Question

In a solid ‘AB’ having the NaCl structure, ‘A’ atoms occupy
the corners of the cubic unit cell. If all the face-centered
atoms along one of the axes are removed, then the resultant
stoichiometry of the solid is
(a) AB₂ (b) A₂B
(c) A₄B₃ (d) A₃B₄

Answer 1

The correct formula will be A3B4.

Explanation:

• According to the structure of NaCl

• Here,  A will occupy 8 corners of cubic unit cell which will contribute 1/8 to each to the cube

• Therefore 8× 1/8 = 1

• And 6 face centered atoms will contribute  1/2 to the cube

• Hence 6× 1/2 =3

• Therefore total contribution of atom 'A' is 3+1=4

• Now B occupies octahedral voids (NaCl structure) which contributes 1/4

• Therefore 1+12× 1/4 =4

• So the formula is A is AB

• Now we are removing all face centered atoms along one axis-

• so the number of atoms removed from cube are 2

• so contribution from 'A' remains 8×1/8 (corneratoms) +4 × 1/2 (facecenteredatoms) = 3

• so the resultant becomes A3B4.

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