Class 12 Chemistry - Chapter The Solid State NCERT Solutions | How can you determine the atomic mass of

Welcome to the NCERT Solutions for Class 12th Chemistry - Chapter The Solid State. This page offers a step-by-step solution to the specific question from Exercise 2, Question 5: how can you determine the atomic mass of an unknow....
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.

Answer

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.

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