Question

An electron and proton are detected in a cosmic ray experiment the fact with kinetic energy 10KeVand the second with 1000KeV.Which is faster,the electron or proton? obtain the ratio of their speeds

Answer 1

Electron is faster; Ratio of speeds is 13.54 : 1

Mass of the electron, me = 9.11 × 10–31 kg
Mass of the proton, mp = 1.67 × 10– 27 kg
Kinetic energy of the electron, EKe = 10 keV = 104 eV
= 104 × 1.60 × 10–19
= 1.60 × 10–15 J
Kinetic energy of the proton, EKp = 100 keV = 105 eV = 1.60 × 10–14 J
For the velocity of an electron ve, its kinetic energy is given by the relation:
EKe = (1/2) mve2
∴ ve = (2EKe / m)1/2
= (2 × 1.60 × 10-15 / 9.11 × 10-31)1/2  =  5.93 × 107 m/s
For the velocity of a proton vp, its kinetic energy is given by the relation:
EKp = (1/2)mvp2
vp = (2 × 1.6 × 10-14 / 1.67 × 10-27 )1/2  =  4.38 × 106 m/s
Hence, the electron is moving faster than the proton.
The ratio of their speeds
ve / vp = 5.93 × 107 / 4.38 × 106  =  13.54 : 1

this is the solution for your question.