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)
Mass of the electron, me=9.11×10−31kg Mass of the proton, mp=1.67×10−27kg Kinetic energy of the electron is Ee=10keV=104eV Ee=104×1.6×10−19=1.60×10−15J Kinetic energy of the proton Ep=100keV=105eV=1.60×10−14J For the velocity of an electron ve, its kinetic energy is given by the relation: Ee=21mve2⇒ve=9.11×10−312×1.6×10−15=5.93×107m/s For the velocity of a proton vp, its kinetic energy is given by the relation: Ep=21mvp2 vp=4.38×106m/s As the velocity of electron is more than that of proton, so electron is faster than proton. The ratio of their speeds is vpve=4.38×1065.93×107=113.54
