Energy Conservation of an electron

AI Thread Summary
To determine the total energy of an electron traveling at 0.98c, the initial calculations used classical kinetic energy formulas, yielding an incorrect result of 0.25 MeV. The correct approach requires applying relativistic equations, specifically the relativistic energy-momentum equation, which accounts for the significant speed of the electron. The rest energy of the electron, calculated using E=mc^2, must also be included in the total energy calculation. The final correct answer is 2.6 MeV, indicating the necessity of using relativistic physics for high-speed particles. Understanding these principles is crucial for accurate energy calculations in particle physics.
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Homework Statement


Determine the total energy of an electron traveling at 0.98 c

A) 0.25 MeV
B) 0.51 MeV
C) 0.76 MeV
D) 1.8 MeV
E) 2.6 MeV

Homework Equations



KE = 1/2 mv^2
E=mc^2 (rest energy)

The Attempt at a Solution



I had found the velocity for an electron by 0.98 * 3.0 *10^8. I squared that number and multiplied by the mass of the electron (9.11 * 10^-31 kg) then multiplied by 0.5

This gave me 3.937 * 10^-14. I divided this by 1.6 * 10^-13 to get MeV which gave me an answer of 0.246 MeV. That would be answer A, but the correct answer was E.

I also took into account for a possible Rest energy, which you would use E=mc^2. Adding up what I got for rest energy and my original answer which gave me A, resulted in the answer for C. I'm still not sure how the answer E came about.
 
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