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Homework Statement:

The intrisinc carrier concentration of single crystal sillcon is ##(1.5*10^{10})## per cubic centimeter.
Bandgap is 1.1eV and density is 2.33g per cubic centimeter.
How many free electron and holes are there per cubic centimeter.
Determine the fraction of valence electrons that are free for conduction at room temperature. Explain where electrons get sufficient energy from in order to be free.
Relevant Equations:
 
For the first part, since this is a intrisinc semiconductor, n=p= intrisinc carrier concentration. Hence free electrons and hole = ##(1.5*10^{10})## per cubic centimeter.
As for part 2, here are my steps. But I'm not sure if it's correct.
I first find the number of atoms of one cubic centimeter of sillcon, (using density and atomic mass of sillcon) then multiply it by 4 (since there is 4 valence electrons per sillcon atom?) I then take :
##(1.5*10^{10})## divided by the number of valence electrons as calculated above. Is this thought process correct? Thanks
As for part 2, here are my steps. But I'm not sure if it's correct.
I first find the number of atoms of one cubic centimeter of sillcon, (using density and atomic mass of sillcon) then multiply it by 4 (since there is 4 valence electrons per sillcon atom?) I then take :
##(1.5*10^{10})## divided by the number of valence electrons as calculated above. Is this thought process correct? Thanks