A proton is located at the origin, and a second proton is located on the x -axis

Question

A proton is located at the origin, and a second proton is located on the x-axis at x1 = 5.22 fm (1 fm = 1015 m).

(a) Calculate the electric potential energy associated with this configuration.
_____J

(b) An alpha particle (charge = 2e, mass = 6.64 1027 kg) is now placed at (x2, y2) = (2.61, 2.61) fm. Calculate the electric potential energy associated with this configuration.
_____J

(c) Starting with the three particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.)
_____J

(d) Use conservation of energy to calculate the speed of the alpha particle at infinity.
_____m/s

(e) If the two protons are released from rest and the alpha particle remains fixed, calculate the speed of the protons at infinity.
_____m/s

Explanation / Answer

a) the electric potential energy = 8.98 * 109 * 1.6 * 10-19 * 1.6 * 10-19/(5.22 * 10-15)

                                                 = 4.4 * 10-14 J

b) electric potential energy = 4.4 * 10-14 + 2 * 8.98 * 109 * 1.6 * 10-19 * 1.6 * 10-19 * (1/3.69 * 10-15 + 1/3.69 * 10-15)

                                         =   2.93 * 10-13 J

c) change in electric potential energy = 2.93 * 10-13 -   4.4 * 10-14

                                                                                 = 2.49 * 10-13 J

d)   the speed of the alpha particle at infinity = sqrt(2 * 2.49 * 10-13 /6.64 1027)

                                                                      = 8.66 * 106 m/s

e) speed of the protons = sqrt(2 * 4.4 * 10-14 /1.67 1027)

                                        = 7.26 * 106 m/s

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