If the distance between ${\mathrm{Na}}^{+}$and ${\mathrm{Cl}}^{-}$ ions in $\mathrm{NaCl}$ crystal is ' $\mathrm{a}$' pm, what is the length of the cell edge ?

The $\mathrm{NaCl}$ compund has a fcc unit cell. As a result, the chloride ions at the corner and the sodium ions in the edge's centre will come into contact along that edge.

So, the edge length of $\mathrm{NaCl}$ can be expressed mathematically as:

$\mathrm{a}=2{\mathrm{r}}_{{\mathrm{Na}}^{+}}+2{\mathrm{r}}_{{\mathrm{Cl}}^{-}}=2\left({\mathrm{r}}_{{\mathrm{Na}}^{+}}+{\mathrm{r}}_{{\mathrm{Cl}}^{-}}\right)$

From the expression, it is clear that $\left({\mathrm{r}}_{{\mathrm{Na}}^{+}}+{\mathrm{r}}_{{\mathrm{Cl}}^{-}}\right)$ represents the distance between sodium and chloride ions.

Hence, the length of the cell edge would be, $2\left({\mathrm{Na}}^{+}+{\mathrm{Cl}}^{-}\right)=2a$.