Question

What is the number of atoms (z) in a simple cubic unit cell?

Answer 1

Simple cubic unit cell:

• A simple cubic unit cell can also be called a primitive cubic unit cell.
• A primitive cubic unit cell has atoms only at its corner. Each atom at a corner is shared between eight adjacent unit cells.
• Only $\frac{1}{8^{\mathrm{th}}}$of an atom (or molecule or ion) actually belongs to a particular unit cell.
• The representation of a simple cubic structure is given below.

Calculation for $\mathrm{Z}$:

• In a simple cubic unit cell since each cubic unit cell has 8 atoms on its corners. Thus, the total number of atoms in one unit cell can be represented as:

$\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{atoms}\mathrm{in}\mathrm{one}\mathrm{unit}\mathrm{cell}=8\times \frac{1}{8}=1$

• Thus, the number of atoms $\mathrm{Z}$ in a simple cubic unit cell is $1$.