Question

An element crystallizes in a body-centered cubic lattice. The edge of the unit cell is 3.28 Å in length, and the density of the crystal is 6.50 g/cm3 .

a.) Calculate the atomic weight of the element.

Answer 1

Since, edge of the unit cell is 3.28 Å

volume of the unit cell = 3 x 3.28 x 10^-8 cm³

= 9.84 x 10^-8 cm³

Given that density of cell = 6.50 = weight of the cell/ volume of the cell

Hence, weight of the cell = 6.5 x (9.84 x 10^-8)

                                                = 63.96 x 10^-8g

But in body cantered cubic lattice contain two atoms each

Hence atomic weight = weight of the unit cell / 2

                                                = 31.98 x 10^-8 g