A compound formed by elements `X` and `Y` has a cubic structure in which `X` atoms are at the corners of the cube of and two atoms `(Y)` are at each body diagonal of the cube.
a. Calculate: (i) `Z_(eff')` (ii) total number of atoms in a cube, and (iii) formula of the compound.
b. If all atoms form one body diagonal of the cube except corners are removed, calculate: (i) `Z_(eff')` (ii) total number of atoms in the cube, and (iii) formula of the compound.

Explanation

a. i. `Z_(eff(X)` at corners `= (1)/(8) xx 8 = 1 = X`
`Z_(eff(Y))` at body diagonal `= 2 "atoms" xx 4` body diagonal
`= 8` atom/unit cell
`= 8 = Y`
`:. Z_(eff(X + Y)) = 1 + 8 = 9`
ii. Total atoms in a cube `= 8` (corners) `+ 8` (body diagonal)
`=16` atoms/unit cube
iii. Formula of the compound:
`Z_(eff(X)) = 1, Z_(eff(Y)) = 8`
Formula `= XY_(8)`
b. i. One body diagonal has `2Y` atoms and they are removed.
`:. Z_(eff(Y))` at body diagnoal left `= 8 - 2`
`= 6` atoms/unit cell
`Z_(eff(X))` at corners `= 8 xx (1)/(8) = 1 = X`
`:. Z_(eff(X + Y)) = 6 + 1 = 7` atoms/unit cell
ii. Total atoms in a cube `= 8 ("corners") + 6` (body diagonal)
`= 14` atoms/unit cube
iii. Formula of the compound:
`Z_(eff(x)) = 1, Z_(eff(Y)) = 6`
Formula: `XY_(6)`