Protons and electrons can be given very high energies in particle accelerators. What is the wavelength in meters of an electron (mass = 9.11 * 10-31 kg) that has been accelerated to 5% of the speed of light? In what region of the electromagnetic spectrum is this wavelength?

Video transcript

Hey everyone, we're asked to determine the de Broglie wavelength of a proton traveling at the speed of light and identify the region in the electromagnetic spectrum for this wavelength. First we need to recall that the mass of a proton is going to be 1.673 times 10 to the negative kg. And the formula that we will be using to answer this question is going to be wavelength equals our plank's constant, divided by our mass times velocity. So, plugging in these values, we know that our planes constant is 6.626 times 10 to the negative 34 kilograms times meters squared over seconds. We will then divide this by our mass of our proton, which we said was 1.673 times 10 to the negative kg. And we were told that our velocity is going to be our speed of light, which is 3.0 times 10 to the 8m/s. Now, when we calculate this out and cancel out all of our units, We end up with a wavelength of 1.3, 2 times 10 to the -15 m. Now, let's go ahead and determine where this lies in our electromagnetic spectrum. Bringing up this chart. We can see right here that at around 10 to the negative m for our wavelength. This will be in the gamma rays region. So our answer here is going to be a wavelength of 1.32 times 10 to the negative m. And this will be in the gamma ray region. Now, I hope that made sense and let us know if you have any questions.