## Calculations involving unit cell dimensions Chemistry Notes

The different calculations of unit cell, are as follows –

Calculations of density of Solid :

Let the edge length of unit cell = a
Volume of unit cell = (a)3
If mass of particle present in unit cell = m
then, mass of unit cell Number of atoms in unit cell × mass of an atom
= Z × m
Where, Z = Number of atoms in unit cell
Mass of an atom present in unit cell  Generally, the density of unit cell is measured in g/cm3. If the length of edge is given in pm (picometer) or A° (Angstrom), then it is converted into cm.
1 pm = 10-12 m = 10-10cm
1 Å= 10-10 m = 10-8 cm Relation Between Edge Length and Radius (r) of Atom
In simple cubic lattice,
a = 2r
In body-centred cubic lattice,
a = $$\frac{4 r}{\sqrt{3}}$$
In face-centerd cubic lattice,
a = 2√2r
Relation Between Distance of Nearest Neighbouring Atoms and Edge Length
For Simple Cubic Unit cell,
d = a
For face-centred cubic unit cell,
d = $$\frac{a}{\sqrt{2}}$$
For body-centred cubic unit cell,
d = $$\frac{\sqrt{3} a}{2}$$