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The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is $10\times 10^{14}\textrm{ GeV/c}^2$ . (a) How many proton masses is this? (b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity $\gamma$ would have to be.)
Question by OpenStax is licensed under CC BY 4.0.
  1. $1\times 10^{14}$
  2. $2\times 10^{17}$
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OpenStax College Physics for AP® Courses Solution, Chapter 33, Problem 15 (Problems & Exercises) (0:45)

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Video Transcript
This is College Physics Answers with Shaun Dychko. A particle that is proposed to unify the electro weak and the strong forces has a mass of 10 to the 14 gigaelectron volts per c squared and question (a) asks how many proton masses is this? So we take the mass that we are given and then divide by proton mass which is 938.27 times 10 to the 6 electron volts per c squared and it is 1 times 10 to the 14 proton masses. And the number of electron masses is the mass of this particle divided by electron mass which is 0.511 megaelectron volts per c squared and that works out to 2 times 10 to the 17 electron masses.