A compound formed by elements `X` and `Y` has a cubic structure in which `X` atoms are at the corner of the cube and also at alternate face entres. `Y` atoms are present at the body centre and also at the alternate edge centre of the cube.
a. Calculate (i) `Z_(eff')` (ii) total number of atoms in the cube, and (iii) formula of the compound.
b. If all the atoms are removed from one of the plane passing through the middle of the cube of the cube which contains atoms both on the edge entre as well as on the face centre, calculate (i) `Z_(eff')` (ii) total number of atoms in the cube, (iii) formula of the compound.
c. If all the atoms are removed from the plane passing through the middle of the cube which contains atoms only on the edge centre but not on face centre, calculate (i) `Z_(eff')` (ii) total number of atoms in t he cube, and (iii) fomula of the compound.
d. If all the atoms are removed from one of the plane passing through the middle of the cube which neither contains atoms on the edge centre nor on the face centre, calculate (i) `Z_(eff')` (ii) total number of atoms in the cube, and (iii) formula of the compound.
e. If all the atoms are removed from on e of the axes passing through the middle of the cube containing face centre atoms, calculate (i) `Z_(eff')` (ii) total number of atoms in a cube, and (iii) formula of the compound.
f. If all the atoms are remove from one of the axes passing through the middle of the cube nor containing face centre atoms, calculate (i) `Z_(eff')` (ii) total number of atoms in a cube, and (iii) formula of the compound.

Explanation

a. i.
`Z_(eff(X)) = (n_(c))/(8) + ("Alternate" n_(f))/(2) = (8)/(8) + (2)/(2) = 1 + 2 = 2`
`Z_(eff(Y)) = (n_(b))/(1) + ("Alternate" n_(e))/(4) = (1)/(1) + (4)/(4) = 1 + 1 = 2`
`Z_(eff(X + Y)) = 2 + 2 = 4`
(ii) Total number of atoms in a cube
`= 8` (corner) `+ 2` (alternate face centre)
`+ 4` (alternate edge centre ) `+ 1` (body centre )
`= 15` atom/unit cube
(iii) Formula: `Z_(eff(X)) = 2, Z_(eff(Y)) = 2`
`:.` Formula `= X_(2) Y_(2) = 2XY`

b. i. `Z_(eff(X)) = (n_(c))/(8) + ("Alternate" n_(f))/(2) = (8)/(8) + ((2 - 2))/(2)`
`= 1 + 0 = 1`
`Z_(eff(Y)) = (n_(b))/(1) + ("Alternate" n_(e))/(4) = ((1 - 1))/(1) + ((4 - 4))/(4)`
`= 0 + 0 =` zero
`Z_(eff(X + Y)) = 1 + 0 = 1`
(ii) Total numbe of atom in a cube
`= 8` (corner) `+` zero (body centre)
`+` zero (face centre) `+` zero (edge centre)
`= 8` atoms/unit cube
(iii) Formula: `Z_(eff(X)) = 1, Z_(eff(Y)) = ` zero
`:.` Formula `= X`
c. i.
`:. Z_(eff(X)) = (n_(c))/(8) + (n_(f) ("Alternate"))/(2) = (8)/(8) + (2)/(2)`
`= 1 + 1 = 2`
`Z_(eff(Y)) = (n_(b))/(1) + ( n_(e)("Alternate"))/(4) = ((1 - 1))/(1) + ((4 - 4))/(4)`
`= 0 + 0 = 0`
`Z_(eff(X + Y)) = 2 + 0 = 2`
ii. Total number of atoms in a cube
`= 8` (corner) `+ 2` (alternate face centre)
`+` zero (body centre)
`= 10` atoms/unit cube
(iii) Formula: `Z_(eff(X)) = 2, Z_(eff(Y)) =` Zero
Formula `= X_(2)`
d. i.
`:. Z_(efff(X)) = (n_(c))/(8) + ( ("Alternate")n_(f))/(2) = (8)/(8) + ((2-2))/(2)`
`= 1 + 1 = 2`
`Z_(eff(Y)) = (n_(b))/(1) + ( ("Alternate") n_(e))/(4) = ((1 - 1))/(1) + ((4))/(4)`
`= 0 + 1 = 0 `
`Z_(eff(X + Y)) = 2 + 1 = 3`.
ii. Total number of atoms in a cube
`= 8` (corner) `+ 2` (alternate face centre)
`+ 4` (alternate edge centre) `+` zero
(body centre)
`= 14` atoms/unit cube
(iii) Formula: `Z_(eff(X)) = 2, Z_(eff(Y)) = 1`
`:.` Formula `= X_(2) (Y)`
e. i.
`:. Z_(eff(X)) = (n_(c))/(8) + ("Alternate" n_(f))/(2) = (8)/(8) + (2)/(2)`
`= 1 + 1 = 2 `
`Z_(eff(Y)) = (n_(b))/(1) + ("Alternate" n_(e))/(4) = ((1 - 1))/(1) + (4)/(4)`
`= 0 + 1 = 1 `
`Z_(eff(X + Y)) = 1 + 1 = 2`.
ii. Total number of atoms in a cube
`= 8` (corner) `+ 2` (edge centre) `+ 4` zero(body centre)
`+` zero (face centre) `= 12` atoms/unit cube.
(iii) Formula: `Z_(eff(X)) = 1, Z_(eff(Y)) = 1`.
`:.` Formula `= X Y`.
f. i. i.
`:. Z_(efff(X)) = (n_(c))/(8) + ("Alternate" n_(f))/(2) = (8)/(8) + (2)/(2)`
`= 1 + 1 = 2 `
`Z_(eff(Y)) = (n_(b))/(1) + ("Alternate" n_(e))/(4) = ((1 - 1))/(1) + (4)/(4)`
`= 0 + 1 = 1 `
`Z_(eff(X + Y)) = 2 + 1 = 3`.
ii. Total number of atoms in a cube
`= 8` (corner) `+ 2` (face centre)
`+ 4` (body centre) `+` zero (body centre)
`= 14` atoms//unit cube.
iii. Formula: `Z_(eff(X)) = 2, Z_(eff(Y)) = 1`.
`:.` Formula `= X_(2) Y`.