A watt is a measure of power, and we didn't talk about watts in our lessons, but I'll describe it here to you. You're familiar with watts when you're talking about lightbulbs, especially our incandescent lightbulbs. So say a 60-watt lightbulb or a 45-watt lightbulb, and then when you get the compact fluorescents, they'll compare them. They'll say this is equivalent to a 60-watt lightbulb. But what a, what a watt is, is we look here is the conversion, or it gives us a dimensional analysis tool basically, between joules and seconds, so one watt is one joule per second. Now this lightbulb that we're describing here, takes 0.01% of all the energy that it consumes and it converts that much to photons that have this wavelength. Now, it produces a lot of other photons as well, across the whole gamut of visible light. But if we were monitoring only the 490 nanometer region, we know that only 0.01% of it is producing photons in that region. And the question here is wanting to know if in one minute's time, how many photons of this wavelength would be produced? Let's begin by writing our conversions that we're given. We know that a watt, is one joule per second, so we really have 60 joules per second as one conversion tool. Now, this is the joule of the light bulb being consumed of the light bulb. Okay? So, this is the joules consumed by the light bulb in one second. We're also given this percent, and any time you have a percent you can take that number over 100, and think about the part and the whole that makes this up. So, what is a 0.01%? Well this is the joules of, and how do I want to say this? We'd, the joules from photons. And not just any photons, but the set 490 nanometer photons. And the 100 is the joules consumed by the light bulb. Okay? So, those are the two relationships. The joules from photons and the joules from the light bulb. So I have those as conversion tools. Let's start with the 60 joules per second. And let us take it from, and this is the joules of the light bulb. And let's configure, let's convert it to joules of photons at 490 nanometers. So we will put the joules from the light bulb down here. And we will put joules from the photons, at the 490 nanometers up here and put the values 0.010 and 100 in. This will give us 0.006 joules per second, second didn't go anywhere per second and this is joules, from the 490 nanometer photons. So that is what we know. When this lightbulb runs for a second, 0.006 joules of photons at 490 nanometers would be generated. Okay, so now we're going to go our next step. Let's figure out the energy, of one of these photons at 490 nanometers. Now we know that E equals h times nu. And when we use this equation, this is the energy of one photon. Now I don't know the frequency but I do know the wavelength, so I can convert this equation to E equals hc over wavelength, and I can plug that information in. So I have h of 6.63 times 10 to the minus 34. And that's joules times seconds, that's Planck's constant. We have 3 times 10 to the 8th meters per second, and that is the speed of light. And we have the wavelength of 490 nanometers, and we're going to be very careful to watch our units. We know the wavelength actually needs to be in meters. So ten to the minus nine meters is a nanometer. All my units will cancel nicely, the nanometers, the meters, the seconds, and I'll be left with joules, and the value for this joules is 4.06 times ten to the minus 19, and that's joules. Now, because this gives me the energy of one photon, I could say it's a joules per photon. And that gives me another dimensional analysis tool. So now I know the joules coming from all of the photons in a second from that light bulb. I know the joules of one little photon. Now I can figure out how much energy, or how many photons are produced in 1 minute? So let us start with our 1 minute. Now let's say it's exactly 1 minute, okay? So put some extra significant figures in there, I have 1 minute. I'm going to go from minutes to seconds. Why would I do that? Well, because if I look at my conversion tool up here, it is in units of seconds.'kay? So I'm going to go to seconds so that I can go up there now, choose that as a dimensional analysis tool and go from seconds to joules. And what is this joules? This is joules from all of the photons at 490 nanometers. Okay. So I want to put 0.006 here and 1 there. Now I know at this point, the total joules being generated by all the full photons at 490 nanometers, but what I really want to know, is the number of photons. So I'm want to go from joules at the photons, the joules from all the photons, to how many photons I have. I know that each individual photon will have this much energy associated with it. So if we let our units do the work for us, we see that the minutes are cancelled, the seconds are cancelled, the joules from the photons cancels, and we're left with just photons. And we will now know how many photons, and the answer is 8.87 times 10 to the 17 photons
