An electron is moving with a speed of 8.00 * 10^6 m/s. What is the speed of a proton that has the same de Broglie wavelength as this electron?

Video transcript

Hey everyone. So this problem is dealing with wave particle duality. Let's see what it's asking us for. We are given the mass of a proton and the mass of a helium nucleus were told that they have the same day broccoli wavelength and were also given the speed of that proton. It simply asks us to calculate the speed of that second. Um the helium nucleus. So this is a pretty straightforward problem. If we can first recall de broccoli's formula, which is the wavelength is given by H Planck's constant over the momentum. P. And then we need to recall that p the momentum is simply the mass times the velocity. So the mass of the proton is 1.67 times 10 to the negative 27 kg mass of the helium nucleus is 6.64 times 10 to the kg. Um from the problem were also given the speed of the proton is 2.75 Times tend to be 5th meters per second. And then let's recall plank's constant is 6.63 times 10 to the negative 30 for jewel seconds. Alright, so we know that both of these um the proton and the helium nucleus have the same wavelength. So we're just going to uh make the de Broglie wavelengths equal each other and we'll write that out as a church over em the mass of the proton times the speed of the proton is equal to h over mass of the helium nucleus times the speed of that. So actually the planks constants cancel there. And when we solve for the speed of the helium nucleus, we are left with a mass of the proton, speed of the proton over mass of the nucleus plug and chug from there 1.67 times 10 to the negative 27 kg Mask that we were given the speed we were given in the problem 2.75 times 10 to the 5th meters per second over the mass of the helium nucleus, 6.64 times 10 to the negative plug that into our calculators. And we are left With 6. times 10 to the 4th meters per second. And when we look at our potential answers or choices, it looks like answer B is the correct choice. That's all for this problem. We'll see you in the next video.