Question

Chromium metal crystallizes as a body-centered cubic lattice. The length of the unit cell edge is found to be $287$ pm. What would be the density (in g cm${}^{-3}$) of chromium?

• A. $3.40$
• B. $5.20$
• C. $12.10$
• D. $7.30$

Answer 1

Answer: (D)

$7.30$

If $a$ is the edge length, then for bcc lattice, we have

$r=\frac{\sqrt{3}a}{4}=\frac{\sqrt{3}\times 287}{4}=124.27\mathring{A}$
Density $\left(\rho \right)=\frac{Z_{eff}\times Mw}{a^3\times N_A}$ $=\frac{2\times 51.99}{(287\times {10}^{-10}{)}^3\times 6.023\times {10}^{23}}$ $=7.30$ g cm${}^{-3}$

Z for BCC is 2.

Hence, the correct option is $\text{D}$