Solid State

Number of atoms in the unit cell:

$\table \text"Unit Cell",scc,bcc,fcc,hcp;\text"No. of atoms",1,2,4,3$

Packing efficiency

$\table scc,bcc,fcc,hcp;52.4%,68%,74%,74%$

Note:

1. Number of tetrahedral voids = 2 Number of atoms
2. Number of octahedral voids = Number of atoms

Relation between radius (r) of an atom and edge length (a) of cubic unit cell

$\table scc,bcc,fcc;r = a/2, r={√3}/{4} a, r = {a}/{2√2}$

Density of the crystal

$d = {z * M}/{a^{3} * N_A}$

where,

z = Number of atoms in unit cell
M = Atomic Mass
a = Edge length of unit cell
$N_A$ = Avogadro Number

Note

1 m = 10 dm = 100 cm = $10^9$ nm = $10^{12}$ pm = 1 $A^{∘$} = $10^{-8}$ cm = 100 pm

Density of unit cell = ${\text"Mass of unit cell"}/{\text"Volume of unit cell"}$

Radius ratio in crystals

$\table \text"Radius ratio", \text"Coordination Number",\text"Crystalline Structure", \text"Example";0.155-0.225,3,\text"Plane triangular",B_{2}O_{3};0.225-0.414,4,Tetrahedral,ZnS;0.414-0.732,6,Octahedral,NaCl;0.73-1,8,cubic,CsCl;1-,12,\text"hcp or ccp",Mg$