Question

If the distance between ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{-}$ ions in $\mathrm{NaCl}$ crystals is 'a' pm. What is the length of the edge of the unit cell?

• A. $2\mathrm{a}\mathrm{pm}$
• B. $4\mathrm{a}\mathrm{pm}$
• C. $\frac{\mathrm{a}}{2}\mathrm{pm}$
• D. $\frac{\mathrm{a}}{4}\mathrm{pm}$

Answer 1

The correct option is A

$2\mathrm{a}\mathrm{pm}$

Explanation:

Calculating the edge length of NaCl crystal:

In the fcc unit cell of NaCl, chloride ions remain present at the corner and sodium ions remain at the edge center touching each other.

The distance between Na+ and Cl- ions in NaCl crystals can be represented as: $({\mathrm{r}}_{{\mathrm{Na}}^{+}}+{\mathrm{r}}_{{\mathrm{Cl}}^{-}})=\mathrm{a}\mathrm{pm}$

Hence, the edge length is calculated as;

$$\begin{gathered} \mathrm{a}=2({\mathrm{r}}_{{\mathrm{Na}}^{+}}+{\mathrm{r}}_{{\mathrm{cl}}^{-}}) \\ =2\mathrm{a}\mathrm{pm} \end{gathered}$$

Thus the calculated length of the edge of the unit cell is twice the distance between sodium and chloride ions in sodium chloride crystal which is given by 2a pm.

Thus, option (A) is correct.