Question

Chromium metal crystallizes with a body-centered cubic lattice. The length of unit is found to be 287 pm. Calculate the atomic radius, the number of atoms per unit cell.

Answer 1

For bcc lattice, $r=\sqrt{3}\times \frac{a}{4}=\frac{\sqrt{3}}{4}\times 287$= 124.27 pm

Now Density $=n\times \frac{at.wt.}{V}\times Av.No.=n\times \frac{at.wt.}{a^3}\times Av.No.$

$N=2$ for bcc; $a=287\times {10}^{-10}cm$

So,

Density $=2\times \frac{51.99}{(287\times {10}^{-10}{)}^3}\times 6.023\times {10}^{23}$ $=7.30$ g/ml