×
Log in to StudySoup

Forgot password? Reset password here

For ultrarelativistic particles such as photons or

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 13P Chapter A

An Introduction to Thermal Physics | 1st Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

4 5 0 363 Reviews
12
1
Problem 13P

For ultrarelativistic particles such as photons or high-energy electrons, the relation between energy and momentum is not E = p2/2m but rather E = pc. (This formula is valid for massless particles, and also for massive particles in the limit E ≫ mc2.)

(a) Find a formula for the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L .

(b) Estimate the minimum energy of an electron con lined inside a box of width 10−15m. It was once thought that atomic nuclei might cont ain electrons; explain why this would be very unlikely.

(c) A nucleon (proton or neutron) can be thought of as a bound state of three quarks that are approximately massless, held together by a very strong force that effectively confines them inside a box of width 10−15 m. Estimate the minimum energy of three such particles (assuming all three of them Lobe in the lowest-energy state), and divide by c2 to obtain an estimate of the nucleon mass.

Step-by-Step Solution:

Step 1 of 4</p>

(a) Find a formula for the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L .

The given formula for energy of an ultrarelativistic particle is,

                                        

Where E is energy which is quantized, P is momentum and c is speed of light.

The value of momentum is also quantized due to the property of wavelength quantization.

That is,                                 

Using the relation,  where h is planck’s constant and  is wavelength.

                                        

Step 2 of 4</p>

The wavelength in terms of width L is given by

Therefore, above equation becomes

                                                ………...1

Hence, the above formula gives the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L

Step 3 of 4

Chapter A, Problem 13P is Solved
Step 4 of 4

Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

Since the solution to 13P from A chapter was answered, more than 240 students have viewed the full step-by-step answer. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. The answer to “For ultrarelativistic particles such as photons or high-energy electrons, the relation between energy and momentum is not E = p2/2m but rather E = pc. (This formula is valid for massless particles, and also for massive particles in the limit E ? mc2.)(a) Find a formula for the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L .________________(b) Estimate the minimum energy of an electron con lined inside a box of width 10?15m. It was once thought that atomic nuclei might cont ain electrons; explain why this would be very unlikely.________________(c) A nucleon (proton or neutron) can be thought of as a bound state of three quarks that are approximately massless, held together by a very strong force that effectively confines them inside a box of width 10?15 m. Estimate the minimum energy of three such particles (assuming all three of them Lobe in the lowest-energy state), and divide by c2 to obtain an estimate of the nucleon mass.” is broken down into a number of easy to follow steps, and 164 words. The full step-by-step solution to problem: 13P from chapter: A was answered by , our top Physics solution expert on 07/05/17, 04:29AM. This full solution covers the following key subjects: Energy, ultrarelativistic, particles, box, estimate. This expansive textbook survival guide covers 10 chapters, and 454 solutions. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1.

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

For ultrarelativistic particles such as photons or

×
Log in to StudySoup
Get Full Access to Physics - Textbook Survival Guide

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Physics - Textbook Survival Guide
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here