(a) An electron moves with a speed of 4.70x10^6 m/s. What is its de Broglie wavelength? (b) A proton moves with the same speed. Determine its de Broglie wavelength.

Video transcript

Hey everyone. So this problem is working with wave particle duality and it is just asking us to calculate the deli wavelength of two different particles. So it's pretty straightforward. The first thing that we need to do is recall the Degli formula is lambda equals H over P lambda is your wavelength H is planks constant. And then p your momentum, let's recall that that can be rewritten as mass times philosophy. So for the first part of the problem, we have an electron, we know the speed of that electron that's 7.9 times 10 to the 7 m per second. We know the mass of an electron. Let's recall that is just a kind of a constant 9.11 times 10 to the negative 31 kg. And then we need to recall that Plank's constant is 6.63 times 10 to the negative 34 dual seconds. So for this first part, it is a very straightforward part one, it's very straightforward plug. And so we are going to take thanks constant. OK. The mass of our electron times our seed plug that into our calculator and we get 9.21 times 10 to the negative 12 meters. So if we go back to our choices, we can see that we've pretty much eliminated every choice except for a, but let's just make sure that uh the second answer comes out correctly just as I did double check. So now they're asking for the de broadly wavelength of a positively charged hydrogen atom moving at the same speed. All right. So there's two kind of tricky things here. The first thing that we need to remember is that a positively charged hydrogen atom is just a proton. So they're not saying it, but you know that that's a proton. That means that the mass of a proton, which is a constant. We can recall that equals 1.67 times 10 to the negative 27 kilograms. And then the speed of the proton is the same as the speed of this emitted electron. So that's the same 7.9 times 10 to the 7 m per second. Thanks constant, obviously doesn't change. And so we are left with another plug-in chub from there. It's gonna look very similar to the first one. the only thing that is changing is the mass of the particle 1.67 times 10 to the minus 27 kg. And the speed again is the same 7.9 m per second. Put that into our calculators and we get 5.02 times tend to be minus 15 m. And then when we look at our answers that does match the answer for number two. So the correct answer is a, that's all for this problem. We'll see you in the next video.