Chapter 21: Q72P (page 629)

An electron is projected with an initial speed $v_{i} = 3 .2 \times 10^{5} \frac{m}{s}$ directly 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 speed $2 v_{i}$ .

Short Answer

Expert verified

The distance between the particles is $r = 1.64 \times 10^{- 9} m$ .

Step by step solution

Step 1: Given

The initial speed of the particle is $v_{i} = 3.2 \times 10^{5} \frac{m}{s}$ .

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

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

Since the total energy is conserved the required relation is:

$\frac{1}{2} m_{e} v_{i}^{2} = \frac{1}{2} m_{e} v_{f}^{2} - \frac{k e^{2}}{r_{f}}$

Here, $r_{f}$ is the distance between the electron and the proton.

For $v_{f} = 2 v_{i}$ , and for $r_{f}$ solve as:

$\begin{matrix} r_{f} = \frac{2 k e^{2}}{m_{e} (v_{f}^{2} - v_{i}^{2})} \\ r_{f} = \frac{2 k e^{2}}{3 m_{e} v_{i}^{2}} \end{matrix}$

$\begin{matrix} r_{f} = \frac{2 (9 \times 10^{9} \frac{{Nm}^{2}}{C^{2}}) {(1.60 \times 10^{- 19} C)}^{2}}{3 (9.11 \times 10^{- 31} kg) {(3.20 \times 10^{5} \frac{m}{s})}^{2}} \\ = 1.64 \times 10^{- 9} m \end{matrix}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Step 1: Given

Determine the concept

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Famous Physicists

Dynamics

Quantum Physics

Circular Motion and Gravitation

Measurements

Study anywhere. Anytime. Across all devices.