Calculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.85 electron volt (eV). (The electron and proton masses are me = 9.11 ✕ 10-31 kg and mp = 1.67 ✕ 10-27 kg. Boltzmann's constant is kB = 1.38 ✕ 10-23 J/K.)

Question

Zain Mathews

Physics

1 June, 23:21

Calculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.85 electron volt (eV). (The electron and proton masses are me = 9.11 ✕ 10-31 kg and mp = 1.67 ✕ 10-27 kg. Boltzmann's constant is kB = 1.38 ✕ 10-23 J/K.)

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Answers (1)

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Grayson Schneider · Answer 1

ve = 8.06 x 10^5 m/s

vp = 1.882 x 10^4 m/s

Explanation:

K = 1.85 eV = 1.85 x 1.6 x 10^-19 J = 2.96 x 10^-19 J

me = 9.11 ✕ 10^-31 kg,

mp = 1.67 ✕ 10^-27 kg

Let the speed of electron is ve and the proton is vp.

For electron:

K = 1/2 me x ve^2

2.96 x 10^-19 = 0.5 x 9.11 x 10^-31 x ve^2

ve^2 = 6.498 x 10^11

ve = 8.06 x 10^5 m/s

For proton:

K = 1/2 mp x vp^2

2.96 x 10^-19 = 0.5 x 1.67 x 10^-27 x vp^2

vp^2 = 3.5449 x 10^8

vp = 1.882 x 10^4 m/s