Q82P Derive Eq. 38-11, the equation f... [FREE SOLUTION]

91影视

Chapter 38: Q82P (page 1185)

Derive Eq. 38-11, the equation for the Compton shift, from Eqs. 38-8, 38-9, and 38-10 by eliminating v and $胃$ .

Short Answer

Expert verified

The equation 38-11 is derived as follows:

$位^{'} - 位 = 螖位 = \frac{h}{m c} (1 - \cos 蠒)$

Step by step solution

Introduction

Consider the equation 38-8

$\frac{h}{m} (\frac{1}{位} - \frac{1}{位'}) + 1 = \frac{v}{\sqrt{1 - {(\frac{v}{c})}^{2}}}$

Consider the equation 38-9

$\frac{h}{m 位} - \frac{h}{m 位'} \cos 蠒 = \frac{v}{\sqrt{1 - {(\frac{v}{})}^{2}}} \cos 胃$

Consider the equation 38-10

$\frac{h}{m 位'} \sin 蠒 = \frac{v}{\sqrt{1 - {(\frac{v}{c})}^{2}}} \sin 胃$

Determine the derivation

On squaring and adding the Equation 38-9 and Equation 38-10. From the equation $\sin^{2} 胃 + \cos^{2} 胃 = 1$ solve as:

${(\frac{h}{m})}^{2} [{(\frac{1}{位} - \frac{1}{位'} \cos 蠒)}^{2} + {(\frac{1}{位'} \sin 蠒)}^{2}] = \frac{v^{2}}{1 - {(\frac{v}{c})}^{2}} {(\frac{h}{m})}^{2} [{(\frac{1}{位} - \frac{1}{位'} \cos 蠒)}^{2} + {(\frac{1}{位'} \sin 蠒)}^{2}] = - c^{2} (1 - \frac{1}{1 - {(\frac{v}{c})}^{2}}) {(\frac{h}{m c})}^{2} [{(\frac{1}{位} - \frac{1}{位'} \cos 蠒)}^{2} + {(\frac{1}{位'} \sin 蠒)}^{2}] + 1 = (\frac{1}{1 - {(\frac{v}{c})}^{2}})$

Now squaring the Equation 38-8, and on comparing the above equation.

${(\frac{h}{m c} (\frac{1}{位} - \frac{1}{位'}) + 1)}^{2} = (\frac{v^{2}}{1 - {(\frac{v}{c})}^{2}}) {(\frac{h}{m c} (\frac{1}{位} - \frac{1}{位'}) + 1)}^{2} = {(\frac{h}{m c})}^{2} [{(\frac{1}{位} - \frac{1}{位'} \cos 蠒)}^{2} + {(\frac{1}{位'} \sin 蠒)}^{2}] + 1$

On solving the above equation we will get this equation that is known as Equation 38-11

$位' - 位 = 鈭� 位 = \frac{h}{m c} (1 - \cos 蠒)$

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Wavelength (nm)	433.9	404.7	365.0	312.5	253.5
Stopping potential (V)	0.55	0.73	1.09	1.67	2.57

91影视

Derive Eq. 38-11, the equation for the Compton shift, from Eqs. 38-8, 38-9, and 38-10 by eliminating v and $胃$ .

Short Answer

Step by step solution

Introduction

Determine the derivation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Force

Modern Physics

Measurements

Further Mechanics and Thermal Physics

Electricity

Study anywhere. Anytime. Across all devices.

91影视

Derive Eq. 38-11, the equation for the Compton shift, from Eqs. 38-8, 38-9, and 38-10 by eliminating v and 胃.

Short Answer

Step by step solution

Introduction

Determine the derivation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Force

Modern Physics

Measurements

Further Mechanics and Thermal Physics

Electricity

Study anywhere. Anytime. Across all devices.

Derive Eq. 38-11, the equation for the Compton shift, from Eqs. 38-8, 38-9, and 38-10 by eliminating v and $胃$ .