Question

An electron is accelerated to a speed where its total energy is 226 times larger than its rest energy.

PART 1

How many times is the kinetic energy of the electron larger than its rest energy?

PART 2

What is the kinetic energy of the electron?

PART 3

What is the speed of the electron in terms of the speed of light?
(In this part of the problem you have to enter your answer with a precision of seven or eight digits!)

PART 4

What is the momentum of the electron measured in MeV/c units? (Enter only a number without the MeV/c unit.)

Answer 1

1) total energy = E_t = Er+Ek = 226Er

                                        Ek = 225 Er

2) Kinetic energy, E_k = 225*Mo c^2 = 225*9.11x10^-31*3x10⁸*3x10⁸ = 1.844x10^-11 J

3) The total energy, Et = Mo c^2

                                 Et = 225Mo c^2

So, = 225, then

         sqrt(1- (v/c)^2) = 1/225

Thus, the speed of the electron is, v = 0.99999c

4) the momentum of the electron is,

                   Et^2 = (pc)^2 + (Er)^2

         (225)²Er^2 = (pc)^2 + (Er)^2

Then, we get

           pc = [[(225)² - 1](Er)^2 ]^1/2

            p = {[[(225)² - 1](M0c²)^2 ]^1/2}/c

               = {[[(225)² - 1](0.0081956x10^-11)^2 ]^1/2}/c

               = 1.844x10^-11 J/c [1 eV / 1.6x10^-19 J]

               = 115.2 MeV/c