   Chapter 16, Problem 19P

Chapter
Section
Textbook Problem

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 × 10−27 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)

To determine
The electric potential energy.

Explanation

Given info: Proton is located at x = 6.00 fm.

Explanation:

Formula to calculate the electric potential energy is,

PE1=kee2x

• ke is the coulomb constant.
• e is the elementary charge.

Substitute 6.00 fm for x, 1.6×1019C for e and 8.99×109 Nm2/C2 for ke

PE1=(8.99×109 Nm2/C2)(1

(b)

To determine
The new electric potential energy.

(c)

To determine
The change in electric potential energy.

(d)

To determine
The speed of alpha particle.

(e)

To determine
The speed of protons at infinity.

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