Question

An electron is accelerated to a speed where its total energy is 157 times larger than its rest energy.

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

What is the kinetic energy of the electron?

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!)

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

Answer 1

given

E = 157 E_o

a )

E = E_o + KE

157 E_o = E_o + KE

KE = 156 E_o

b )

KE = 156 m c²

KE = 156 X 9.1 X 10^-31 X 9 X 10¹⁶

KE = 1.27 X 10^-11 J

c )

( - 1 ) m c = 1.27 X 10^-11

( ( 1 / ( 1 - v² / c² )^1/2 - 1 ) = 1.27 X 10^-11 / 9.1 X 10^-31 X 9 X 10¹⁶

( 1 / ( 1 - v² / c² )) = 157²

( 1 - v² / c² ) = 4.056 X 10^-5

1 - 4.056 X 10^-5 = v² / c²

v = 0.99995944 c

d )

p = m v

= ( 1 / ( 1 - 0.99995944² )^1/2 ) X 9.1 X 10^-31 X 0.99995944 c

p = 111.03 X 9.1 X 10^-31 X 0.99995944 c

p = 1.01 X 10^-28 c

p = 42 MeV / c