# 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 = 9.11×10-31 kg, proton mass = 1.67×10–27 kg, 1 eV = 1.60 ×10–19 J).

For an electron:

Mass of the electron, me= 9.11×10-31kg

Let ve be the velocity of the electron.

Kinetic energy of the electron, Ke = meve2

10 = meve2

meve2=20 ……………….(1)

For a proton:

Mass of the proton, mp= 1.67×10-27kg

Let vp be the velocity of the proton.

Kinetic energy of the proton, Kp=mpvp2

100 = mpvp2

mpvp2=200 ……………………(2)

Dividing equation (1) by (2),

= 13.54

ve:vp = 13.54 : 1

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