Question

Properties of matter

A metal crystallises in a face-centred cubic lattice.The edge of the unit cell is 286pm,and the density of the crystal is 7.92gcm^-3.Calculate the atomic mass of the element?

Answer 1

Solution :-

Given data

Edge length = 286 pm

Density = 7.92 g/cm3

Atomic mass of the element = ?

In the FCC unit cell it contains 4 atoms

Therefore lets first calculate the volume of the unit cell

Lets first convert the edge length into the cm from pm

286 pm * 1 cm / 1E10 pm = 2.86E-8 cm

now lets calculate the volume of the unit cell

volume of unit cell = (d)³

                                   = (2.86E-8 cm)³

                                   = 2.339E-23 cm3

Now lets calculate the mass of the unit cell

Mass = volume * density

          = 2.339E-23 cm3 * 7.92 g per cm3

         = 1.8525E-22 g

Now 1 unit cell contains 4 atoms

Therefore lets calculate the atomic mass for the 1 mole of the atoms

4 atom = 1.8525E-22 g

6.022E23 atoms = ? g

6.022E23 atoms * 1.8525E-22 g / 4 atoms = 27.9 g/mol

Therefore the atomic weight of the element is 27.9g per mol