Determine electron density with impurites

[PeoplesChamp]

Homework Statement

Let’s introduce an imaginary atom which can replace the silicon atom and
generate one mobile electron. What is electron density when all silicon atoms are replaced by this imaginary
atom

Homework Equations

The Attempt at a Solution

I have tried looking for a formula to determine electron density, but they all look beyond my current understanding. I believe that the answer comes about when solving (electron denisty new)/(electron density silicon) and cancellations occur. I know I don't know much about this, but I am very unsure how to go about this.

 

[mark726]

First, to calculate the electron density, we need to know the number of electrons in the atom and the volume of the atom. Since we are dealing with an imaginary atom, we can assume that it has the same number of electrons as a silicon atom, which is 14. However, the volume of the atom will be different since it is a different element.

To calculate the volume of the atom, we can use the formula for the volume of a sphere, V = (4/3)πr^3, where r is the radius of the atom. The radius of an atom is typically in the range of 0.1-0.5 nanometers (nm). Let's assume a radius of 0.3 nm for our imaginary atom.

Plugging in the values, we get V = (4/3)π(0.3 nm)^3 = 0.113 cm^3 (note that we converted nanometers to centimeters).

Now, to calculate the electron density, we divide the number of electrons (14) by the volume of the atom (0.113 cm^3).

Electron density = 14/0.113 = 123.9 electrons/cm^3

So, when all the silicon atoms are replaced by this imaginary atom, the electron density will be 123.9 electrons/cm^3.

Note: This is a very simplified calculation and does not take into account the actual structure of the atom and the interactions between the atoms. It is also important to note that this is just an imaginary scenario and cannot be applied to real-life situations.