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Determine the ratio of the electron's speed

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?
 
138
4
That's what I would do.
 
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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