Question

Calculate the number of atoms per unit cellin each type of cubic unit cell.

Enter three integers separated bycommas (e.g., 1,2,3) in the following order: primitivecubic, body-centered cubic, and face-centered cubic.

Answer 1

Primitive or simple cubic has 1 atom/cell (8 x 1/8 =1)
body: 2 atoms/cell (8 x 1/8 +1 =2)
face: 4 atoms/cell (8 x 1/8 + 6 x 1/2) = 4)

Answer 2

In primitive cubic unit cell all the eight cornersare occupied by atoms. Each corner contributes (1/8)th atom to oneunit cell.

∴ Total number of atomsin  primitive cubic unit cell = 8*1/8

                                                                                 = 1 atom .

In body-centered cubic unit cell all theeight corners and center of the cube are occupied by atoms.Each corner contributes (1/8)th atom to one unit cell andone atom present at center of the unit cell.

    ∴ Total number of atomsin  primitive cubic unit cell = 1*1 + 8*1/8

                                                                                 = 1+ 1

                                                                                  =2 atoms

In   face-centered cubic unit cell all theeight corners and all the faces of the cube are occupiedby atoms. Each corner contributes (1/8)th atom to one unit celland each face contributes 1/2 atom to one unit cell.

    ∴ Total number of atomsin  primitive cubic unit cell = 6*(1/2) + 8*1/8

                                                                                 = 3+ 1

                                                                                  = 4atoms