## 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/cm^{3}. 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^{-10}cm

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 = \(\frac{\sqrt{3} a}{2}\)