I am not understanding why you half the atomic mass of both Na and Cl for this e

Question

I am not understanding why you half the atomic mass of both Na and Cl for this equation. In a simple cubic structure, shown below, I see that there is one fourth of each atom shared in the cube. Half of them are Na and half of them are Cl, resulting in one Na and one Cl per simple cubic. Not half of one Na and hald of one Cl atom...

2. What is the density of NaCi? Na: atomic weight 23g/mol, radius I Cl: atomic weight 35.5g/mol, radius 1.8A unit cell with a = 2.8A by hard sphere approximation ½ Na and ½ Cl atoms per unit cell = -2 +35.5m-4.86.10" 6.02-1023 tnol cell density =-486-102L = 2.24 (2.3-10"cm) The hard sphere approximation is comprable wh the easured 217 The hard sphere approximation is comparable with the measured 2.17 density density

Explanation / Answer

NaCl has an fcc arrangement in a cubic cell crystal lattice.

In an fcc arrangement , each unit cell has 4 atoms at the 4 lattice points and 4 octahedral sides.

If Na+ ions occupies the lattice points, Cl- occupies the octahedral sites(4 in number) or vice versa.But in both situations,each unit cell has 4 Na+ and 4Cl- or 1/2 number of Na and 1/2 number of Cl.

So in the above problem, 1/2 of the total atoms present in a unit cell is taken to be Na and the other half to be cl

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