Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm)

Video transcript

Hey everyone in this example, we need to calculate the number of photons present in a laser pulse carrying 4.15 million joules of energy and a wavelength of 4 87 nanometers. We should first recognize that we're going to need to convert our energy from units of millet jewels, two jewels and our wavelength from units of nanometers two m. So beginning with our wavelength we should recall, the symbol is represented by lambda. Were given 487 nanometers. And again we want to go from nanometers in the denominator two m in our numerator, our final unit, we should recall that our prefix nano tells us we have 10 to the negative ninth power meters. Now we're able to go ahead and cancel out nanometers, leaving us with meters as our final unit for wavelength. And this is going to give us a value of 4.87 times 10 to the negative seventh power meters. So now that we have converted our meters to the proper unit, we're going to also convert that energy value that we had. And so according to the problem, our value for energy for the laser pulse is 4.15 million joules. So we're going to convert from in our denominator millet jewels to our final unit jewels in the numerator. And so we should recall that our prefix milli tells us we have for one million jewel 10 to the negative third power jewels. So now we're able to cancel out millet jewels leaving us with jewels as our final unit. And this is going to give us an amount of 4.15 times 10 to the negative third power jewels as our unit of energy. Now we should recall that our formula for energy of a photon is equal to Planck's constant times the speed of light divided by our wavelength. So we're going to calculate that because right now we only have the energy of the laser pulse as a whole, meaning all of the photons in our laser pulse. But we want the energy value of a single photon. So we're going to take plank's constant H, which we should recall is 6.626 times 10 to the negative 34th power jewels. Time seconds. We're going to multiply that by our speed of light, which we should recall is three point oh oh Times 10 to the 8th power in units of m/s. And now we can go ahead and divide by our wavelength, which thankfully we convert it to meters as 4.87 times 10 to the negative seventh power meters. And it was important for us to convert it to meters because we can go ahead and now cancel out our units of meters as well as our inverse seconds here with the seconds over here, leaving us with jewels as our final unit of energy, which is what we want. And so this is going to give us an energy value Per photon where we get 4.08 Times or sorry, 4.08 17, 2 times 10 to the negative 19th power jewels per photon. So this is the energy of one photon. And now we can go ahead and find our number of photons By taking the energy for all of our photons, which is given as 4.15 times 10 to the negative third power jewels, which we converted above. And then we're going to multiply by our conversion factor where we're going to say according to our calculation above, we have 4.08172 times 10 to the negative 19th power jewels per photon. And so this allows us to go ahead and cancel our units of jewels leaving us with photons as our final unit. And so this gives us our number of photons equal to 1.02 times 10 to the 16th power photons. So this is how many photons we have in our laser pulse. And this is going to be our final answer to complete this example. So I hope that everything we reviewed was clear. But if you have any questions, please leave them down below. And I will see everyone in the next practice video