Question

Important Formulae of 1. Density of unit cell. 2. Packing efficiency.

Answer 1

1. Density of unit cell:

i. Mass of one atom =\(\cfrac{Atomic\,\,mass}{Avogadro\,\,number}\)

ii. Volume of unit cell = a³

iii. Density =\(\cfrac{Mass\,\,of\,\, unit\,\, cell}{Volume\,\,of\,\, unit\,\, cell}\)

2. Packing efficiency =\(\cfrac{Volume\,\,occupied\,\, by\,\,spheres\,\,in\,\, unit\,\, cell}{Volume\,\,of\,\, unit\,\, cell}\times100\)

Answer 2

1).Density= mass of particle/volume of particle

=Z*M/a³                 

                                                      ^{For simple cubic unit cell(S.C.)  Z=1} 

                                                    ^{For body-centered  cubic unit cell(B.C.C.C) Z=2}

                                                   ^{For Face Centered Cubic Unit Cell (F.C.C)  Z=4}

Density=Zm/a³Na     (Multiply and divide by N_a)

m.N_a=M=mass of one-mole particle

Z=no. of particle

a=edge length of the unit cell

2).   Packing Efficiency=Volume of particlex100/Volume of the unit cell

4/3πr³/a³