Question

How many sodium ions and chloride ions are present in a unit cell of sodium chloride crystal?

Answer 1

Four sodium ions and four chloride ions are present in a unit cell of sodium chloride crystal.
Chloride ions form cubic closed packing (ccp) arrangement and sodium ions occupy octahedral sites.
There are 8 chloride ions at 8 corners of a cube and 6 chloride ions at 6 face centres. Each corner chloride ion contributes one eighth to the unit cell and each face centred chloride ion contributes one half to the unit cell. Total number of chloride ions in the unit cell $=8\times \frac{1}{8}+6\times \frac{1}{2}=1+3=4$.
There are 12 sodium ions on the edges and one in the centre of the unit cell. Each sodium ion present on the edge contributes one fourth to the unit cell and sodium ion present at body centre contributes one to the unit cell. Total number of sodium ions in the unit cell $=12\times \frac{1}{4}+1\times \frac{1}{1}=3+1=4$.