Question

an electron and a Proton are detected in 1 cosmic ray experiment first with kinetic energy 10keV, and the second with 100keV.which is faster the electron or the proton obtain the ratio of their speeds

Answer 1

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Answer 2

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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
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