An electron has a speed of 0.67 c. (The rest energy for an electron is 0.511 MeV

Question

An electron has a speed of 0.67 c. (The rest energy for an electron is 0.511 MeV, and the rest energy of a proton is 938.3 MeV.)

(a) Find the speed of a proton that has the same kinetic energy as the electron.
.0195 c

(b) Find the speed of a proton that has the same momentum as the electron.
______km/s

Explanation / Answer

Speed of electron = 0.67*(3 x 10^8) = 2.01 x 10^8 m/s Kinetic energy of electron = 1/2*m*v^2 = (1/2)*(9.11×10^-31)*(2.01 x 10^8)*(2.01 x 10^8) = 18.4 x 10^-15 J = Kinetic energy of proton =>Velocity of proton = v = sqrt{(18.4 x 10^-15)/[(1/2)*(1.67 x 10^-27)]} = 4.69 x 10^3 km/s Now proton and electron have same momentum =>(9.11×10^-31)*(2.01 x 10^8) = (1.67 x 10^-27)*V => V = 109.6 km/s

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