Question

Polonium is the only element that takes a simple cubic structure, all others being ionic compounds. If its density is 9.14 g/cm³, determine its atomic radius in pm.

Answer 1

Polonium is the only element that takes a simple cubic structure, all others being ionic compounds. If its density is 9.14 g/cm³, determine its atomic radius in pm.

Density of simple cubic cell is given by following expression:

d = Z* M / a^3*N_A

here d = density; 9.14 g/cm³

M = molar mass ; 208.98 g/ mole

Z= number of particle in cube

For simple cubic it is 1

a= edge length in cm

N = Avogadro number

For simple cubic radius; r= a/2

Now first we calculate the as follows:

d = Z* M / a^3*N_A

9.14 = 1*208.98 / a^3*6.023*10^23

a^3= 3.79*10^-23

a=3.36*10^-8 cm

= 336 picometers

Radius = a/2

= 336 pm/2

168 pm