Question

Polonium is the only metal that forms a simple cubic unit cell. The radius of the polonium atom is 1.67 x 10⁻⁸ cm. Determine the mass and volume of the unit cell for polonium. An average polonium atom weighs 209 amu. Calculate the density (in g/cm³) of polonium.

a) The distance between touching spheres equals twice the sphere radius

b) Remember to account for the number of atoms in each unit cell

c) 1.00 amu = 1.66 x 10⁻²⁴ g

Answer 1

for simple cube :

a = 2 r

a = edge length , r = radius

a = 2 x 1.67 x 10^-8

a   =   3.34 x 10^-8

volume = a^3 = (3.34 x 10^-8)^3

           = 3.73 x 10^-23 cm^3

volume = 3.73 x 10^-23 cm^3

number of atoms per unit cell = 1 in simple cubic system

mass = Z M = 1 x 209 amu

mass = 209x (1.66 x 10^-24)

mass = 3.47 x 10^-22 g

density = mass / volume

              = 3.47 x 10^-22 / 3.73 x 10^-23

             = 9.30 g / cm^3

density = 9.30 g / cm^3