A crystalline solid consists of atoms of A forming a face-centred cubic (fcc) lattice, and atoms of B occupying all the tetrahedral voids. If all the atoms lying along one body diagonal of the unit cell are removed, the simplest empirical formula of the resulting solid is A _x B _y . The value of x + y is ________.

Step-by-step solution

In an fcc lattice, atoms of A are present at the 8 corners and 6 face centres. Atoms of B occupy all 8 tetrahedral voids. A body diagonal of a cube passes through 2 opposite corners, the body centre, and 2 tetrahedral voids. It does not pass through any face centres. When atoms along one body diagonal are removed: Number of corner atoms of A removed = 2 Number of tetrahedral voids (atoms of B) removed = 2 Remaining atoms of A in the unit cell: Corners: 6 atoms remaining 6 1 8 = 3 4 Face centres: 6 atoms remaining 6