Chemical analysis of a silicon crystal reveals gallium at a level of 3.091×10−8 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?

(6.023*10^23)/(12.05)=m

m*(3.091*10^-8)*(10^-2)=

This is a question from the second midterm of 3.091x by edx. Stop cheating, it's silly and pointless.

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Let's play around! Go GO Go!!! FIre in you hole!

To determine the density of free charge carriers in the silicon crystal, we need to know the number of free charge carriers per unit volume. This can be calculated using the following formula:

Density of free charge carriers = (Number of free charge carriers / Volume of crystal)

To find the number of free charge carriers, we first need to determine the number of gallium atoms in the crystal. We know that the atomic percent of gallium is 3.091×10^(-8), which represents the ratio of the number of gallium atoms to the total number (gallium + silicon) of atoms in the crystal.

To calculate the number of gallium atoms, we need to know the total number of atoms in the crystal. Silicon has a density of about 2.33 g/cm³, and its atomic weight is approximately 28.086 g/mol. Therefore, the molar volume of silicon is approximately 28.086 g/mol / 2.33 g/cm³ = 12.03 cm³/mol.

Next, we need to determine the molar fraction of gallium in the crystal. The atomic percent can be converted to a mole percent by dividing by the atomic weight ratio (atomic weight of gallium / atomic weight of silicon) and multiplying by 100. The atomic weight of gallium is approximately 69.723 g/mol. Therefore:

Mole percent of gallium = (3.091×10^(-8) / (69.723 / 28.086)) * 100

Now, we can calculate the number of gallium atoms per unit volume of silicon crystal using the molar fraction and Avogadro's number (6.022 × 10^23).

Number of gallium atoms = mole percent of gallium * Avogadro's number * (Density of silicon / molar volume of silicon)

Finally, we can use the number of gallium atoms to calculate the density of free charge carriers:

Density of free charge carriers = Number of gallium atoms / Volume of crystal

Therefore, to find the density of free charge carriers in the Si crystal, you would need to input the appropriate values into these formulas and perform the calculations.