A proton has a mass of 1.67×1027 kg1.67\times 10^{-27}\textrm{ kg} . A physicist measures the proton’s total energy to be 50.0 MeV. (a) What is the proton’s kinetic energy? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
Question by OpenStax is licensed under CC BY 4.0
Final Answer
  1. 887 MeV-887\textrm{ MeV}
  2. A negative kinetic energy is nonsense.
  3. Total energy must be greater than or equal to mc2mc^2

Solution video

OpenStax College Physics, Chapter 28, Problem 70 (Problems & Exercises)

OpenStax College Physics, Chapter 28, Problem 70 (PE) video thumbnail

In order to watch this solution you need to have a subscription.

Start free trial Log in
vote with a rating of votes with an average rating of .

Calculator Screenshots

  • OpenStax College Physics, Chapter 28, Problem 70 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. A proton's total energy is supposedly 50.0 megaelectron volts and the question is how much kinetic energy does it have? Well kinetic energy is γ minus 1 times mc squared and total energy is γ times mc squared. So we can rearrange this for γ by dividing both sides by mc squared and so we get that the Lorentz factor, γ, is the total energy divided by the rest mass energy and we can substitute this in place of γ here and so we see the kinetic energy is the difference between the total energy and the rest mass energy. So that's 50.0 megaelectron volts minus 1.67 times 10 to the minus 27— rest mass of the proton— times speed of light squared and then we convert this, which will be in units of joules, into megaelectron volts because we are going to subtract it from this number which has units of megaelectron volts. So we times by 1 elecron volt for every 1.602 times 10 to the minus 19 joules and then times by 1 megaelectron volt for every 10 to the 6 electron volts and this joule here cancels with the joules that'd result here. This works out to negative 887 megaelectron volts. A negative kinetic energy is nonsense and so we can't assume that the total energy is going to be 50.0 megaelectron volts; the total energy always has to be greater than or equal to the rest mass energy.