Determine the ratio of the electron's speed

Thread starter lovelylm1980
Start date Jul 15, 2005
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Ratio Speed

AI Thread Summary

To determine the ratio of the electron's speed to the proton's speed at the end of their trajectories, the kinetic energy formula can be used for both particles. The kinetic energy of the electron is given as 5.29 keV, which allows for the calculation of its velocity. By applying the relationship between mass and velocity, the ratio can be derived as v/u = sqrt(M/m), where M is the proton mass and m is the electron mass. This results in a calculated speed ratio of approximately 42.85, valid under the condition that the speed is much less than the speed of light. The method effectively illustrates the significant difference in speeds due to the mass disparity between the electron and proton.

Jul 15, 2005

lovelylm1980

Determine the ratio of the electron's speed over that of the proton at the end of their respective trajectories? KE = 5.29keV

My question is do I use the kinetic energy to get velocity of electron then proton separately, and afterwards divide the results to obtain the ratio?

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Jul 15, 2005

Jelfish

That's what I would do.

Jul 15, 2005

faruk

electron: m, v
proton: M, u

mv²/2 = Mu²/2
mv² = Mu²
v²/u² = M/m
v/u = sqrt(M/m) = sqrt(1836) = 42.85

(valid for v << c)

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