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Chapter 21: Q72P (page 629)

An electron is projected with an initial speedvi=3.2×105 msdirectly toward a very distant proton that is at rest. Because the proton mass is large relative to the electron mass, assume that the proton remains at rest. By calculating the work done on the electron by the electrostatic force, determine the distance between the two particles when the electron instantaneously has speed2vi.

Short Answer

Expert verified

The distance between the particles is r=1.64×10−9 m.

Step by step solution

01

 Step 1: Given

The initial speed of the particle isvi=3.2×105 ms.

02

Determine the concept

According to the principle of conservation of energy, energy is neither creatednor destroyed.It may only transform from one type to another

03

Calculate the distance between the two particles when the electron instantaneously has speed2vi

Since the total energy is conserved the required relation is:

12mevi2=12mevf2−ke2rf

Here,rfis the distance between the electron and the proton.

Forvf=2vi, and forrfsolve as:

rf=2ke2me(vf2−vi2)rf=2ke23mevi2

rf=2(9×109 Nm2C2)(1.60×10−19 C)23(9.11×10−31 kg)(3.20×105 ms)2=1.64×10−9m

.

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