To calculate the packing factor, first calculate the area and volume of unit cell.
Area is calculated as:
Here, R is radius and is related to a as follows:
Putting the value in expression for area,
The value of a is 0.4961 nm
Since,
Thus,
Putting the value,
Now, volume can be calculated as follows:
The value of c is 1.360 nm or
Putting the value,
now, number of atom in unit cell can be calculated by using the following formula:
Here, A is atomic mass of is 151.99 g/mol.
Putting all the values,
Thus, there will be 18 units in 1 unit cell.
Since, there are 2 Cr atoms and 3 oxygen atoms thus, units of chromium and oxygen will be 2×18=36 and 3×18=54 respectively.
The atomic radii of and
is 62 pm and 140 pm respectively.
Converting them into cm:
Thus,
and,
Volume of sphere will be sum of volume of total number of cations and anions thus,
Since, volume of sphere is ,
Putting the values,
The atomic packing factor is ratio of volume of sphere and volume of crystal, thus,
Thus, atomic packing factor is 0.758.