Answer:
The atomic radius is:- [tex]1.68\times 10^{-9}\ cm[/tex]
Explanation:
The expression for density is:
[tex]\rho=\frac {Z\times M}{N_a\times {Volume}}[/tex]
[tex]N_a=6.023\times 10^{23}\ {mol}^{-1}[/tex]
M is molar mass of polonium = 209 g/mol
For Simple Cubic unit cell , Z= 1
[tex]\rho[/tex] is the density = 9.142 g/cm³
Thus,
[tex]Volume=\frac {Z\times M}{N_a\times {\rho}}[/tex]
[tex]Volume=\frac{1\times 209}{6.023\times 10^{23}\times 9.142}\ cm^3[/tex]
[tex]Volume=\frac{209}{10^{23}\times \:55.062266}\ cm^3[/tex]
[tex]Volume=37.95\times 10^{-24}\ cm^3[/tex]
Also, Volume = [tex]{(Edge\ length)}^3[/tex]
Thus, edge length = [tex]{Volume}^{\frac{1}{3}}[/tex] = [tex]\left(37.95\times \:\:10^{-24}\right)^{\frac{1}{3}}\ cm=3.36\times 10^{-9}\ cm[/tex]
Also, for Simple Cubic unit cell,
[tex]Radius = \frac{Edge\ length}{2}=\frac{3.36\times 10^{-9}}{2}\ cm=1.68\times 10^{-9}\ cm[/tex]
Hence, the atomic radius is:- [tex]1.68\times 10^{-9}\ cm[/tex]
