An electron has a de Broglie wavelength of 2.80x10^-10 m. Determine (a) the magnitude of its momentum and (b) its kinetic energy (in joules and in electron volts).

Video transcript

Hey everyone. So this problem is working with wave particle duality. So let's see what they're asking us. We know we're working with protons if the proton To broadly wavelength they give us is .49 nm. They're asking us for the protons, momentum and the kinetic energy. And then they do note for the kinetic energy. We have to give our answer in both jewels and electrical. So we're gonna be doing some unit work here. So the first thing to recall is the broccoli formula. So the wavelength is given as H over P where H is Planck's constant and P is our momentum. So we are solving for that momentum. So the part one is a straight plug in shot. We are given the wavelength in the problem. It's 0.49 nanometers. And another way to write nanometers is just 10 to the negative nine m. And then we can recall that Plank's constant is 6.63 times 10 to the negative 30 four jewel seconds. We're going to rearrange that equation to solve for momentum. So that would be a church over lambda. And then it's just plug and chug from there. Thanks constant. Divided by our wavelength that in to our calculator and get 1. times 10 to the -24 m. So that's the answer for part one. We can then look at our possible choices and from Just part one, we know that a and B are not going to be the correct answer. The second part of the problem is asking us to calculate kinetic energy. Now broccoli's formula doesn't give us kinetic energy but we are working with momentum and we can recall the relationship between kinetic energy and momentum is given as kinetic energy equals P squared over two M. We're also told in the problem that we were working with protons. The mass of a proton is a constant that we can recall equals 1.67 times 10 to the -27 kg. So from there we can rearrange from there, we can just plug in. We've solved for our momentum. So we'll just plug that into our kinetic energy equation. Okay, equals p squared over two M. So we are going to take the momentum. We just solved 4, 1.35 times 10 to the negative 24 m squared over two times 1.67 times 10 to the negative 27 kg, Plug that into our calculators and get 5.46 times 10 to the negative 22nd jewels. They do ask for this kinetic energy in both jewels and electron volts. So the last thing that we need to do is recalled that one electron volt equals 1.6 oh two times to the negative 19 jewels. Will use that conversion factor to solve For our kinetic energy in terms of electron volts. And that comes out to 3.4 times 10 to the negative three electron bowls. Okay, so that those answers are the same in two different units for part two. So we're just gonna go back up to our potential answers, and it looks like answer C is the correct one. It has the correct kinetic energy in jewels, correct kinetic energy in electron volts, and we already determined it had the correct momentum. So that's it. Your answer for this problem is see that's all for this problem. We'll see you in the next video.