At what velocity does a proton have a 6.00-fm wavelength (about the size of a nucleus)? Assume the proton is nonrelativistic. (1 femtometer = $10^{-15}\text{ m}$. )

Video Transcript

This is College Physics Answers with Shaun Dychko. At what speed does a proton have a de Broglie wavelength of 6 femtometres? So the wavelength is Planck's constant divided by momentum and momentum is mass times velocity and we are told that this velocity is going to be non-relativistic which is why we can use this formula for momentum. And we'll substitute that in for p and we get λ is h over mv. And we can solve this for the speed then by multiplying both sides by v over λ. And this gives the speed is Planck's constant divided by mass times the wavelength. So that's Planck's constant—expressed in joule seconds— divided by the mass of a proton— 1.6726 times 10 to the minus 27 kilograms— times the wavelength, which is 6 femtometers, which means 6 times 10 to the minus 15 meters which gives a speed of 6.60 times 10 to the 7 meters per second.