A cubic solid is formed by elements X, Y, and Z. X atoms are present at all the corners, Y atoms are at all the face centers, and Z atoms are at all the edge centers as well as the body center. If all the atoms lying along one of the body diagonals are removed, the empirical formula of the resulting compound is

Step-by-step solution

A body diagonal of a cube passes through two opposite corners and the body center. It does not pass through any face centers or edge centers. When all atoms along one body diagonal are removed, 2 corner atoms and 1 body center atom are removed. Remaining X atoms (at corners) = 8 - 2 = 6 Effective number of X atoms = 6 1 8 = 3 4 Remaining Y atoms (at face centers) = 6 Effective number of Y atoms = 6 1 2 = 3 Remaining Z atoms (at edge centers) = 12 (the body center Z atom is removed) Effective number of Z atoms = 12