Question

Barium crystallizes in a body-centered cubic system with atoms at all lattice points and an edge length of 5.02 angstroms. Calculate its density in g/cm3.

Answer 1

Answer : The density is, $3.60g/cm^{3}$

Explanation :

Formula used :  

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$ .............(1)

where,

$\rho$ = density  = ?

Z = number of atom in unit cell (for BCC = 2)

M = atomic mass  of barium = 137.3 g/mole

$(N_{A})$ = Avogadro's number =  $6.022\times 10^{23} mol^{-1}$

a = edge length of unit cell  = $5.02\AA=5.02\times 10^{-8}cm$

Conversion used : $(1\AA=10^{-8}cm)$

Now put all the values in above formula (1), we get

$\rho=\frac{2\times (137.3g/mol)}{(6.022\times 10^{23}mol^{-1}) \times (5.02\times 10^{-8}cm)^3}=3.60g/cm^{3}$

Thus, the density is, $3.60g/cm^{3}$