Q24P If I=0, then j=s聽,mj=ms, and th... [FREE SOLUTION]

91影视

Introduction to Quantum Mechanics

David J. Griffiths

Physics

2nd Edition 路 469 pages

ISBN: 9780131118928

Chapter 6: Q24P (page 280)

If I=0, then j=s, $m_{j} = m_{s}$ , and the "good" states are the same $(n m_{s})$ for weak and strong fields. Determine $E_{z}^{1}$ (from Equation) and the fine structure energies (Equation 6.67), and write down the general result for the I=O Zeeman Effect - regardless of the strength of the field. Show that the strong field formula (Equation 6.82) reproduces this result, provided that we interpret the indeterminate term in square brackets as.

Short Answer

Expert verified

The $E_{Z}^{1} = \frac{e}{2 m} B_{ext} 2 m_{s} 魔$ and the fine structure energies is

$E = - \frac{13.6 e V}{n^{2}} [1 + \frac{伪^{2}}{n^{2}} (n - \frac{3}{4})] + 2 m_{s} B_{e x t} \frac{e 魔}{2 m}$

Step by step solution

Definition of Zeeman Effect.

In the presence of a static magnetic field, the Zeeman Effect causes a spectral line to break into numerous components.

Step2: Structural isomers of carboxylic acids.

Use the equation 6.72,

$E_{z}^{1} = \frac{e}{2 m} B_{e x t} . (L + 2 S) = \frac{e}{2 m} B_{ext} 2 m_{s} 魔$

Fine structure energy (with j=1/2),

$E_{nj} = - \frac{13.6 e V}{n^{2}} [1 + \frac{伪^{2}}{n^{2}} (n - \frac{3}{4})] E_{tot} = - \frac{13.6 eV}{n^{2}} [1 + \frac{伪^{2}}{n^{2}} (n - \frac{3}{4})] + 2 m_{S} B_{ext} \frac{别魔}{2 m}$

Fine structure term is proportional to $伪^{2}$ ;

$E_{f s}^{1} = - \frac{13.6 e V}{n^{4}} 伪^{2} (n - \frac{3}{4}) = \frac{13.6 eV}{n^{3}} 伪^{2} (\frac{3}{4 n} - 1)$

{Same as equation } with the term in square brackets set equal to 1.

$E_{f s}^{1} = \frac{13.6 e V}{n^{3}} 伪^{2} \{\frac{3}{4 n} - [\frac{I (I + 1) - m_{I} m_{s}}{I (I + 1 / 2) (I + 1)}]\}$

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.

91影视

Short Answer

Step by step solution

Definition of Zeeman Effect.

Step2: Structural isomers of carboxylic acids.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Electrostatics

Atoms and Radioactivity

Force

Mechanics and Materials

Scientific Method Physics

Study anywhere. Anytime. Across all devices.