Metallic magnesium has a hexagonal close packed structure and a density of 1.74 g//cm^3. Assuming magnesium atoms to be spherical, calculate the volume of eachatom and atomic radius of Mg atom (Atomic mass of Mg =24)

Metallic magnesium has a hexagonal close packed structure and a densit

1.	Metallic magnesium has a hexagonal close packed structure and a density of 1.74 g//cm^3. Assuming magnesium atoms to be spherical, calculate the volume of eachatom and atomic radius of Mg atom (Atomic mass of Mg =24)
Answer» Solution :As MG has HEXAGONAL close packed structure , no. of atoms per unit cell = 6 , i.e., Z=6 `rho=(ZxxM)/(a^3xxN_0)=(ZxxM)/(VxxN_0)` (V=`a^3`=volume of the unit cell) `therefore 1.74 =(6xx24)/(Vxx(6.023xx10^23))` or `V=1.374xx10^(-22) cm^3` Now , as in hexagonal close packing , 74% of the space is occupied by atoms, therefore, volume occupied by atoms =`74/100xxV` `=74/100xx1.374xx10^(-22) =1.018xx10^(-22) cm^3` As a unit cell contains 6 Mg atoms, therefore , volume of each Mg atom `=(1.018xx10^(-22))/6=1.697xx10^(-23) cm^3` As Mg atom is ASSUMED to be spherical, `therefore 4/3pir^3 =1.697xx10^(-23)` On SOLVING, we GET `r=1.594xx10^(-8)` cm =1.594 Å