In a solid 'XY' having the NaCl structure, 'X' atoms occupy the corners of the cubic unit cell. If all the face centred atoms along one of the axes are removed, then the resultant stiochiometry of the solid is found to be X m Y n . Find the sum of m + n?

Step-by-step solution

Na in NaCl has eight corner and six face atoms and thus, if we remove face centred atom of one axis, then two faces atoms are removed. Thus, X is at 8 corners and Y is at 4 faces. Number of X atoms per unit cell = 8 × 1 8 + 4 × 1 2 = 3 Number of Y atoms per unit cell = 12 × 1 4 + 1 = 4 Thus, formula is X 3 Y 4 . Hence, m = 3, n = 4 sum of m + n = 3 + 4 = 7.