How will derive the formula of density of a unit cell ?

Explanation

(i) Using the edge length of a unit cell, we can calculate the density `(rho)` of the crystal by considering a cubic unit cell as follows.
`"Density of the unit cell "rho=("Mass of the unit cell")/("Volume of the unit cell")" ...(1)"`
`"Mass of the unit cell"={{:("Total number of atoms belong"),(" to that unit cell"):}}xx"mass of one atom"`
`"Mass of one atom"=("Molar mass "("g mol"^(-1)))/("Avagardo number "("mol"^(-1)))" ...(2)"`
`m=(M)/(N_(A))" ...(3)"`
Substitute the value (3) in (2)
`"Mass of the unit cell "=nxx(M)/(N_(A))`
For a cubic unit cell, all the edge lengths are equal, i.e., `a=b=c`
`"Volume of the unit cell"=axxaxxa=a^(3)`
`therefore" Density of the unit cell "=rho=(nM)/(a^(3)N_(A))`