91Ó°ÊÓ

In the body centred cubic unit cell there are 2 atoms in each unit cell. The atomic radius of body centered cubic unit cell is equal to \(\dfrac{{\sqrt 3 }}{4}a\). Here ' \(a\) ' indicates the edge length. Density can be calculated the below formula.

Density of solid \( = \dfrac{{{\rm{Z}} \times {\rm{M}}}}{{{{\rm{a}}^3}\;{{\rm{N}}_{\rm{a}}}}}\)

The edge length of face-centered cubic unit cell is directly related to atomic radius. Edge length can be further used to calculate the density of so

Atomic radius \( = \dfrac{{\sqrt 3 }}{4}a\)

Given, edge length \( = 5.025{A‌^o}\)

Atomic radius

\(\begin{aligned}{}& = \dfrac{{\sqrt 3 }}{4} \times 5.025{A‌^o}\\ &= 2.176{A‌^o}\end{aligned}\)

The atomic radius of body centered packed structure is \(\dfrac{{\sqrt 3 }}{4}\) of edge length. Hence, the atomic radius of Barium in structure is\(2.176{A‌^o}\).

Density of solid \( = \dfrac{{{\rm{Z}} \times {\rm{M}}}}{{{{\rm{a}}^3}\;{{\rm{N}}_{\rm{a}}}}}\)

\({\rm{Z}} = 2\); for body centred packed structure

\({\rm{M}}\)molar mass \( = 137.32\,{\rm{g/mol}}\)

\({\rm{a}} = \) edge length \( = 2.176{A‌^o} = 2.176 \times {10^{ - 8}}\;{\rm{cm}}\)

\({{\rm{N}}_{\rm{a}}} = \)Avogadro number \( = 6.023 \times {10^{23}}\)

Density \( = \dfrac{{2 \times 137.32\;{\rm{g}}/{\rm{mol}}}}{{{{\left( {2.176 \times {{10}^{ - 8}}\;{\rm{cm}}} \right)}^3} \times 6.023 \times {{10}^{23}}}} = 4.42\;{\rm{g}}/{\rm{c}}{{\rm{m}}^3}\)

The density of barium is \(4.42\;{\rm{g}}/{\rm{c}}{{\rm{m}}^3}\) with body centered packed structure.