Question

Given a face-centred unit cell as shown... Given a face-centred cubic cell as shown for an element, how many atoms does the unit cell contain?

Answer 1

Are there not 4 atoms per unit cell?

Explanation:

Each vertex of the cube shares `1/8` of an atom, and thus 1 atom from the 8 vertices; each face of the cube shares `1/2` an atom, and 3 atoms from the 6 faces. And thus 4 atoms per unit cell in total.....

And so if the volume of a sphere is `V`, thus each unit cell has `4V` with respect to occupied volume. And the cube length is `a`, hence the cubic volume is `a^3`.

And so occupied volume is `(4V)/a^3`, i.e. `" option a"`......

It has been a long time since I had to do this sort of stuff. But remember all I did was to consider the 8 vertices and 6 faces of the cube. Your inorganic text will tell you this definitively in the section on crystal packing and structure.