Question

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

Answer 1

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

Let ‘a’ be the edge length of a unit cell of a crystal, ‘d’ be the density of the metal, ‘m’ be the atomic mass of the metal and ‘z’ be the number of atoms in the unit cell.

Now, density of the unit cell

[Since mass of the unit cell = Number of atoms in the unit cell × Atomic mass]

[Volume of the unit cell = (Edge length of the cubic unit cell)³]

From equation (i), we have:

Now, mass of the metal (m)

Therefore,

If the edge lengths are different (say a, b and c), then equation (ii) becomes:

From equations (iii) and (iv), we can determine the atomic mass of the unknown metal.