1. Tardigrade
  2. Question
  3. Chemistry
  4. The edge length of unit cell of a metal having molecular weight 75 g / mol is 5 mathringA which crystallizes in cubic lattice. If the density is 2 g / cc, then find the radius of metal atom. (N A =6 × 1023). Give the answer in pm.

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Q. The edge length of unit cell of a metal having molecular weight $75\, g / mol$ is $5 \,\mathring{A}$ which crystallizes in cubic lattice. If the density is $2\, g / cc$, then find the radius of metal atom. $\left(N_{ A }=6 \times 10^{23}\right)$. Give the answer in pm.

The Solid State

Solution:

$\rho=\frac{Z M}{N_A V}$
$Z=\frac{\rho N_A V}{M}=\frac{2 \times 6 \times 10^{23} \times\left(5 \times 10^{-8}\right)^3}{75}$
$Z=2$, which represents $b c c$ structure
$\therefore r=\frac{\sqrt{3}}{4} a=\frac{\sqrt{3}}{4} \times 5=2.165 \,\mathring{A}=216.5\, pm \approx 217\,pm$