Problem: Silicon has a face-centered cubic crystal structure with unit cell edge length of 5.43 Å and four atoms per unit cell.Suppose you dope that 1 - cm3 sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

We’re asked to determine how many milligrams of 1 ppm phosphorus, P is required to dope (fill in the gaps) a 1 cm³ sample of silicon, Si having a face-centered cubic (FCC) crystal structure and unit cell edge length of 5.43 Å and four atoms per unit cell.

To do so, we need to do these steps:

Step1: Calculate the mass and volume one unit cell of Si to determine its density. Recall that the density  cube is given by the equation:

$\boxed{\mathbf{density}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Step 2: Calculate the mass of 1 cm³ sample of Si

Step 3: Determine mass (in mg) of 1 ppm P needed to dope the 1 cm³ sample of Si.  Recall that ppm is given by the equation: 

$\boxed{\mathbf{ppm}\mathbf{=}\frac{\mathbf{g}\mathbf{ }\mathbf{solute}}{\mathbf{g}\mathbf{ }\mathbf{solution}}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}}$