Question

Lithium has a bcc structure. Its density is $530{\text{kg m}}^{-3}$ and its atomic mass is $6.94{\text{g mol}}^{-1}$. Calculate the edge length of a unit cell of Lithium metal.
$N_A=6.02\times {10}^{23}{\text{mol}}^{-1}$

• A. $154\text{pm}$
• B. $352\text{pm}$
• C. $527\text{pm}$
• D. $264\text{pm}$

Answer 1

The correct option is B $352\text{pm}$

$d=\frac{M\times z}{N_A\times a^3}$


$Z_{eff}$ in BCC:
​​​​​​​$0.530=\frac{6.94\times 2}{6\times {10}^{23}\times a^3}$
$a^3=\frac{6.94\times 2}{6\times {10}^{23}\times 0.53}$
$a^3=4.36\times {10}^{-23}\times \frac{10}{10}$
$a^3=43.6\times {10}^{-24}$
$a=(43.6{)}^{\frac{1}{3}}\times {10}^{-8}\text{cm}$
$=3.52\times {10}^{-8}\text{cm}$
$=352\text{pm}$