I want to figure out the spacing between neighbouring atoms in a cubic meter of a large amount of 10^17 atoms were placed in perfect cubic structures within the cubic meter.

I’m not sure how to go about this. I can only manage to think that you will need 8 atoms for the very first cube, and to add 4 more to create the neighbouring cube in each dimension. Then fill this so that the total in all directs is equal to 10^17?


closed as off-topic by Emilio Pisanty, David Z Oct 8 '18 at 11:36

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  • $\begingroup$ Welcome to Physics SE. I suggest that you visualize the cubic lattice of atoms, and focus on the region of space that surrounds a single atom, and is closer to it than to any other atom. What shape is this region? If you did this for every atom, would you fill up all the space? $\endgroup$ – user197851 Oct 8 '18 at 10:12
  • $\begingroup$ I’m not sure what you’re saying exactly. My take is that each surface of the cube has 4 atoms associated with it. The spacing between the atoms cubed is equal to 4 divided by the total number of atoms. This gives me 1.9x10^-8m spacing between atoms. $\endgroup$ – Swimmer12345 Oct 8 '18 at 11:32
  • $\begingroup$ Your question needs some clarifications. I assume that you are not 100 % sure what do you want to ask. I will give an answer to your question and I hope you will understand why your question is a bit misleading. Polonium has a simple cubic crystal structure and the lattice constant (side of the cube) is ~336 pm. Atomic radius of Polonium is ~135 pm. That means that irrespective of the number of atoms you put together, the shortest distance between neighbouring Polonium atoms is $336-135=201pm$. And for a different element with it will be different. $\endgroup$ – physicopath Oct 8 '18 at 12:18