🤓 Based on our data, we think this question is relevant for Professor Billman's class at Abilene Christian University.

We’re asked to determine** how many milligrams of 1 ppm phosphorus, P is required** to **dope** (fill in the gaps) a **1 cm ^{3} sample of silicon, Si **having a

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:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

*Step 2: Calculate the mass of 1 cm ^{3} sample of Si*

*Step 3: Determine mass (in mg) of 1 ppm P needed to dope the 1 cm ^{3} sample of Si*. Recall that

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

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 - cm^{3} 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?