How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.

The atomic mass of an unknown metal can be determined by knowing its density and the dimension of unit cell.

Let ‘a’ be the edge length of a unit cell of a crystal.

‘d’ is the density of the metal

‘m’ is the atomic mass of the metal.

‘z’ is the number of atoms in the unit cell.

Now, the density of the unit cell

As we know that, mass of the unit cell = Number of atoms in the unit cell × atomic mass

And the volume of the unit cell = (Edge length of the cubic unit cell)³

Therefore, d --------- (i)

---------------- (ii)

Now, since mass of the metal (m)

Therefore, from equation (ii) we have

--------------- (iii)

If the edge lengths are different (say a, b and c), therefore, equation (iii) can be written as

----------- (iv)

Thus, using equation (iii) and the atomic mass of an unknown metal can be determined.