Chemistry Question

Question

How many atoms are in primitive cubic unit cell (simple cubic unit), Body Centered cubic unit cell, Face centered cubic unit cell.

Iron solid adopts a body-centered cubic structure with a unit cell edge length of 287 pm. Based on this information, calculate the density in g/mL of iron.

Answer 1

In a primitive cubic unit cell (simple cubic unit), there is only one atom located at each corner of the cube.

In a body-centered cubic unit cell, there is one atom at each corner of the cube and one atom at the center of the cube.

In a face-centered cubic unit cell, there is one atom at each corner of the cube and one atom at the center of each face of the cube.

Therefore, the number of atoms in each type of unit cell is:

Primitive cubic unit cell: 1 atom

Body-centered cubic unit cell: 2 atoms

Face-centered cubic unit cell: 4 atoms

Now, to calculate the density of iron:

The unit cell edge length of the body-centered cubic structure of iron is given as 287 pm (1 pm = 1 × 10^-12 m). The volume of the unit cell can be calculated as:

V = (edge length)^3 = (287 pm)^3 = 2.087 × 10^-23 m^3

The mass of the unit cell can be calculated using the atomic mass of iron (Fe) from the periodic table, which is 55.845 g/mol. The number of iron atoms in the unit cell is 2 (since it is a body-centered cubic unit cell), so the mass of the unit cell can be calculated as:

mass = (2 atoms) × (55.845 g/mol) = 111.69 g/mol

Now we can use the density formula, which is:

density = mass / volume

Substituting the values we obtained:

density = 111.69 g/mol / 2.087 × 10^-23 m^3 = 5.35 g/cm^3 = 5.35 g/mL

Therefore, the density of iron is 5.35 g/mL.