Question

We can estimate the physical density of any material based on the unit cell, the known size of the atoms it encompasses, and their atomic mass. Since density=mass/volume, for the mass in the unit cell we simply need to determine the number of atoms per cell * their mass from the periodic table / Avogadro’s number. For the volume of the unit cell, we just need to determine the lattice parameter of the unit cell (a) following the same rules as for the ideal or atomic packing factor (i.e. along which axes do the atoms touch and how many radii are touching along this distance?).

For polonium, which was the first element discovered by Marie Curie, what is this calculated physical density in g/cm^3? Po has an amu of 209, a simple cubic unit cell, and each Po atom in an equilibrium bond has a radius of 0.167 nanometers. Note: there are 10^9 nm per meter.

Answer 1

Simple cubic (SC) unit cell means there are 8 atoms at the corner of the cubic cell, and every atom belongs to neighboring 8 cells. So, SC contains 8*(1/8) atoms/cell = 1 atom per cell. The side length of a cell is 2*radius as they touch each other along.

density = mass of (1/8)*1 Po atom / volume of one cell = 209 amu / (2 * 0.167 nm)3

converting amu to kg  and nm to m

density= ( 209 amu) * (1.66054 * 10-27 kg/amu) / (8 * 0.1673 *10-27 m3)

= ( 209 * 1.66054 kg) / (8 * 0.1673 m3)

=9,314.4 kg/m3

Or, 9.3 g/cm3

to be noted,