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An ionic solid A+B- crystallises in the rock-salt structure. Given that r(A+) / r(B-) = sqrt(2) - 1, identify the INCORRECT statement. [Use: (sqrt(2)-1)³ = 0.07, pi / sqrt(2) = 2.22]

1. Anions are in contact with each other
2. Cations are in contact with each other
3. Edge length of the unit cell a = 2*sqrt(2) * r(B-)
4. The packing fraction is approximately 0.79

Correct answer: Cations are in contact with each other

Solution

With r(A+)/r(B-) = sqrt(2)-1 and a = 2*sqrt(2)*r(B-), anions touch along the face diagonal (4r(B-) = a*sqrt(2) = 4r(B-) checks out). The nearest cation-cation gap = a/sqrt(2) = 2r(B-), but 2r(A+) = 2(sqrt(2)-1)r(B-) < 2r(B-), so cations are NOT in contact. The packing fraction calculation also comes out to ~0.79.

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