Question

A solid is formed and it has three types of atoms x, y, z. x forms a fcc lattice with y atoms occupying all the tetrahedral voids and z atoms occupying half the octahedral voids. the formula of the solid is :

Answer 1

In fcc there R total 4 atoms per unit cell. hence x= 4 .,,,,, each sphere or atom (N) forms two tetrahedral voids. that is 2* N where N is no. atoms as we know in fcc 4 atoms are per unit cell hence tetrahedral voids =2*4=8 ,,,,,,therefore y =8. .# each atom form only one octahedral void hence no. of total octaheral voids is 1* 4 (atoms) =4 .,,,,,,,,
but z is half of total o-voids hence z= 4/2 =2.
#Therefore x:y:z=4 : 8 : 2 = 2 : 4 : 1

i.e. X2Y4Z