.e. Google) a direct question:

What is the total weight of Earth's atmosphere?

prior to posting your answer.

Please submit your estimate in a format N.PQ *10^r kg.
Provide your reasoning as well.
We shall jointly evaluate the accuracy later.