The edge length of the unit cell for nickel is 0.3524 nm. The density of Ni is \(8.90\;{\rm{g}}/{\rm{c}}{{\rm{m}}^3}\). Does nickel crystallize in a simple cubic structure? Explain.

The number of Ni atoms per unit cell in the given crystalline solid is calculated as shown in equation (1).

\(\begin{aligned}{}d& = \frac{{Z \times M{M_{Ni}}}}{{{N_A} \times {a^3}}}\\Z &= \frac{{d \times {N_A} \times {a^3}}}{{M{M_{Ni}}}} \ldots ..(1)\end{aligned}\)

Now on substitution, the value for \(Z\) is 4, which means that Ni crystallizes into a face-centered crystalline structure and not in a simple cubic structure.

\(\begin{aligned}{}1nm &= 1 \times {10^{ - 7}}\;{\rm{cm}}\\Z &= \frac{{d \times {N_A} \times {a^3}}}{{M{M_{Ni}}}}\\ &= \frac{{8.90\;{\rm{g}}/{\rm{c}}{{\rm{m}}^3} \times 6.022 \times {{10}^{23}}\;{\rm{mo}}{{\rm{l}}^{ - 1}} \times {{\left( {0.3524 \times {{10}^{ - 7}}\;{\rm{cm}}} \right)}^3}}}{{58.69\;{\rm{g}}/{\rm{mol}}}}\\ &= 4\end{aligned}\)