Energy Conservation of an electron

[Chaggi]

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.

 

[LowlyPion]

Welcome to PF.

Maybe consider:
http://en.wikipedia.org/wiki/Mass_in_special_relativity#The_relativistic_energy-momentum_equation

 

[nlightner]

I would like to point out that the correct answer is E, 2.6 MeV. This can be calculated using the formula for relativistic kinetic energy, KE = (gamma - 1)mc^2, where gamma is the Lorentz factor given by gamma = 1/sqrt(1-v^2/c^2). Plugging in the values of v=0.98c and m=9.11*10^-31 kg, we get a gamma value of 5.05. Substituting this into the formula for KE, we get KE = (5.05 - 1)*(9.11*10^-31 kg)*(3.0*10^8 m/s)^2 = 2.6 MeV. This is the total energy of the electron, taking into account both its kinetic energy and rest energy.

It is important to note that the formula KE = 1/2 mv^2 is only valid for non-relativistic speeds, meaning speeds much smaller than the speed of light. For speeds close to the speed of light, we need to use the relativistic formula to accurately calculate the energy. This highlights the importance of understanding and using the appropriate equations in scientific calculations.