# Answer the following in brief. Obtain the relationship between density of a substance and the edge length of unit cell. - Chemistry

Short Note

Obtain the relationship between the density of a substance and the edge length of the unit cell.

#### Solution

Relationship between the density of a substance and the edge length of the unit cell:

1. If the edge length of the cubic unit cell is ‘a’, then the volume of the unit cell is a3.

2. Suppose that mass of one particle is 'm’ and that there are ‘n’ particles per unit cell.

∴ Mass of unit cell = m × n          …(1)

3. The density of unit cell (ρ), which is same as density of the substance is given by:

rho = "Mass of unit cell"/"Volume of unit cell" = ("m" xx "n")/"a"^3 = Density of substance     …(2)

4. Molar mass (M) of the substance is given by:

M = mass of one particle × number of particles per mole

= m × NA (NA is Avogadro number)

Therefore, m = "M"/"N"_"A"        ....(3)

5. Combining equations (1) and (3), gives

rho = "n M"/("a"^3 "N"_"A")       ....(4)

Concept: Cubic System
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#### APPEARS IN

Balbharati Chemistry 12th Standard HSC for Maharashtra State Board
Chapter 1 Solid State
Exercise | Q 3.1 | Page 27