Calculation of Density of a Cubic Crystal from its Edge Length.
The edge length of a cubic crystal can be obtained from X-ray studies and knowing the crystal structure possessed by it so that the number of particles per unit cell are known, the density of the crystal can be calculated.
Case 1
For cubic crystals of elements (e.g., Fe, Cu)
Let edge length = a pm
Number of atoms per unit cell = Z
Atomic mass of the element = M
Volume of Unit cell = (a pm)3 = a3 x 10-30 cm
Mass of unit cell = Number of atoms per unit cell x Mass of each atom
= Z x m
where,
Density of the substance is same as the density of the unit cell.
Case 2
For cubic crystals of ionic compounds (NaCl, ZnS). The formula is the same except that now, Z is the Number of formula units present in one unit cell and M is Formula mass.
The above equation involves five parameters. Knowing any four, the fifth can be calculated.
With the help of the above formula and the relation between a and r of ions, the ionic radius can be calculated for ionic crystals.