A silicon sample is doped with phosphorus at 1.23 parts per million. Phosphorus

Question

A silicon sample is doped with phosphorus at 1.23 parts per million. Phosphorus acts as an electron donor, providing one free electron per atom. The density of silicon is 2.33 g/cubed cm and its atomic mass is 28.09 g/mol. Calculate the number of free electrons per unit volume of the doped silicon.

Compare the above result with the no. of conduction electrons per unit volume of copper wire, assuming that each copper atom produces one free conduction electron. The density of copper is 8.96 g/cm^3 and it's atomic mass is 63.54 g/mol.

Explanation / Answer

for unit volume there is 2.33 gm silicon in one cm^3

hence total moles = 2.33/28.09 = 0.0829 moles

1 mole has 6.023*10^23 atoms hence 0.0829 moles has 5 *10^22 silicon atoms

given thatsilicon has 1.23 parts per million phosphorus in it that means 1.23 atoms per 10lakh atoms

therfore for 5 *10^22 silicon atoms we have 1.23* 5 *10^22/10^6 atoms = 6.14 *10^16 atoms of phosphorus

density of copper is 8.96 g/cm^3 and it's atomic mass is 63.54 g/mol.

for unit volume there is8.96 gm scopper in one cm^3

hence total moles = 8.96/63.54 = 0.141 mole

1 mole has 6.023*10^23 atoms hence 0.141moles has 8.5*10^22 copper atoms

given that each copper atom produces one free conduction electron hence 8.5*10^22 copper atoms produces

8.5*10^22 free electrons

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