1. Tardigrade
  2. Question
  3. Chemistry
  4. A metal crystal has bcc lattice. Find the % fraction of edge length not covered by atom.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A metal crystal has bcc lattice. Find the % fraction of edge length not covered by atom.

NTA AbhyasNTA Abhyas 2020

Solution:

$\text{In bcc, }\textit{r}=\frac{\sqrt{3}}{4}\textit{a}$
Also, edge length of unit cell $=a$
radius of atom $=r$
$\therefore $ Edge length not covered by atom $=a-2r$
or $=\textit{a}-\frac{\sqrt{3}}{2}\cdot \textit{a}=\textit{a}\left[\frac{2 - \sqrt{3}}{2}\right]$
$\therefore $ Percentage fraction not covered
$=\frac{\textit{a} \left[\frac{2 - \sqrt{3}}{2}\right]}{\textit{a}}\times 100=\text{0.134}\times 100=\text{13.4\%}$