Red light with a wavelength of 660 nm from a 3.0 mW diode laser shines on a solar cell. (b) How much current (in amperes) flows in the circuit of the solar cell if all the photons are absorbed by the cell and each photon produces one electron?

Video transcript

Hi everyone. This problem reads blue light with a wavelength of 460 nanometers from a 3.5 million watts dioxide laser illuminates on a solar cell. If every photon is absorbed by the cell and every photon creates an electron, how much current? And Millie emperors passes through the solar cell circuit. Okay, so the question that we want to answer here is how much current, Okay. And Millie Ambers passes through the solar cells circuit. So let's start off by calculating how much energy per photon is produced. And the equation that we use that shows the relationship between energy of a photon and wavelength is energy is equal to Planck's constant times the speed of light over lambda. So let's just go ahead and write the values for each of these. Okay, Plank's constant H is 6.626 times To the negative 34 jewel seconds. The speed of light c is 3.00 times 10 to the eight m/s. And Lambda represents wavelength. And then the problem, we're told that our wavelength is 460 nm. However, we see that our speed of light unit is in meters. So we need to convert our wavelength from nanometers two m. So let's just go ahead and do that. Now. In one nanometer, there is 10 to the negative nine m. Our units for nanometers cancel and our answer in meters is 4. times 10 to the negative seven meters. Alright, So now we have all the values that we need to solve for the energy. So let's go ahead and plug those values in. So we have energy is equal to Planck's constant 6.626 times 10 To the negative 34 jewel seconds times the speed of light over wavelength. And the wavelength we converted to meters is 4. times 10 to the negative seven m. So let's go ahead and do this calculation When we do this calculation, the energy that we're going to get is 4.32 1, 3 times 10 To the negative jewels per photon. So this is the energy per photon. Alright, so now we want to calculate the number of photons right now, we know the energy per photon, but we need to calculate the number of photons. And the way we're going to calculate the number of photons is we're going to take we're going to convert our, wait, we're gonna convert our 3.5 mil a watts to jules per second, or we're gonna convert this to watts. Okay, so we're gonna take our Mila watts and divide this by our energy. So let's first convert our Mila watts. Okay, so we know we have 3.5. Excuse me. Okay, yes, so we have 3.5 Mila watts and we want to go from Mila watts to Watts and let's just recall that one watt is equal to one jewel per second. So we're going to write this as jewels per second. Alright, so first we want to go from mila watts to Watts in one Mila wat, there is 10 to the negative three watts. Okay, so our units of Mila Watts cancel and we're left with watts and in one watt there is one jewel per second. So our watts canceled. And now we have jewels per second. So when we do this calculation, we're going to get 3.5 times 10 to the negative three jewels per second. So we want to take this value for our jewels per second and we're going to we're going to divided by our energy. Alright, so what we want to do is we want to take our jewels per second or watts and divided by our energy. So let's go ahead and do that. Alright, so we have 3.5 times 10 to the negative three jewels per second divided by the energy that we calculated, which is 4.3213 times 10 to the negative 19 jewels per photon. And you'll see here that our units for jules cancel and we're going to be left with Photons per second. So let's go ahead and do this calculation when we do this calculation we're going to get 8. Times 10 to the 15 jewels or excuse me photons per second. Alright, so now that we know how many photons per second we have, we can calculate the number of electrons are number of electrons is going to equal our number of photons. Okay, so this number that we just calculated is also going to be the same thing as electrons per second. Okay, so let's go ahead and write this. Our number of electrons is going to equal 8.9994 times 10 to the 15 electrons per second. So now what we want to do, let me rewrite this second. Okay, so now what we want to do is we want to go from electrons per second to milli amperes. Okay, so the first conversion that we're going to need to do is we're going to go from electrons per second. Two moles of electrons. Okay, and we're going to do that using avocados number. Alright, so four. So what we're going to do is so we know we have the following electrons per second. So in one mole of electrons avocados number tells us we have 6.22 times 10 to the electrons. Let me write that a little bit clearer. 10 to the 23 electrons. Okay, so our units for electrons cancel. All right, So now we want to go from electrons to Kalu comes. Okay, so in one more of electrons there is 96,500 colom's Our units for electrons cancel and now we have units of Colom's. So when we do this calculation we're going to get 1.2979 times to the negative three. Okay, so now our value is going to be columns per second. So let's just go ahead and rewrite this. So 1.2979 times 10 to the negative three columns per second. And this is equal to and pairs. Alright, so this is our value for AM pairs. So let's go ahead and right and pairs here. So now we want to go from Amperes two million pairs. Alright, so our conversion is in one million AM pair, There is 10 to the negative three and pears. So this cancels and the answer that we're going to get is 1.2979 milli amp pairs. And when we round this, our final answer is going to be 1.30 million and pears. So this is going to be our final answer. This is how much current and million pairs passes through the solar cells circuit. That is it for this problem. I hope this was helpful