Exercise 2
Question 5
How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.
If we know the density and the dimenstions of unit cell of an unknown metal, the atomic mass of the metal can be determined easily.
Let us assume a cubic crystal,then Its volume of unit cell will be = a3
&
No of atom in each cell = z
Also molar mass of the metal =M,
Mass of each atom = m
Now we know, mass of unit cell = no of atom in each cell x Mass of each atom -------------------(1)
Also Mass of each atom = molar mass / avagadro number ,i.e M/NA ------------(2)
Putting the values of 2 in 1 we get,
Mass of unit cell = Mz / NA ------------------(3)
Now density of unit cell (d) = mass of unit cell / volume of unit cell
Therefore from 1,2,3 we,get
d = Mz / a3 NA---------------------------(4)
From 4th equation we can calculate the atomic mass of unknown metal.
