Question

Calculate the packing efficiency of a metal crystal for body centred cubic structure

Answer 1

★ Let take edge length or side of the cube = a,

Let take radius of each particles               = r

The diagonal of a cube is always a√3

The relation between radius and edge a will

 a√3 = 4r

divide by root 3 we get

                        a          = 4r/√3

total number of atoms in body centered cubic

number of atoms at the corner = 8 x 1/8 = 1

number of atoms at the center = 1

total number of atoms               = 2

The volume of the cubic unit cell    = side3

                                                            = a3

                                                            = (4r/√3)3

The volume of the occupied space = (4/3)πr3