Metallic magnesium has a hexagonal close packed structure and a density of 1.74 g//cm^(3) . Assuming magnesium atoms to be spherical, calculatethe volume of each atom and atomic radium of Mg atoms (Atomic mass ofMg= 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, calculatethe volume of each atom and atomic radium of Mg atoms (Atomic mass ofMg= 24)
Answer» <P> Solution :As MG has hexagonal close packed structure , no. of atoms per unit cell = 6 ,i.e,Z = 6 `p= (Z XX M)/( a^(3)xxN_(0)) = (Z xxM)/(V xx N_(0)) "" (V =a^(3)`= VOLUME of the unit cell) ` 1.74 = ( 6xx24)/( V xx (6.023 xx10^(23))) orV = 1.374 xx 10^(-22)cm^(3)` Now ,as in hexagonal close packing, 74%of the space is occupiedby atoms, therefore, volume occiped by atoms ` = 74/100 xx V` ` = 74/100 xx 1.734 xx 10^(-22) = 1.018 xx 10^(-22)cm^(3)` As a unit cell contains 6 Mg atom, therefore, volume of each Mg atom. `( 1.018 xx 10^(-22))/6= 1.697 xx 10^(-23) cm^(3)` As Mg is assumed to be spherical. ` 4/3 pir^(3) = 1.697 xx 10^(-23)` on solving we get ` r =1.594 xx 10^(-8)cm= 1.594Å`