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) AB_2. (B) A₂B. (C) A₄B_3. (D) A₃B₄

Answer 1

According to NaCl structure

so 'A' occupies 8 corners of the cubic unit cell which contribute 1/8 each to this cube

therefore 8*1/8 = 1

also 6 face centered atoms contribute 1/2 to this cube

therefore 6*1/2=3

Therefore total contribution of atom'A' is 4

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

therefore 1+12*1/4 = 4

So the formula is A4B4 or AB

Now you are removing all the face centered atoms along one axis(any axis origin at centre of cube)

so the number of atoms removed from cube are 2

so contribution from 'A' remains 8*1/8(corner atoms) + 4*1/2(facecentered atoms) = 3

so the resultant becomes A3B4