Question

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

• A. $154pm$
• B. $527pm$
• C. $264pm$
• D. $352pm$

Answer 1

The correct option is D $352pm$

$\text{Density of unit cell,}\rho =\frac{ZM}{N_A{a}^3}$
where,
Z is the number of atoms in unit cell
M is the molar/atomic mass
$N_A$ is the avogadro's number
$a$ is edge length of unit cell

$Z$ for bcc is 2

$a^3=\frac{ZM}{N_A\rho }$

$a^3=\frac{6.94\times {10}^{-3}\times 2}{6.022\times {10}^{23}\times 530}$
$a^3=43.5\times {10}^{-30}$
$a=3.52\times {10}^{-10}m$
$a=352\times {10}^{-12}m$
$a=352pm$

Hence, option (b) is correct.