Many elements crystalize with a unit cell that is hexagonally shaped (6 sided).

Question

Many elements crystalize with a unit cell that is hexagonally shaped (6 sided). The calculations of the unit cell dimension are not significantly more complicated than those for cubic unit cells. A hexagonal unit cell is shown below. 2 3 3 a c 2 Volume 6 atoms per unit cell The cell dimension "a" is twice the radius (r) of the atom. 2r-a. For most elements the dimension "c" is approximately 1.633x "a" The element zirconium (Zr) crystallizes with a Simple Hexagonal unit cell. The density of a zirconium is 6.5 g/cm3, Use this information to calculate the metallic radius of zirconium in picometers (pm). 1 pm = 1x10-12 meters. You may assume that the dimension c=1.633-a [Note: The theoretical value for the radius may be different from the experimentally determined value. Simply Googling the radius may not yield the correct result] pm Check

Explanation / Answer

density (d) =mass / volume

volume = 3*sqrt(3)*a^2*C / 2

     C = 1.633 a

     a = 2r

   C = 1.633*2r

volume = (3*sqrt(3)*(2r)^2*1.633*2r)/2

mass = At.wt*6 atoms

      = (91.224/(6.023*10^23))*6

      = 9.087*10^-22 g

density = 6.5 g/cc

6.5 = (9.087*10^-22)/((3*sqrt(3)*(2r)^2*1.633*2r)/2)

r = radius of Zr = 1.603*10^-8 cm

    = 160.3 pm

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