Question

A compound of cadmium, tin, and phosphorus is used in the fabrication of some semiconductors. It crystallizes with cadmium occupying one-fourth of the tetrahedral holes and tin occupying one-fourth of the tetrahedral holes in a closest packed aligned of phosphide ions. What is the formula of the compound? Explain your answer.

Short answer

The molecular formula of cadmium, tin and phosphorus is \({{\rm{P}}_2}{\rm{CdSn}}\).

Step-by-step solution

Define the coordination number of a sphere

The coordination number of a sphere occupying tetrahedral hole is 4 . They are smaller than the cubic or octahedral holes. Face- centred cubic arrangement has tetrahedral (8) and octahedral holes (4). The example used to see a tetrahedral structure is methane. Here, the carbon atom is attached to four equidistance hydrogen atoms placed at the corners of tetrahedrons.

Find the molecular formula.

Assume\(x\) be the number of phosphide ions present in the lattice. Hence, the number of tetrahedral holes is 2x.

One-fourth of the tetrahedral holes are occupied by cadmium ions.

The mathematical representation is as follows: \(\frac{1}{4} \times 2x = \frac{x}{2}\)

One-fourth of the tetrahedral holes are occupied by tin ions.

The mathematical representation is as follows: \(\frac{1}{4} \times 2x = \frac{x}{2}\)

Hence, the molecular formula of cadmium sulphide is \({{\rm{P}}_x}{\rm{C}}{{\rm{d}}_{\frac{x}{2}}}{\rm{S}}{{\rm{n}}_{\frac{x}{2}}}\).

To get the whole number, multiply with \(\frac{2}{x}\) then molecular formula is \({{\rm{P}}_2}{\rm{CdSn}}\).Thus, the molecular formula of cadmium, tin and phosphorus is \({{\rm{P}}_2}{\rm{CdSn}}\).