A photovoltaic cell contains a p–n junction that converts solar light to electricity. (a) Silicon semiconductors with a band-gap energy of 107 kJ/mol are commonly used to make photovoltaic cells. Calculate the wavelength that corresponds to the band-gap energy in silicon.

Video transcript

Hey everyone, we're told that photovoltaic cells contain P N junctions to convert light from the sun to electricity. A cadmium telluride semiconductor. Using photovoltaic cells has a band gap energy of 144 kg joules per mole, determine the wavelength that correspond to the band gap energy of cadmium telluride and identify its region in the electromagnetic spectrum. First, let's go ahead and determine our change in energy. And we can do so by taking that band gap energy of 144 kg joules per mole of photon. Now we want to convert this into jewels per photon. So using our dimensional analysis we know that one kill a jewel contains 10 to the third jewels. And we know that one mole of photons Contains 6.02, 2 times 10 to the 23rd photon. So when we calculate this out and cancel out all of our units, We end up with a change in energy of 2.391, 2 times 10 to the -19 joules per photon. Now that we have our change in energy, we know that this is equal to our planks constant, times our speed of light divided by our wavelength. And we want to isolate our wavelength. So our wavelength is going to be equal to our plank's constant, times our speed of light divided by our energy plugging in these values, we get 6.626 times 10 to the negative 30 for jules time seconds, which is our planks constant. And we're going to multiply this by our speed of light which is 3.0 times 10 to the eight m/s. Now we can go ahead and divide this by our energy, which we calculated to be 2.3912 times 10 to the -19 joules per photon. So when we calculate this out and cancel out all of our units, we end up with a wavelength of 8. times 10 to the negative seven m. And when we go ahead and look at this chart right here, we can see that 8.31 times 10 to the negative seven m falls in our infrared region, which will be right here. So our answer here is going to be 8.31 times 10 to the negative seven m, which is in our infrared region. Now I hope that made sense. And let us know if you have any questions