Question

Nickel crystallizes in a face-centered cubic structure, its density is $8.9$ g cm${}^{-3}$. Calculate the radius (in $\mathring{A}$) of the nickel atom. [Given that the atomic weight of Ni is $58.89$ amu.]

• A. $2.4$
• B. $3.2$
• C. $1.2$
• D. $0.8$

Answer 1

The correct option is C $1.2$

As we know, density $=\frac{nM}{V{N}_A}$, where n is the number of atoms per unit cell.

Here, we have $n=4$

Density $=8.9=\frac{4\times 59}{\left(a^3\right)(6\times {10}^{23})}⟹a=3.53\mathring{A}$

For fcc, $a=2\sqrt{2}r$ $⟹r=1.2\mathring{A}$