Question

The edge length of unit cell of a metal (molecular weight $=24$ g/mol) having cubic structure is $4.53\mathring{A}$. If the density of metal is $1.74$ g cm${}^{-3}$, the radius (in pm) of metal is:

[use $N_A=6\times {10}^{23}$]

• A. $180$
• B. $160$
• C. $140$
• D. $190$

Answer 1

The correct option is B $160$

Density, $d=\frac{zM}{N_A\times a^3}$

$1.74=\frac{z\times 24}{6.02\times {10}^{23}\times (4.53\times {10}^{-8}{)}^3}$

$\Rightarrow z=4$

$z=4$ is for fcc unit cell.

We know that, for fcc unit cell

Radius, $\text{r}=\frac{a}{2\sqrt{2}}=\frac{4.53}{2\times 1.414}=1.60\mathring{A}=160pm$

Hence, radius, $r=160pm$

Hence, the correct option is $\text{B}.$