Change the chapter
Question
The velocity of a proton emerging from a Van de Graaff accelerator is 25.0% of the speed of light. (a) What is the proton’s wavelength? (b) What is its kinetic energy, assuming it is nonrelativistic? (c) What was the equivalent voltage through which it was accelerated?
1. $5.29 \textrm{ fm}$
2. $4.70 \times 10^{-12} \textrm{ J}$
3. $29.3 \textrm{ MV}$
Solution Video

# OpenStax College Physics Solution, Chapter 29, Problem 59 (Problems & Exercises) (1:27)

Rating

No votes have been submitted yet.

Quiz Mode

Why is this button here? Quiz Mode is a chance to try solving the problem first on your own before viewing the solution. One of the following will probably happen:

1. You get the answer. Congratulations! It feels good! There might still be more to learn, and you might enjoy comparing your problem solving approach to the best practices demonstrated in the solution video.
2. You don't get the answer. This is OK! In fact it's awesome, despite the difficult feelings you might have about it. When you don't get the answer, your mind is ready for learning. Think about how much you really want the solution! Your mind will gobble it up when it sees it. Attempting the problem is like trying to assemble the pieces of a puzzle. If you don't get the answer, the gaps in the puzzle are questions that are ready and searching to be filled. This is an active process, where your mind is turned on - learning will happen!
If you wish to show the answer immediately without having to click "Reveal Answer", you may . Quiz Mode is disabled by default, but you can check the Enable Quiz Mode checkbox when editing your profile to re-enable it any time you want. College Physics Answers cares a lot about academic integrity. Quiz Mode is encouragement to use the solutions in a way that is most beneficial for your learning.

## Calculator Screenshots

Video Transcript
This is College Physics Answers with Shaun Dychko. A proton emerges from a Van de Graaff accelerator with a velocity of 25 percent the speed of light and the first question is, what is its wavelength? So that is going to be Planck's constant divided by its momentum and since we are told that its velocity is non-relativistic, we'll say that the momentum is mass times velocity which we can then replace p with. So lambda then is Planck's constant over mass times velocity. So we have Planck's constant divided by the mass of a proton times 0.250 times the speed of light, which gives 5.29 femtometers, is its de Broglie wavelength. Its kinetic energy is one-half mass times velocity squared so that's one-half times mass of a proton times 0.250 times the speed of light, all squared, giving 4.7 times 10 to the minus 12 joules of kinetic energy. Then in part (c), we are asked to figure out what voltage must it have been accelerated through? Well, all of this kinetic energy was given to the proton by this potential difference and that amount of energy will be the potential difference times the charge. And so we'll divide both sides by the charge q. And so we get the voltage is the kinetic energy divided by q. So this is the kinetic energy we found in part (b), divided by the elementary charge in a proton which is 29.3 megavolts.