Answer:
ve/vp = 42.8
Explanation:
According to the exercise, the proton accelerates from A to B. According to the principle of energy conservation:
Final energy of the proton at point B = KEp1B + EPEp1B
Total proton energy at point A = KEp1A + EPEp1A
KEp1B = EPEp1A - EPEp1B
The initial energy of the proton is equal to zero, since it is at rest. Therefore the electric potential of a charge will be equal to:
EPE = qv, where v is the charge potential
The proton's final kinetic energy will be equal to:
KEp1B = EPEp1A - EPEp1B = q (vA - vB) (eq. 1)
If an electron is negatively charged, we have that qe = -qp
The kinetic energy of the electron will be equal to:
KEp1A = EPEe1B - EPEe1A = -q (vB - vA) = q (vA - vB) (eq. 2)
Comparing equations 1 and 2:
KEp1B = KEe1A, (mp * vp ^ 2) ^ 2 = (me * ve ^ 2) / 2
We solve and solve for ve / vp:
ve / vp = (mp / me) ^ 1/2 = (1.67x10 ^ -27kg / 9.11x10 ^ -31kg) ^ 1/2 = 42.8
