Question

Metallic barium crystallizes in a body-centered cubic lattice, with one Ba atom per lattice point. If the metallic radius of Ba is 217 pm, what is the volume of the unit cell in pm3 and in cm3?

Answer 1

1.26 x 10⁸pm³ and 1.26 x 10⁻²²cm³

Explanation: Calculating for a body centered cubic lattice, the formula is

3d²= 16r²

where d = edge length of unit cell

r=radius of atom

3d²= 16 x (217)²

3d²=753424

d²=251141.3

d= 501.1pm

volume of unit cell= d³= (501.1)³= 1.26 x 10⁸pm³

converting to cm³= 1.26 x 10⁸(10⁻¹²m)³

=1.26 x 10⁸(10⁻¹⁰cm)³ = 1.26 x 10⁻²²cm³