an element A crystallises in fcc structure . 200g of this element has 4.12*10^24 atoms. the density of A is 7.2g/cm^3.calculate the edge length of the unit cell

Let length of each edge = a cm

     volume of  unit cell =a³ cm³

 

Mass of each atom = 200 / (4.12 x 10²⁴)

                           =48.54 x 10^-24    g

 For fcc   Z =4

 Mass of unit cell  = 4 x 48.54 x 10^-24

                         = 194.16 x10 ^-24 g

 

Density =mass / volume

 7.2 =194.16  x 10^-24/a³

a³ =194.16 x10^-24/ 7.2 =26.97 x 10^-24

a = 2.999 x10^-8 cm

   =299.9 pm