Q.1.5 how can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell?Explain.

solution:- 

calculation of the atomic mass of an element-

Let the atomic mass of the element which is to be determined=M

Density of the element=d gcc^-1

Let the edge of the unit cell=a cm 

volume of the unit cell=a^3 cm^3

Density of the unit cell will be the same as the density of the element.

Mass of the unit cell=d×a^3 g

Atomic mass of the element(M)= Mass of the atom × N0

where    N0=avogardo's number =6.023 × 10^23

Now the mass of the unit cell=No. of atoms in the unit cell × mass of the each atom 

                                              =Z× m

M=(6.023 × 10^23×a^3×d)/Z

Hence Atomic mass M= (N0 ×a^3×d)/Z

where   z=4 for fcc 

z=2 for bcc

z=1 for simple cubic.

Ans