Solution Found!

Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 42 / Problem 22E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

Change Question

Solved: Calculate for free electrons with average kinetic

Chapter 42, Problem 22E

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Calculate \(v_{\mathrm{rms}}\) for free electrons with average kinetic energy \(\frac{3}{2} k T\) at a temperature of 300 K. How does your result compare to the speed of an electron with a kinetic energy equal to the Fermi energy of copper, calculated in Example 42.7? Why is there such a difference between these speeds?

Text Transcription:

v_rms

3/2 kT

Questions & Answers

QUESTION:

Calculate \(v_{\mathrm{rms}}\) for free electrons with average kinetic energy \(\frac{3}{2} k T\) at a temperature of 300 K. How does your result compare to the speed of an electron with a kinetic energy equal to the Fermi energy of copper, calculated in Example 42.7? Why is there such a difference between these speeds?

Text Transcription:

v_rms

3/2 kT

ANSWER:

Introduction

We have to first calculate the speed of the electrons in given temperature. Then we have to compare the speed with the speed of the electron at the fermi energy level.

Step 1

The average kinetic energy of the electrons at temperature is given by

Here we have

and

Hence the average kinetic energy of the electron is

Now the kinetic energy is also given by

Hence the rms speed of the free electron at the 300 K is $1.17\times{}1{0}^{5}$ m/s.

Study Tools You Might Need

Chapter: 5 Problem: 81P

Introductory Chemistry 5
Write a formula for each acid. (a) phosphoric acid (b) hydrobromic acid (c) sulfurous acid

Chapter: 13 Problem: 85P

Introductory Chemistry 5
To what volume should you dilute 25 mL of a 12 M stock HCl solution to obtain a 0.500 M HCl solution?

Chapter: 13 Problem: 88P

Principles of General Chemistry 2
Problem 88P The bond angles in the nitrite ion, nitrogen dioxide, and the nitronium ion (NO2+) are 115, 134, and 180, respectively. Explain these values using Lewis structures and VSEPR theory.

Chapter: 8 Problem: 2

Campbell Biology 9
Most cells cannot harness heat to perform work because a. heat is not a form of energy. b. cells do not have much heat; they are relatively cool. c. temperature is usually uniform throughout a cell. d. heat can never be used to do work. e. heat must remain constant during work

Chapter: 6 Problem: 17

Psychology 1
Compare and contrast classical and operant conditioning. How are they alike? How do they differ?

Chapter: 13 Problem: 1

Introduction to Psychology: Gateways to Mind and Behavior 13
Exercise, meditation, and progressive relaxation are considered effective ways of countering negative self-statements. T or F?

Chapter: 1 Problem: 5

Advanced Engineering Mathematics 10
Solve the ODE by integration or by remembering a differentiation formula. \(y^{\prime}=4 e^{-x} \cos x\)

Chapter: 21 Problem: 1

Principles of Economics 9
Homer buys pizza for $10 and Pepsi for $2. He has income of $100. His budget constraint will shift inward if a. the price of pizza rises to $12. b. the price of Pepsi falls to $1. c. his income rises to $150. d. the price of pizza, the price of Pepsi, and his income all rise by 50 percent.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account