Chemical analysis of a silicon crystal reveals gallium at a level of 3.091*10^-7 atomic percent. Assuming that the concentration of thermally excited charge carriers from the Si matrix is negligible, what is the density of free charge carriers (free carriers/cm3) in this Si crystal?
(atomic percent/100*6.02*10^23)/ atomic volume of element
Sorry hina but it didn't work
CHEAT!
Do NOT help this person. They are trying to cheat in a midterm exam.
(6.023*10^23)/(12.05)=m
m*(3.091*10^-7)*(10^-2)=
To determine the density of free charge carriers in the silicon crystal, we need to know the atomic percent of gallium and the density of the silicon crystal.
We are given that the atomic percent of gallium is 3.091*10^-7. This means that for every 10^7 silicon atoms, there are 3.091 gallium atoms.
Next, we need to calculate the number of silicon atoms in the crystal. We can do this by using Avogadro's number, which states that there are 6.022 x 10^23 atoms in one mole of any substance. The atomic mass of silicon is 28.086 g/mol. Let's assume the density of the silicon crystal is 2.329 g/cm^3.
We can calculate the number of silicon atoms per cubic centimeter using the following steps:
1. Calculate the molar volume of silicon:
Molar volume = Atomic mass / Density = (28.086 g/mol) / (2.329 g/cm^3)
2. Calculate the number of silicon atoms per cubic centimeter:
Number of atoms/cm^3 = (6.022 x 10^23 atoms/mol) / Molar volume
3. Calculate the number of gallium atoms per cubic centimeter:
Number of gallium atoms/cm^3 = Number of silicon atoms/cm^3 * (Atomic percent of gallium / 100)
Finally, to determine the density of free charge carriers in the silicon crystal, we need to consider that gallium contributes one extra charge carrier for each atom. So the density of free charge carriers is equal to the number of gallium atoms per cubic centimeter.
Let's calculate it:
1. Molar volume of silicon:
Molar volume = 28.086 g/mol / 2.329 g/cm^3 = 12.043 cm^3/mol
2. Number of silicon atoms per cubic centimeter:
Number of atoms/cm^3 = (6.022 x 10^23 atoms/mol) / 12.043 cm^3/mol = 4.997 x 10^22 atoms/cm^3
3. Number of gallium atoms per cubic centimeter:
Number of gallium atoms/cm^3 = 4.997 x 10^22 atoms/cm^3 * (3.091 x 10^-7 / 100) = 1.548 x 10^16 atoms/cm^3
Therefore, the density of free charge carriers in the silicon crystal is 1.548 x 10^16 free carriers/cm^3.