Trying to find an infinite sum from a picture

Question

kainui · Answer

http://www.metafysica.nl/turing/nacl_complex_motif_2.gif Pretend this is an infinite grid and at that center Na+ you want to know the potential energy it feels. So in some simple units we can add up all the contributions from the nearby 6 Cl- $$6*\frac{-1}{\sqrt{1^2+0^2+0^2}} $$ Then further out there are 8 Na+ atoms, $$8*\frac{+1}{\sqrt{1^2+1^2+0^2}}$$ etc... infinitely out. The potential energy of a single charge depending on whether it's positive or negative at some distance r, $$U = \frac{\pm 1}{|r|}$$

unklerhaukus · Answer

can you use cube numbers here?

dan815 · Answer

why isnt it 12 Na+

dan815 · Answer

okay the numbers re not important so i think the best thing to do is to split this up into planes, there are 4 or 5 planes are considering that should intersect with all the points  in this grid,

we should see the distribution of points on each grid

dan815 · Answer

http://prntscr.com/9uh72m the 3 orthogonal planes and the 2 purple planes u can clearly do some symmetry stuff by considering just 1 orthogonal plane and just 1 purple plane

dan815 · Answer

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