Question

What is the speed of an electron whose kinetic energy is 1.80 MeV ?

Answer 1

We know that kinetic energy of the electron

K=(-1)m₀c² ....1

here K=1.80MeV, m₀c² =0.511MeV (rest energy of the electron ) =1/(1-v²/c²)

put these value in equation 1

K=(-1)0.511MeV=1.8MeV

-1=1.80/0.511=3.52

=4.52

1/(1-v²/c²)=4.52

1=4.52*1-v²/c²

squaring both side

1=20.4304(1-v²/c²)

20.4304v²/c²=19.4304

v²=19.4304c²/20.4304

v=0.9752c

v=0.9752*3*10⁸

v=2.9256 *10⁸ m/s answer.