Shaillee Kaushal is teaching live on Unacademy Plus
XII -01 Solid State VII
Densitv of lattice matter Density- Mass of the unit cell Mass of the unit cell- number of atoms in the unit cell X Mass of each atom = Density N XV Volume of the unit cell mass of each atom Atomic mass Avogadro snumber N Z = number of atoms in a unit cell
Packing efficienc Simple cubic structure: Let 'a' be the edge and ' be the radius V- volume of the unit cell a Since one atom is present in a unit cell its volume 4 Nowr Therefore a(2r)3- 8r3 Packing effeciency v 3 x8 2 v4tr - 0.52 ie 52% of the unit cell is occupied by atoms and 48% is empty.
Face centered cubic structure Since 4 atoms are present in a unit cell their volume is 4 a 2V2r Packing effeciency v 4X4nr3 V 3X16/2r3 0.74 ie 74% ofthe unit cell is occupied and 26% is empty
Body centered Since there are 2 constituent particles per unit cell therefore Volume of spheres - 2Xr3 Volume of cube a3 r- a 4r V3 3 6473 2x4XnXr3x3V3 Packing efficiency 3X64730.68 ie 68 f the unit cell is occupied by atoms and 32% is empty.
Characterstics ofcubic unit cell are summarised below in the table Simple Body centered Face centered Volume conventional cell Lattice points er cell Volume primitive cell Lattice points per unit volume Number of nearest neighbours Nearest neighbour distance Packing fraction 4 12 0.524 0.680 0.740