Question

An element ' X' ( Atomic mass = 40 g / mol ) having f.c.c. structure,has unit cell edge length of 400 pm.Calculate the density of 'X' and number of unit cell in 4gm of x

Answer 1

We know that :  

d= Z * M/a^3* NA

Molar mass(M)=40 g /mol

Edge length(a)=400 pm=400*10^-10 cm

Z for FCC=4

d=4 * 40 / [400*10^-10]^3 * 6.023*10^23

d= 4.1  g/cm^3

We know that,

Number of atoms in a unit cell of FCC=4

Number of atoms in 4 g=4/40 x 6.023*10^23

                         =6.023*10^22 atoms .

Since , 1 unit cell has------------>4 atoms

                    ? < ------------------   6.023*10^22 atoms

         No. of unit cells=6.023*10^22/4

          =1.50*10^22 unit cells in 4 g of X.