An electron starting from rest acquires 3.34keV of kinetic energyin moving from

Question

An electron starting from rest acquires 3.34keV of kinetic energyin moving from point A to point B. How much kinetic energy would aproton acquire, starting from rest at B and moving to point A?
the2nd part of it Determine the ratio of their speeds (speed of electron/speedof proton) at the end of their respective trajectories.

An electron starting from rest acquires 3.34keV of kinetic energyin moving from point A to point B. How much kinetic energy would aproton acquire, starting from rest at B and moving to point A?
the2nd part of it Determine the ratio of their speeds (speed of electron/speedof proton) at the end of their respective trajectories.

Explanation / Answer

Kietic energy of the electron K = 3.34keV = 3340eV So, potential difference between points A and B is V = 3340 eV/ charge of electron                                                                                = 3340 eV / e                                                                                = 3340 V Speed of the proton in this potential differnce v =[ 2Vq / m ] kinetic energy of proton K ' = ( 1/ 2) M v ^ 2                                            =( 1/ 2) M ( 2Vq / m]                                          = (M / m ) Vq                                          = ( 1837 m / m ) V q where M = mass of proton = 1837 m           m =mass of electron           q =charge of proton = 1.6 * 10 ^ -19 C plug the values weget K ' = 1837 * 3340 *1.6* 10 ^ -19                                      = 9.81 * 10 ^ -13 J Speed of electron / speed of proton = [2Ve ./m ]/ [ 2Vq / M ]                                                       = [M / m ]   Since q= e                                                       = 1837                                                      = 42.86

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