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Question
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 = $10^{-15} \textrm{ m}$. )
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Final Answer
$6.60 \times 10^{7} \textrm{ m/s}$
Solution Video

OpenStax College Physics Solution, Chapter 29, Problem 51 (Problems & Exercises) (0:53)

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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 <i>p</i> and we get <i>λ</i> is <i>h</i> over <i>mv</i>. And we can solve this for the speed then by multiplying both sides by <i>v</i> over <i>λ</i>. 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.