I am going to build complete spherical copper nano particle in the size range of 1-10 nm.
but i don't know, how many copper can build complete spherical shape, which the the surface atoms are in the same situation.
Up-vote on the response of Aras Kartouzian.
To elaborate, it sounds like you are interested in the magic clusters. Magic clusters are clusters of atoms consisting of some integer number of complete shells of atoms about a single central atom. Suppose you take a single atom and surround it with exactly one layer of atoms in a close-packed arrangement. It takes exactly 12 balls to completely surround a central ball (Try it with tennis balls, if you can find enough tennis balls.) This is smallest magic cluster. It has one central atom and 12 surface atoms for a total of 13. If we add a second shell of atoms, it takes 42 atoms to complete the second layer. This cluster has 55 atoms total, 13 in the interior and 42 on the surface. It takes 92 atoms to make a third shell. This cluster has a total of 147 atoms. The next cluster has 309 atoms. The sequence is: 1, 13, 55, 147, 309... These are the "centered icosahedral numbers".
https://en.wikipedia.org/wiki/Centered_icosahedral_number
Re: Remi Cornwall response: Dividing sphere volume by effective atom volume to get the number of atoms is straightforward, but to guarantee that, "the surface atoms are in the same situation" as in the OP, requires high symmetry and an integer number of complete shells, i.e. magic number clusters.
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