Question

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass = 9.11x10^–31 kg, proton mass = 1.67x 10^–27 kg, 1 eV = 1.60x10^–19 J).

Answer 1

Electron is faster; Ratio of speeds is 13.54 : 1
Mass of the electron, m_e = 9.11 x 10^–31 kg
Mass of the proton, m_p = 1.67 x 10^{– 27} kg
Kinetic energy of the electron, E_Ke = 10 keV = 10⁴ eV

= 10⁴ x1.60 x 10^–19
= 1.60x 10^–15 J

Kinetic energy of the proton, E_Kp = 100 keV = 10⁵ eV = 1.60 x 10^–14 J

For the velocity of an electron v_e its kinetic energy is given by the relation:

For the velocity of a proton v_p its kinetic energy is given by the relation:

Hence, the electron is moving faster than the proton.
The ratio of their speeds: