The watt is the derived SI unit of power, the measure of energy per unit time: 1 W = 1 J>s. A semiconductor laser in a DVD player has an output wavelength of 650 nm and a power level of 5.0 mW. How many photons strike the DVD surface during the playing of a DVD 90 minutes in length?

Video transcript

Everyone in this example, we have a laser cutting through an acrylic board in 29 seconds and we need to calculate the number of photons used in cutting if the laser has a wavelength of 1, nm and a power of 120 watts. So what we should recall is our formula, which relates the energy of a photon two planks constant, which we recall is simple. H multiplied by our speed of light and then divided by our wavelength given in the problem. We should call that our units for wavelength. We want to be in meters and that is due to the fact that our speed of light has units of meters per second. And we want to cancel those meter units out. So we're going to get into our formula. And what we're going to have is that our energy of our photon is equal to in our numerator, we would recall that plank's constant is 6.626 times 10 to the negative 34th power in units of joules times seconds. So this is then multiplied by the speed of light, which we would recall is 3.0 Times 10 to the 8th power m/s. In our denominator. We're going to plug in our wavelength given in the problem as 1064 nanometers, which we're going to convert into meters by recalling that for one nanometer, we have 10 to the negative ninth power meters. So now we're able to cancel our units of nanometers as well as meters, we can also cancel out seconds with inverse seconds. And we're left with jewels as our final unit for energy. And what we're going to get is that the energy of our photons is equal to a value of 1.86, 8 Times 10 to the negative 19th power jewels per photon. So now we're going to utilize this value to find the number of photons from our laser. And according to the prompt, we have 120 watts of power. And so we should recall that one watt is equal to one jewel per second. We're told in the prompt that the laser Cuts in seconds. So because we understand that one watt is equal to one joule per second, we can say that 1 120 watts is equal to 120 jewels per second. And we're going to multiply this by 29 seconds. Where we would be able to cancel our units of seconds leaving us with jewels. And this is going to give us a power equal to a value of the product of times 29, which would give us 3480 jewels. And so now we want to find our number of photons By taking our power value in the numerator, which we converted to jewels. So we have 3480 jewels of power. And dividing that by the energy of our photons, which above we calculated to have a value here Of in our denominator, we're plugging that in as 1.868 times 10 to the negative 19th power jewels per photon. And so now we're able to cancel out our units of jewels, leaving us with photons as our final unit. And this gives us our number of photons equal to a value Of 1.86 times 10 to the 22nd Power Photons. And this would be our final answer as the amount of photons in our laser that cuts our acrylic board in 29 seconds. So what's boxed in is our final answer? If you have any questions, please leave them down below and I will see everyone in the next practice video.