# Is the density of a unit cell the same as the density of the substance?

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**Hint:**The unit cell is described as the small repeating unit having the full symmetry of a crystal structure. A crystal structure is defined in terms of the geometry of the arrangement of particles in the unit cell. Generally, a primitive cell is a crystal lattice of eight molecules bound in a geometric structure.

**Complete Step By Step Answer:**

The mass of one unit cell can add the mass of all the atoms in that particular cell. The number of atoms depends on the kind of cell. To obtain the mass of a unit cell we have to multiply the number of atoms “$n$” with the mass of each atom ”$m$”.

Mass of Unit Cell = $m \times n$

Now, the mass of an atom is represented in terms of its Avogadro Number${N_A}$

It is many units in one mole of any substance and the molar mass of an atom. the mass of an atom can be written as follows,

Mass of an Atom = Molar Mass $ \times $ Avogadro Number

Mass of an Atom =$M{N_A}$

So the formula for Mass of Unit Cell is given as follows

Mass of Unit Cell = $n \times M{N_A}$

the density of a unit cell formula is,

The density of a Unit Cell = Mass of Unit Cell / Volume of Unit Cell

The density of a Unit Cell $ = \dfrac{{n \times M{N_A}}}{V}$

Now for a cube of length of each side $a$ , volume $V = {a^3}$

So, The density of a Unit Cell $ = \dfrac{{n \times M{N_A}}}{{{a^3}}}$

Finally, the given statement is true. The density of a unit cell is equal to the density of the substance.

**Note:**

A repeating unit of the entire crystal is known as a unit cell.

It is a structural unit, in which the whole lattice can be built up by continuous repetition in three dimensions

The mass of the unit cell is equal to the product of the number of atoms in a unit cell and the mass of each atom in the unit cell.

Last updated date: 21st Sep 2023

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