A compound has cubical unit cell in which X atom are present at 6 corner, Y atom are at remaining corner & only at those face centres which are not opposite to each other & Z atoms are present at remaining face centre & body centre then find.
(i) Formula of compound (ii) Density if edge length `= 2 Å`
Given: Atomic mass of X = 40 amu, Y = 60 amu, Z = 80 amu

Explanation

(i) `X = (1)/(8) xx 6 = (3)/(4)`
`Y = (1)/(8) xx 2 + (1)/(2) xx 3 = (7)/(4)`
`Z = (1)/(2) xx 3 + 1 + 1 = (5)/(2) = (10)/(4)`
For formula: `X_(3) Y_(7) Z_(10) = X_(3) Y_(7) Z_(10)`
(ii) 1 amu `= 1.67 xx 10^(-24)` gram
1 amu `= (1)/(6.02 xx 10^(23))` gram.
Density `= ("Mass")/("Volume") = ((3)/(4) xx 40 + (7)/(4) xx 60 + (10)/(4) xx 80)/((2 xx 10^(-8))^(3))` amu/cc `= (335 xx 1.67 xx 10^(-24))/(8 xx 10^(-24)` = 69.8` gram/cc