An alpha particle (a helium nucleus, having charge +2e and mass 6.64 × 10-27 kg) moves head-on at a fixed gold nucleus (having charge +79e). If the distance of closest approach is 2.0 × 10-10 m, what was the speed of the alpha particle when it was very far away from the gold? (k = 1/4πε0 = 9.0 × 109 N • m2/C2, e = 1.60 × 10-19 C)

An alpha particle (a helium nucleus, having charge +2e and mass 6.64 × 10-27 kg) moves head-on at a fixed gold nucleus (having charge +79e). If the distance of closest approach is 2.0 × 10-10 m, what was the speed of the alpha particle when it was very far away from the gold? (k = 1/4πε0 = 9.0 × 109 N • m2/C2, e = 1.60 × 10-19 C)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter26: Electric Potential

Section: Chapter Questions

Problem 13PQ: A proton is fired from very far away directly at a fixed particle with charge q = 1.28 1018 C. If...

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A proton is fired from very far away directly at a fixed particle with charge q = 1.28 1018 C. If the initial speed of the proton is 2.4 105 m/s, what is its distance of closest approach to the fixed particle? The mass of a proton is 1.67 1027 kg.
A proton is located at the origin, and a second proton is located on the x-axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 1027 kg) is now placed at (x, y) = (3.00, 3.00) fm. Calculate the electric potential energy associated with this configuration. (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.) (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. (e) If the two protons are released from rest and the alpha panicle remains fixed, calculate the speed of the protons at infinity.
A proton is released from rest at the origin in a uniform electric field in the positive x direction with magnitude 850 N/C. What is the change in the electric potential energy of the protonfield system when the proton travels to x = 2.50 m? (a) 3.40 1016 J (b) 3.40 1016 J (c) 2.50 1016 J (d) 2.50 1016 J (e) 1.60 1019 J
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How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?
Four particles are positioned on the rim of a circle. The charges on the particles are +0.500 C, +1.50 C, 1.00 C, and 0.500 C. If the electric potential at the center of the circle due to the +0.500 C charge alone is 4.50 104 V, what is the total electric potential at the center due to the four charges? (a) 18.0 104 V (b) 4.50 104 V (c) 0 (d) 4.50 104 V (e) 9.00 104 V
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A proton and an alpha particle (charge = 2e, mass = 6.64 1027 kg) are initially at rest, separated by 4.00 1015 m. (a) If they are both released simultaneously, explain why you cant find their velocities at infinity using only conservation of energy. (b) What other conservation law can be applied in this case? (c) Find the speeds of the proton and alpha particle, respectively, at infinity.