The density of iridium is 22400 kg/m3 and the cell volume is 5.66 x 10-23 cm3. Determine the number of atoms in the unit cell. Note: the number of atoms in a unit cell is a whole number.

The molar mass of iridium is 192.22.
I know that this can either be a bcc, cap, or hcp arrangement.

To determine the number of atoms in the unit cell, we need to consider the arrangement of atoms in each type of crystal structure.

1. BCC (Body-Centered Cubic):
In a BCC unit cell, there are 2 atoms.

2. FCC (Face-Centered Cubic):
In an FCC unit cell, there are 4 atoms.

3. HCP (Hexagonal Close-Packed):
In an HCP unit cell, there are 6 atoms.

Since we do not know which crystal structure iridium adopts, we need to calculate the number of atoms for each possibility and choose the one that gives a whole number.

Let's start with the calculation for BCC:

Given that the density of iridium is 22400 kg/m^3, and the molar mass is 192.22 g/mol, we can calculate the number of moles per unit volume using the formula:

Number of moles = Density / Molar mass

Number of moles = 22400 kg/m^3 / 192.22 g/mol

Now, convert the volume of the unit cell from cm^3 to m^3:

Unit cell volume = 5.66 x 10^-23 cm^3 = 5.66 x 10^-23 x (1 m^3 / 10^6 cm^3)

Next, calculate the number of iridium atoms in the unit cell for BCC:

Number of atoms = Number of moles x Avogadro's number

Avogadro's number = 6.022 x 10^23 atoms/mol

Repeat the same calculations for FCC and HCP arrangements.

After calculating for all three crystal structures, compare the number of atoms obtained with all three possibilities. The one that gives a whole number will be the correct crystal structure for iridium.