Metal x forms FCC (edge length Lx ) Metal y forms BCC (edge length Ly ) Metal z forms SC (edge length Lz ) Given rz=
√3
2
ry and ry=
8
√3
rx ∴rz=
√3
2
×
8
√3
rx=4rx Mz=
3
2
MyMz=3Mx ∴My=2Mx Packing efficiency FCC>BCC>SC Packing efficiency unit cell x>y>z In FCC unit cell:- atoms along the face diagonals are in contact. ∴√2Lx=4rx⇒Lx=2√2rx In BCC unit cell: atoms along the body diagonal are
∴√3Ly=4ry⇒Ly=
4
√3
ry=
4
√3
×
8
√3
rx=
32
3
rx
Ly=
32
3
rx In SC unit cell, atoms along the edge are in contact ∴Lz=2rz =2×4rx=8rx Lx=2√2rx Ly=
32
3
rx Lz=8rx ∴Lyy>Lzz>Lx Density of x (Number of atoms of x per unit cell (z)=4 ) dx=
zMx
(Lx)3NA
=
4×Mx
(2√2rx)3×NA
=
4Mx
16√2rx3NA
=
Mx
4√2rx3NA
Density of y : (Number of atoms of y per unit cell (z)=2 )