# At room temperature , Sodium crystallizes in a b.c.c lattice with edge length $a = 4.24A^{\large\circ}$ . Find the theoretical density of sodium.

$(a)\;1\qquad(b)\;2\qquad(c)\;3\qquad(d)\;4$

Total no. of atoms (Z) per unit cell = $8\times\large\frac{1}{8}+1$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=2$
Density $\rho = \large\frac{Z\times at.wt}{Av.No.\times a^3}$
$=\large\frac{2\times23}{6.023\times10^{23}\times(4.24\times10^{-8})^3}$
$=1.0 gcm^{-3}$