Question

3. An alloy of copper and gold has the structure shown in the figure (a=D=C =3.77 Å, and a=B=y=90 degrees). Calculate the composition of the cell. Given that 24-carat gold is pure gold what carat does this alloy represent? What is the density of the crystal in grams/cm'?

Answer 1

A point that is located at the corner of a unit cell is shared together by eight such unit cells, that is each unit cell has a share of 1/8th of such a point.

A face-centered point is shared between two unit cells and therefore, only half of each such point lies within any one cell.

8 Gold atoms are present at the corners, Contributions from 8 corners = 8 x 1/8 = 1 gold atom

copper atoms centers of the faces, total points contributed by face-centered points i.e. 6 faces of a cube

                                                = 6 x 1/2 = 3 copper atoms

The composition of the crystal is Au₁Cu₃.

Given that the 24 carat gold is pure gold i. e 100% gold is 24 carat

the percentage of gold in the crystal is 25%.

The given alloy represent 25*24/100 = 6 carat gold.

Density of the crystal, d= Z*M/N*a³ where Z= effective number of atoms in the unit cell, M = molar mass of the unit cell, N = Avagadro number, a = edge length

Density of the crystal, d= Z*M/N*a³ = 4*387.604/(6.023*10^23*3.77*10^-8)^3 = 48.04 gm/cm3