Question

The metal nickel crystallizes in a face centred cubic structure. Its density is $8.9$ g cm${}^3$. Calculate (a) the length of the edge of the unit cell and (b) the radius of the nickel atom (in angstrom).

[Given that the atomic weight of Ni is $58.89$ amu.]

• A. (a) $3.52$ and (b) $1.24$
• B. (a) $1.24$ and (b) $3.52$
• C. (a) $3.52$ and (b) $3.52$
• D. (a) $1.24$ and (b) $1.24$

Answer 1

The correct option is A (a) $3.52$ and (b) $1.24$

As we know,

Density $=\frac{n\times M}{V{N}_0}$

Here, $n=4$

So, density $8.9=\frac{4\times 58.89}{(a{)}^3\times (6\times {10}^{23})}$

$a=3.52\mathring{A}$

$r=a/2\sqrt{2}=\frac{3.52}{2\times 1.4}=1.24\mathring{A}$