An ultrashort pulse has a duration of 9.00 fs and produces light at a wavelength of 556 nm. What are the momentum and momentum uncertainty of a single photon in the pulse?

Video transcript

Welcome back, everyone. We are making observations about a light of wavelength that originates from a laser. Now, we are told that a light or that the light has a wavelength of 640 nanometers or 40 times 10 to the negative ninth meters. Now, we are also told that the time it takes for the pulse is 8.12 fem seconds or 8.12 times 10 to the negative 15th seconds. And we are tasked with finding for a single photon in the pulse, the magnitude of our momentum as well as the uncertainty of our momentum here. Let me change my color real quick and let's start off with finding the magnitude of our momentum. This is going to be given by planks pink. Sorry Plank's constant divided by our wavelength. What we get is 6.626 times 10 to the negative 34th divided by 6 40 times 10 to the negative ninth when we plug this into a what we get is one point oh four times 10 to the negative 27th kilograms meters per second. Wonderful. Now let me go ahead and change color again. Here. And we are going to now calculate the uncertainty in our momentum. Well, according to the uncertainty principle, we can say that the spatial length times the uncertainty in our momentum is equal two planks constant divided by four pi. Now we know that spatial length is simply equal to the speed of light divided by the time it takes four hours very short pulse. So plugging this in into our equation and then solving for our uncertainty in our momentum. What we get is that our uncertainty is equal to planks constant divided by four pi times the speed of light times our very short pulse. So let's go ahead and plug in all of our values. What we get is 6.6 to 6 times 10 to the negative 34th divided by four pi times 2.998 times 10 to the eighth times 8.12 times 10 to the negative 15th. And what we get for our uncertainty is 2. times 10 to the negative 29th kilograms meters per second. So now we have found both the magnitude of our momentum and the uncertainty in our momentum which corresponds to our final answer. Choice of a. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.