Question

Nickel crystallizes in a face-centered cubic structure. If its density is $8.9$ g cm${}^{-3}$, then calculate the edge length (in $\mathring{A}$) of the unit cell.

• A. $3.52$
• B. $35.2$
• C. $70.4$
• D. $175.0$

Answer 1

The correct option is A $3.52$

As we know,

density $=\frac{nM}{V{N}_A}$,

where n is the number of atoms per unit cell.

Here, $n=4$
Density $=\frac{4\times 59}{\left(a^3\right)\times (6\times {10}^{23})}=8.9$

$⟹a=3.52\times {10}^{-8}cm$

$⟹a=3.52\mathring{A}$