Work, Power and Energy

Question : 12

Total: 30

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, 1‌eV=1.60×10–19 J.)

Solution:

Mass of electron me=9.11×10−31kg
Velocity of electron =ve
Mass of proton mp=1.6×10−27kg
Velocity of proton =vp
Kinetic energy of electron,

meve2=10‌KeV ...(i)
Kinetic energy of proton,

mpvp2=100‌KeV ...(ii)
Divide (i) by (ii),

meve2

mpvp2

10×1.6×10−16J

100×1.6×10−16J

⇒

meve2

mpvp2

=√

1.67×10−27

10×9.11×10−31

=13.54
Therefore, electron moves faster than proton.

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