Question #f2a5b
1 Answer
Don't let the language scare you. This is actually solvable on general chemistry principles, once we distill this down to something more understandable.
I will show you that most jargon aside, this question is really asking:
"What is the wavelength corresponding to the minimum energy needed to excite an electron from the valence band to the conduction band?"
GERMANIUM AS AN INTRINSIC SEMICONDUCTOR
According to Band Theory, since
Because its conductivity increases with temperature, it is an intrinsic semiconductor, requiring no dopant (such as silicon).
It has an energy gap (
At the Fermi level, which commonly is right around the HOMO-LUMO gap at
Raise the temperature a little, or add a bit of energy (say,
SOLVING FOR THE MAXIMUM WAVELENGTH
We know that wavelength
Next,
So, asking how to "generate an electron-hole pair" simply says:
"How does one annihilate one of the two electrons, and then create an excited one in a higher-energy, previously-unoccupied orbital?"
Thus, the question is really asking:
"What is the wavelength corresponding to the minimum energy needed to excite an electron from the valence band to the conduction band?".
Hence, we should solve the following equation from general chemistry:
#\mathbf(E = hnu = (hc)/lambda)#
Now that we've clarified the language, this is pretty easy, no? No unit conversion necessary.
#color(blue)(lambda) = (hc)/E#
#= (12400 cancel("eV")cdot"Å")/(0.72 cancel("eV"))#
#=# #color(blue)("17222 Å")#
This web page seems to agree with me.