Distance to 3rd and 5th nearest ion to S2- in ZnS structure

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The discussion centers on determining the distances to the 3rd and 5th nearest S2- ions in the ZnS structure, which has a cubic close-packed arrangement. A user seeks clarification on why these distances are expressed as √11a/4 and √19a/11. Participants suggest using geometric principles and the Pythagorean theorem to derive these distances. There is some disagreement on the accuracy of the proposed values, with one participant indicating that their calculations yield different results. The conversation highlights the importance of geometric understanding in solid-state chemistry.
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Please post this type of questions in the HW section using the template and showing your work.
Hey folks

ZnS has a ccp structure with S2- ions forming FCC lattice with Zn2+ ions at half the tetrahedral voids

zbcell.gif


Attached is a table showing no. of nearest neighbours and their distance for an S2- ion

'a' is edge length of the unit cell

I want to know how the distance to the 3rd & 5th nearest ion is √11a/4 & √19a/11, i.e how to prove this.
upload_2018-10-13_16-17-34.png
Thanks ... any help is appreciated
 

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Have you you tried to follow the geometry? Often it is enough to find right right triangles and use Pythagorean theorem.
 
I think those numbers are wrong. They're not what I get (with quick mental arithmetic).
 
yes i did pythogarus & got it ... thanks ...
 
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