Respuesta :
Answer:
Approximate atomic radius for polonium-209 is 167.5 pm .
Explanation:
Number of atom in simple cubic unit cell = Z = 1
Density of platinum = [tex]9.232 g/cm^3[/tex]
Edge length of cubic unit cell= a = ?
Atomic mass of Po (M) = 209 g/mol
Formula used :
[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex]
where,
ρ = density
Z = number of atom in unit cell
M = atomic mass
[tex](N_{A})[/tex] = Avogadro's number
a = edge length of unit cell
On substituting all the given values , we will get the value of 'a'.
[tex]9.232 g/cm3=\frac{1 \times 209 g/mol}{6.022\times 10^{23} mol^{-1}\times (a)^{3}}[/tex]
[tex]a = 3.35\times 10^{-8} cm[/tex]
Atomic radius of the polonium in unit cell = r
r = 0.5a
[tex]r=0.5\times 3.35\times 10^{-8} cm=1.675\times 10^{-8} cm[/tex]
[tex]1 cm = 10^{10} pm[/tex]
[tex]1.675\times 10^{-8} cm=1.675\times 10^{-8}\times 10^{10}=167.5 pm[/tex]
Approximate atomic radius for polonium-209 is 167.5 pm.
