Question

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

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

Answer 1

Answer: (B)

$352pm$

Density, $d=530kg/m^3=0.530g/c{m}^3$

$(\because 1kg/m^3={10}^{-3}g/c{m}^3)$

Molar atomic mass, $M=6.94g/mol$

For bcc unit cell, the number of atoms per unit cell, $Z=2$

Density, $d=\frac{ZM}{a^3{N}_A}$

$0.530=\frac{2\times 6.94}{a^3\times 6.023\times {10}^{23}}$

$a^3=4.34\times {10}^{-23}$

$\Rightarrow a=3.52\times {10}^{-8}cm$

The edge length, $a=3.52\times {10}^{-8}cm=352\times {10}^{-12}m=352pm$

$(\because 1m=100cm$ and $1pm={10}^{-12}m)$