Explanation 1) Concept: We can equate the centripetal force and Coulomb force between the muon and the H e + nucleus to find the equation for square of velocity. By using quantization condition, we can find the radius. By substituting these values in the equation for total energy, we can prove the given equation. 2) Formula: i) F = - m v 2 r ii) F = - k Z e 2 r 2 iii) L = n ℏ = m v r iv) K = 1 2 m v 2 v) U = - k Z e 2 r 3) Given: i) Charge of muon is - e ii) Mass of muon is m = 207 m e = 207 × 9.11 × 10 - 31 k g 4) Calculations: Suppose the muon of mass m is orbiting in circular uniform motion around the H e + nucleus with velocity v .It, thus, experiences a centripetal force given by F = - m v 2 r This force must be balanced by the Coulomb force between the muon and the H e + nucleus, which is given as F = - k Z e 2 r 2 Where, k = 1 / 4 π ε 0 Therefore, - m v 2 r = - k Z e 2 r 2 v 2 = k Z e 2 m r … … … … … … … … … … … … … … … … … … … … … … ( 1 ) Since the magnitude of the angular momentum is quantized as L = n ℏ where ℏ = h / 2 π And as L = m v r , we get, m v r = n ℏ Rearranging this equation for v , v = n ℏ m r Substituting this in equation ( 1 ) , n ℏ m r 2 = k Z e 2 m r On simplifying, r = n 2 ℏ 2 k Z e 2 m … … … … … … … … … … … … … … … … … … … … … … ( 2 ) Now, the kinetic energy of muon is K = 1 2 m v 2

Fundamentals Of Physics 11th Edition Loose-leaf Print Companion Volume 2 With Wileyplus Card Set

11th Edition

ISBN: 9781119463252

Author: David Halliday

Publisher: John Wiley and Sons

See similar textbooks

Concept explainers

Quantum mechanics and hydrogen atom

Consider an electron of mass m moves with the velocity v in a hydrogen atom. If an electron is at a distance r from the proton, then the potential energy function of the electron can be written as follows:

Isotopes of Hydrogen Atoms

To understand isotopes, it's easiest to learn the simplest system. Hydrogen, the most basic nucleus, has received a great deal of attention. Several of the results seen in more complex nuclei can be seen in hydrogen isotopes. An isotope is a nucleus of t…

Mass of Hydrogen Atom

Hydrogen is one of the most fundamental elements on Earth which is colorless, odorless, and a flammable chemical substance. The representation of hydrogen in the periodic table is H. It is mostly found as a diatomic molecule as water H2O on earth. It is …

Question

Chapter 39, Problem 68P

To determine

To show:

The energy levels of the system are given by

E=-11.3 keVn2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 39, Problem 67P

Chapter 39, Problem 69P

Students have asked these similar questions

4. In the figure below what is the value of the angle 0? A 30

PLEASE help with the experimental setup for this theory because i am so confused.

Part 2 - Geometry and Trigonometry 1. Line B touches the circle at a single point. Line A extends radially through the center of the circle. A B (a) Which line is tangential to the circumference of the circle? (b) What is the angle between lines A and B. 2. In the figure below what is the angle C? 30 45 3. In the figure below what is the value of the angle 0? 30° 4. In the figure below what is the value of the angle 0? A 30°

Chapter 39 Solutions

Fundamentals Of Physics 11th Edition Loose-leaf Print Companion Volume 2 With Wileyplus Card Set

Ch. 39 - Prob. 1Q Ch. 39 - Prob. 2Q Ch. 39 - Prob. 3Q Ch. 39 - Prob. 4Q Ch. 39 - Prob. 5Q Ch. 39 - Prob. 6Q Ch. 39 - Prob. 7Q Ch. 39 - Prob. 8Q Ch. 39 - Prob. 9Q Ch. 39 - Prob. 10Q

Ch. 39 - Prob. 11Q Ch. 39 - Prob. 12Q Ch. 39 - Prob. 13Q Ch. 39 - Prob. 14Q Ch. 39 - Prob. 15Q Ch. 39 - Prob. 1P Ch. 39 - Prob. 2P Ch. 39 - Prob. 3P Ch. 39 - Prob. 4P Ch. 39 - Prob. 5P Ch. 39 - Prob. 6P Ch. 39 - Prob. 7P Ch. 39 - Prob. 8P Ch. 39 - Prob. 9P Ch. 39 - Prob. 10P Ch. 39 - Prob. 11P Ch. 39 - Prob. 12P Ch. 39 - Prob. 13P Ch. 39 - Prob. 14P Ch. 39 - Prob. 15P Ch. 39 - Prob. 16P Ch. 39 - Prob. 17P Ch. 39 - Prob. 18P Ch. 39 - Prob. 19P Ch. 39 - Prob. 20P Ch. 39 - Prob. 21P Ch. 39 - Prob. 22P Ch. 39 - Prob. 23P Ch. 39 - Prob. 24P Ch. 39 - Prob. 25P Ch. 39 - Prob. 26P Ch. 39 - Prob. 27P Ch. 39 - Prob. 28P Ch. 39 - Prob. 29P Ch. 39 - Prob. 30P Ch. 39 - Prob. 31P Ch. 39 - Prob. 32P Ch. 39 - Prob. 33P Ch. 39 - Prob. 34P Ch. 39 - Prob. 35P Ch. 39 - Prob. 36P Ch. 39 - Prob. 37P Ch. 39 - Prob. 38P Ch. 39 - Prob. 39P Ch. 39 - Prob. 40P Ch. 39 - Prob. 41P Ch. 39 - Prob. 42P Ch. 39 - Prob. 43P Ch. 39 - Prob. 44P Ch. 39 - Prob. 45P Ch. 39 - Prob. 46P Ch. 39 - Prob. 47P Ch. 39 - Prob. 48P Ch. 39 - Prob. 49P Ch. 39 - Prob. 50P Ch. 39 - Prob. 51P Ch. 39 - Prob. 52P Ch. 39 - Prob. 53P Ch. 39 - Prob. 54P Ch. 39 - Prob. 55P Ch. 39 - Prob. 56P Ch. 39 - Prob. 57P Ch. 39 - Prob. 58P Ch. 39 - Prob. 59P Ch. 39 - Prob. 60P Ch. 39 - Prob. 61P Ch. 39 - Prob. 62P Ch. 39 - Prob. 63P Ch. 39 - Prob. 64P Ch. 39 - A diatomic gas molcculc consistsof two atoms of...Ch. 39 - Prob. 66P Ch. 39 - Prob. 67P Ch. 39 - Prob. 68P Ch. 39 - Prob. 69P Ch. 39 - Prob. 70P Ch. 39 - An old model of a hydrogen atom has the charge e...Ch. 39 - Prob. 72P Ch. 39 - Prob. 73P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Intro Spectroscopy
Physics
ISBN:9781305221796
Author:PAVIA
Publisher:Cengage
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax