A photovoltaic cell contains a p–n junction that that converts
s...

Question

A photovoltaic cell contains a p–n junction that that converts 
solar light to electricity. An optimum semiconductor 
would have its band-gap energy matched to the wavelength 
of maximum solar intensity at the Earth’s surface. 
(b) Which of the following semiconductors absorb at a 
wavelength matched with maximum solar intensity? 
CdTe with a band-gap energy of 145 kJ/mol or ZnSe 
with a band-gap energy of 248 kJ/mol.

Accepted Answer

Hi everyone. This problem reads a P. N junction in a photovoltaic cell turned solar light into electrical current. The wavelength of maximum sun intensity at the earth's surface would be matched to the band gap energy of an ideal semiconductor? Which semiconductor among the following absorbs at a wavelength that corresponds to the maximum solar intensity wavelength is equal to 500 nanometers. A cadmium sulfide semiconductor with a band gap energy equal to 241 kg joules per mole or a gallium arsenide semiconductor with a band gap energy equal to 138 kg joules per mole. Okay, so our goal here is to answer the question of which semiconductor among the two is going to absorb at a wavelength that corresponds to the maximum solar intensity. Okay, so what we're going to want to do here is we're going to want to calculate the energy and kill a jewels per mole. Okay. And the equation that we're going to use that relates or that shows the relationship between the energy of a photon and the wavelength is going to be energy is equal to Planck's constant times the speed of light over wavelength and the answer that we're going to get is going to be energy and this energy is going to be and jewels per photon. So this is going to give us the energy per photon. Okay, and we want to calculate this for nanometers? And whatever answer we get, We want to see which semiconductor is going to be. Is it going to have the closest value to. Okay, so let's go ahead and write in or fill in what we need to fill in. So energy is equal to HS. Plank's constant. This value is 6.6 26 times 10 to the negative 34 jewel seconds. And c is the speed of light. This value is three times 10 to the eight m per second. Okay. And lambda represents wavelength. Alright, so in the problem we're told the wavelength is 500 nanometers. But as you can see our unit for speed of light is in meters. So we need to convert this 500 nanometers two m. So let's go ahead and do that. Okay. And one nanometer, there is 10 to the negative nine m. So our units four nanometers cancel and we're left with units of meters. So when we do this we're going to get five times 10 to the negative seven m. So we can go ahead and plug that in. So we have five times to the negative seven m. So let's go ahead and do this calculation when we do this calculation, we're going to get the energy is equal to 3.9756 times 10 to the negative 19 jewels per photon. This is the amount of energy per photon. However, we want to know the energy and kill a jules per mole. That way we can compare it to our two semiconductors where the energy is given in. Kill jules per mole. So we're going to convert this jules per photon to kill a jules per mole. Alright, so the first thing we want to do is go from photons to moles and we're gonna do this using avocados number And one mole. There is 6.02, 2 times 10 to the 23 photons. Our units of photons cancel. And now we're left in units of joules per mole. But we want our answer and kill a jules per mole. So now we need to go from jewels to kill a jewels and one kill a jewel. There is 1000 jewels jules now cancel. And we're left with the energy and killing joules per mole. So let's go ahead and do this calculation when we do this calculation, the energy that we're going to get is 239.41 kg joules per mole. So let's go ahead and compare this value to the to semiconductors that were given the first semiconductor which is cadmium cell five C. D. S. Semiconductor. It has a band gap energy of 241 kg joules per mole. And our second semiconductor gallium arsenide has a band gap energy of 138 kg joules per mole. So the value that we just calculated this 239.41 kg joules per mole has a closer band gap energy to the energy of the wavelength that corresponds to the maximum solar intensity. So our answer here is going to be the c d. S semiconductor or the cadmium sulfide semiconductor. Okay, so that is the answer for this problem, and that is the answer we just highlighted that is it for this problem? I hope this was helpful.

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