# Find relativistic momentum of electron given kinetic energy.

**1. The problem statement, all variables and given/known data**

At what energy does an electron become “relativistic”? Consider electrons with

kinetic energies of 50 eV, 50 keV, and 50 MeV. For each case, calculate the momentum

of the electron first using the non-relativistic formula for kinetic energy, and then using

the correct relativistic formulas. Express the momentum in units of eV/c, or keV/c, or

MeV/c (whichever is appropriate), as discussed in section 2.13 of Thornton and Rex.

(For this you need to know that the rest energy of an electron is 0.511 MeV.) Compare

your answers for each case. When is it important to use the relativistic formulas?

**2. Relevant equations**

Non-relativistic:

K_{e}=[itex]\frac{1}{2}[/itex]mv^{2}

p=mv

Relativistic:

p=[itex]\frac{mv}{\sqrt{1-(\frac{v}{c})^2}}[/itex]

**3. The attempt at a solution**

I was able to use the non-relativistic equations to find momentums by equating the equation for kinetic energy and momentum with the final result of:

p=[itex]\sqrt{2K_em}[/itex]

When it comes to the relativistic momentum, however, I can’t seem to remember how to find v! From what I remember it is straight forward but I can’t find what I need. Any suggestions are welcome, thank you!

http://ift.tt/PeXfJT

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