Atomic radius is1.349*10-23
hcp unit cell you can see that that the spheres touch each other along
so 2rMg = a where rMg is the radius of a Mg ion and = 0.6745*10^-23
There are three levels of atoms in the hcp structure.
Six atoms form a hexagonal arrangement in the top and bottom layers, while a seventh atom sits in the centre of the hexagonal arrangement.
Three atoms in the intermediate layer are tucked away in the top and bottom plane's triangular grooves.
Mg hcp c/a = 1.635
hcp is close-packed example ABABAB etc
V = sin(60)*a*a*1.635 a
V = 1.635 *0.866*a^3
V = 1.887*a^3 cm3
Z = 2 (atoms inside unit cell)
Mass inside unit cell is = (2 * 24.305)/(6.022*10^23) = 8.071*10^-23 g
D =M/V
1.74 = 8.071*10^-23/1.887*a^3
a^3 = 8.071*10^-23/1.887*1.74 = 2.458*10^-23
a = 1.349*10^-23
Hence Atomic radius is 1.349*10^-23
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