Q.Explain simple cubic, body centred cubic and face centred cubic unit cells and find the total number of atoms per unit cell of each.

Contribution per atom depends on its position: corner = 1/8, face-centre = 1/2, body-centre = 1 (whole).

Simple cubic unit cell: Atoms are present only at the 8 corners of the cube. Each corner atom is shared among 8 unit cells, so it contributes $\frac{1}{8}$ to one unit cell.

Total atoms per unit cell $= 8 \times \frac{1}{8} = 1$.

Body-centred cubic (bcc) unit cell: In addition to the 8 corner atoms (contributing 1 atom), there is one atom at the body centre, wholly belonging to that unit cell.

Total atoms per unit cell $= 1 (\text{from corners}) + 1 (\text{body centre}) = 2$.

Face-centred cubic (fcc) unit cell: In addition to the 8 corner atoms (contributing 1 atom), there are 6 atoms at the face centres, each shared between 2 unit cells, contributing $\frac{1}{2}$ each.

Total atoms per unit cell $= 1 (\text{from corners}) + 6\times\frac{1}{2} (\text{faces}) = 1 + 3 = 4$.

OR (numerical problem): Given: bcc structure, edge length $a = 288\ pm = 2.88\times10^{-8}\ cm$, density $\rho = 7.2\ g/cm^3$, $Z = 2$ (for bcc).

$a^3 = (2.88\times10^{-8})^3 = 2.389\times10^{-23}\ cm^3$

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