Q .5. How can you determine the atomic mass of an unknown metal if you know its density?

Q .5. How can you determine the atomic mass of an unknown metal if you know its density?

Let consider a cubic crystal:

Let take volume of a unit cell         = a³

Number of atoms in unit cell         = z

Mass of each single atom            = m

Molar mass of metal                    =M

Avogadro number                        =N_A

Use formula

Mass of the unit cell            = number of atoms in unit cell × mass of each atom

                                                = z × m                                   …(1)

Mass of each atom(m)        = Molar mass / Avogadro number

Plug the value of m in equation (1) we get

Mass of unit cell                   =ZM /N_A                                            … (2)

Density of the unit cell        = mass of unit cell / volume of unit cell

Using above formula we can calculate the atomic mass of unknown metal