The radius of a barium atom is r = 2.19 [tex]\times[/tex] 10^-8
Explanation:
The atomic weight of barium is 137.34.
The body-centered cubic structure has two atoms per unit cell.
Therefore, the mass of Ba in a unit cell is calculated as,
[tex]m =[/tex] [tex]\frac{2 \times 137.34}{6.023 \times 10^2^3}[/tex]
[tex]m = 4.56 \times 10^{-22} g[/tex]
volume = mass / density
[tex]= \frac{4.56 \times 10^{-22} }{3.50}[/tex]
volume = [tex]1.30 \times 10^{-22} cm^3[/tex]
The edge length of a cube then is the cube root of[tex]1.30 \times 10^{-22} cm^3[/tex] or
[tex]a = 5.06 \times 10^{-8}[/tex]
The body diagonal is 4 x the radius and equals a 1.732,
Therefore r = (a [tex]\times[/tex] 1.732) / 4
= (5.06 [tex]\times[/tex] 10^-8
[tex]r = 2.19 \times10^{-8}[/tex]
The radius of a barium atom is [tex]r = 2.19 \times10^{-8}[/tex]cm.
