Among the elementary subatomic particles of physics is the muon, which decays within a few microseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at 8.85 * 105 cm/s.

Video transcript

Hey everyone, we're asked to calculate the D broccoli wavelength associated with an electron neutrino. To answer this question, we need to recall the formula wavelength equals our plank's constant divided by our mass times velocity To calculate the mass of our electron neutrino. We're going to take the mass of our electron which is 9.1094 times 10 to the negative 31st grams. And we're going to divide this by 2.32 times 10 to the fifth. Since we were told that it was 2.32 times 10 to the fifth times smaller than our electron. This will get us to a value of 3.93 times 10 to the negative 36 g. But since our planks constant uses kilograms, we can go ahead and convert this into kilograms and we know that per one kg we have 10 to the third grams. So our mass comes up to 3.93 times 10 to the negative 39 kg. Now, let's go ahead and plug in our values. So we have our planks constant which is 6.626 times 10 to the negative 34 kilograms times meters squared over seconds. And we're going to divide this by our mass of 3.93 times 10 to the -39 kg. And we're also going to divide it by our velocity of 2.98 times 10 to the 8th m/s. And when we calculate this out and cancel out all our units, We end up with a value of 5.66 times 10 to the -4 m. And this is going to be our final answer. So I hope that made sense and let us know if you have any questions.