Q.Gold (atomic radius = 0.144 nm) crystallises in a face-centred unit cell. What is the length of a side of the cell?

A unit cell is the smallest repeating unit of a crystal lattice, and its size and shape are fully described by six parameters.

• Three edge lengths: $a$, $b$, $c$ (dimensions along the three axes).
• Three angles between the edges: $\alpha$ (between $b$ and $c$), $\beta$ (between $a$ and $c$), and $\gamma$ (between $a$ and $b$).

Different combinations of these parameters define the seven crystal systems (cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic). For a cubic cell, $a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$. …