Fine Structure of Sodium D Lines

Spectrum of Neutral Sodium and the D-Line Doublet

1. Electronic Structure of Sodium

• The neutral sodium atom (Na) has 11 electrons.
• 10 electrons are tightly bound in closed inner shells (core electrons).
• These contribute no net angular momentum to the atom.
• The 11^th (valence) electron determines the optical properties and spectrum.

2. Principal Series and the D-Line

The D-line doublet (5890 Å and 5896 Å) belongs to the principal series, arising from transitions between:

• Upper state: P-orbital (L = 1)
• Lower state: S-orbital (L = 0)

Fine Structure Terms:

P-state (L = 1): Spin-orbit coupling splits it into two fine-structure levels:

• ²P_3/2 (J = 3/2)
• ²P_1/2 (J = 1/2)

S-state (L = 0): Only one term:

• ²S_1/2 (J = 1/2)

3. Allowed Transitions

The D-line doublet consists of two allowed transitions:

• D₁ line (5896 Å): ²P_1/2 → ²S_1/2
• D₂ line (5890 Å): ²P_3/2 → ²S_1/2

Selection Rules:

• ΔL = ±1
• ΔJ = 0, ±1 (but J = 0 → J = 0 is forbidden)

4. Origin of the Doublet

The energy splitting between ²P_3/2 and ²P_1/2 is due to spin-orbit coupling. This fine-structure splitting explains the two closely spaced D-line wavelengths.

Compton Effect - Detailed Derivation

Download Question Bank for Atomic and Nuclear Physics

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Compton Effect - Detailed Derivation -Click The Link To Download As PDF

Click Here To Download  Detailed Derivation of Compton Shift in Wavelength of  Gamma Ray Photon in Inelastic Scattering with An Electron  

This derivation is simpler than the one usually provided in the text book. I purposely elaborated the derivation clearly showing every minor algebraic step. Of course, you cannot write all the steps in your examination else you might lose time but understanding with clarity is the greatest aid to boost your memory with lot of side gains. Lagging a bit of detail I see Which I suppose add in future versions. Best of Luck with Hard Work to Assist That Luck !

Compton Shift Vs Scattering Angle Polar Plot

Wilhelm Conrad Röntgen - First Nobel Laureate In Physics

Wilhelm Conrad Röntgen

First medical X-ray by Wilhelm Röntgen of his wife Anna Bertha Ludwig's hand

Lande's g Factor - BB Snapshot

Lande's Factor Derivation

Spectral Line Splitting in Normal Zeeman Effect - BB Snapshot

Spectral Line Splitting in Normal Zeeman Effect 

Quantum Theory of Zeeman Effect - BB Snapshot

Quantum Theory of Zeeman Effect 

Larmor's Theorem BB Snapshot

Larmor's Theorem

Fine Structure of Sodium D Line - BB Snapshot

Fine Structure of Sodium D -Line

CAUTION: Please Read D1 as D2 and Vice Versa in BB Diagram. It is a bit of mistake on my part and I apologize. 

Stern-Gerlach Experiment Lecture - BB Snapshot

Stern-Gerlach Experiment  - BB Snapshot

Finding Electron's Mass - Classic Experiment Video

Finding Electron's Mass - Illustrate Many Things I Discussed During The Lectures

Atomic and Electronic Magnetic Moments Lecture - BB Snapshot

Atomic and Electronic Magnetic Moments Lecture  - BB Snapshot

Vector Atom Model - Quantum Numbers - Space Quantization - BB Snapshot

Vector Atom Model - Quantum Numbers

Vector Atom Model - BB Snapshot

Drawbacks of Bohr Atom Model

Time line of Atomic Models

A Brief History and Evolution of Atom Models

Einstein's Photoelectric Equation and Millikan's Experiment - BB Snapshot

Einstein's Photoelectric Equation and Millikan's Experiment

The Annotated and Hyper-linked Syllabus - Atomic and Nuclear Physics - Unit I

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COURSE CODE: 4BPH4C1

CORE COURSE VIII – ATOMIC AND NUCLEAR PHYSICS

Unit I                     POSITIVE RAYS

Properties of positive rays – e/m of positive rays – Aston’s, Bainbridge’s mass spectrograph-  critical potential – experimental determination of critical potential –Davis and Goucher‘s experiment.

Photo electricity: Photoelectric emission – laws – Lenard’s experiment – Richardson and Compton experiment – Einstein’s photo electric equation – experimental verification of Einstein’s photo electric equation by Millikan’s experiment – Photoelectric cells.

POSITIVE RAYS

• A Historical Exposition of Positive Rays from Cambridge University with beautiful and very explanatory animations.
• A Wikipedia article on Anode Rays
• Click to download  "Rays of positive electricity, and their application to chemical analyses"  by J.J.Thomson, Master and Originator of the Subject. This file is in DJVU format, which has many advantages over PDF. Main advantage is it is light weight and does not consume RAM space. To view this file type, please download WinDjView program(only 2.8 MB file size) for Windows platform here. Android users just search for a suitable App in the Google Play Store of which there are plenty.
• Click to download J.J.Thomson's Paper on positive rays 

Anode ray tube showing the rays passing through the perforated cathode and causing the pink glow above it

              By Kkmurray - Own work, CC BY-SA 3.0, 

              https://commons.wikimedia.org/w/index.php?curid=14960885

What are Positive Rays?

When a high voltage (~10000 volt) is applied between anode and perforated cathode of a gas discharge tube maintained at high vacuum (~0.001 mm of Hg), faint luminous rays are seen to extent from the back of the cathode. These rays are experimentally shown to possess positive charge. These rays are called positive rays.

Properties of Positive Rays

1. Positive rays consist of positively charged particles.

2. The nature of these rays depends on the gas used in the discharge tube.

3. These rays travel in straight lines. They cast a shadow of the object in their path.

4. These rays get deflected by an electrical field, and bend towards the negative plate. Thus the deflection of the positive rays is in a direction opposite to that shown by the cathode rays.

5. These rays are also deflected by the magnetic fields in the direction opposite to that of the cathode rays.

6. These rays can produce mechanical as well as chemical effects.

7. The ratio of charge (e) to mass (m), i.e.,(e/m) for the particles in the positive rays is not the same for all gases.

8. The ratio e / m for the positive rays is very low as compared to the e / m value for cathode rays.

9.  Positive rays affect photographic plate.

10. They can produce ionization in gases.

11. They cause fluorescence.

Specific Charge (or) Charge to Mass Ratio (e/m) of Positive Rays

Charge to Mass ratio of a charged particle serves much like a signature of that particular species of that particle. Charge and Mass along with Spin constitute key characteristics of molecular, atomic and sub-atomic particle species. If we neglect relativistic effects, which we can always do with greater confidence in discharge tube experiments, charge to mass ratio alias specific charge becomes the single most important characteristic of charged particle species  determining their behavior under the action of electromagnetic field. 

For Cathode e/m ratio is a constant immaterial of the gas used inside the discharge tube. This is because cathode rays consist of electrons emitted from negative electrodes, which has a fixed charge to mass ratio. On the other hand positive rays consist of gas ions and hence their charge to mass ratio depends on the gases used to fill the discharge tube. Positive rays have thousands of  times less specific charge than the cathode rays.

What is a Spectrum ?

spectrum (n.) 1610s, "apparition, specter," from Latin spectrum (plural spectra) "an appearance, image, apparition, specter," from specere "to look at, view" . Meaning "visible band showing the successive colors, formed from a beam of light passed through a prism" first recorded 1670s. Figurative sense of "entire range (of something)" is from 1936.

Credit:http://www.etymonline.com

So, A spectrum is an entire range of color,charges,masses,speeds or something. 

Mass Spectrum is sorting ions with respect to their masses or more particularly their Mass to Charge ratio or Charge to Mass ratio(works just as fine).

Aston's Mass Spectrograph

Francis William Aston (1 September 1877 – 20 November 1945)

• Aston won the 1922 Nobel Prize in Chemistry for his prominent work in Physics(!!?). Click Here to Download and Read Aston's Nobel Lecture.
• For Historical Details Please Visit Here.
• Click Here to read a Nice Paper on Development of Mass Spectrometers.
• Download a History Poster Here.

Aston Working With His Mass Spectrometer - Can You See the Large Electromagnet? 

Bainbridges's Mass Spectrograph

Laws of Photoelectric Emission

1.    For a given photo sensitive material, there is a minimum frequency called the threshold frequency, below which emission of photoelectrons stops completely, however great the intensity may be.

2.   For a given photosensitive material, the photo electric current is directly proportional to the intensity of the incident radiation, provided the frequency is greater than the threshold frequency.

3.  The photoelectric emission is an instantaneous process. i.e. there is no time lag between the incidence of radiation and the emission of photo electrons.

4.  The maximum kinetic energy of the photo electrons is directly proportional to the frequency of incident radiation, but is independent of its intensity.

Richardson-Compton Experiment Figures

Experimental Findings of Richardson Compton Experiment on Photoelectric Effect