The document discusses j-j coupling, a method for describing angular momentum coupling in heavy atoms, and explains its significance in calculating total angular momentum through detailed examples. It also covers x-ray spectra, highlighting the work of early scientists and differentiating between atomic and molecular x-ray spectra, along with their key features and applications in analyzing material composition and molecular structure. Key techniques like x-ray fluorescence spectroscopy and x-ray absorption spectroscopy are mentioned as important tools for studying atomic and molecular physics.

4. J-J Coupling :-
jj coupling is a
method used to describe the coupling of
angular momenta in atoms,
particularly useful for heavy elements
with high atomic numbers. In these
elements, the spin-orbit interaction
becomes very strong, influencing how
the total angular momentum of an
atom is calculated.

5. l*=orbital angular momentum due to orbital motion of
electron around a nucleus
s*=spin angular momentum due to rotation of electron
about its own axis.
Consideration :-
Let we have an item which have two electrons in its
valance shell (mean a heavy atom)
+

6. So,
1st
electron= l1*, s2*
2nd
electron = l2*, s2*
So angular momenta for first electron
j1* =l1* + s1* -------(1)
Resultant angular momenta for 2nd electron
j2*=l2* + s2*------------(2)
Total angular momenta
J* = j1*+ j2*=(l1*+s1*)+(l2*+s2*)
Also. J*= J(J+1)
√
Where J=J1+J2, J1+J2-1,… … ,|J1-J2|

7. Example of jj coupling:-
Consider the case of one of electron in a
P-orbit (l1=1) and one electron in a d-orbit.
Solution :
for p-electron
l1=1 , s1=1/2
j1=(l1±s1)
j1=(1±1/2) =(1-1/2 ,1+1/2)
j1= (1/2 , 3/2)
For d-electron :
l2=2 , s2=1/2
j2=l2±s2

8. j2= (2± ½) =(2-1/2 , 2+1/2)
j2= 3/2 , 5/2
Now lets calculate J :-
J

9. Solved
😁

11. X-rays Spectra:-
The idea of X-ray spectra began to take shape
through the pioneering work of scientists such
as Wilhelm Röntgen, Charles Glover Barkla, and
Henry Moseley in the late 19th
and early 20th
centuries.

13. Introduction:-
**X-ray spectra** refer to the characteristic
emission or absorption lines produced when X-rays
interact with matter, often at an atomic or
molecular level. X-ray spectra are a powerful tool
for studying the structure of atoms and molecules
due to their ability to penetrate matter and interact
with electrons in high-energy states.

14. Spectrosco
py by x-
rays

15. 1. Atomic X-ray Spectra
Atomic X-ray spectra are
primarily concerned with the
energies released when electrons
transition between inner atomic
orbitals, particularly in the K, L,
and M shells, where the X-ray
energy levels are significantly
high.

17. ### Key Characteristics
- **X-ray Emission Lines**: When high-energy
electrons impact an atom, they may eject an
electron from an inner shell (usually the K or L
shell), leaving the atom in an excited, unstable
state. An electron from a higher-energy level
falls into this vacancy, emitting energy in the
form of X-rays. This results in characteristic X-
ray lines, such as Kα, Kβ, etc., each
corresponding to specific electron transitions.

18. - **Auger Effect**: Following inner-shell ionization,
instead of emitting an X-ray photon, the atom can
release energy via the Auger process, ejecting
another electron and leading to a detailed spectrum
of Auger electrons rather than X-rays.
- - **Energy Levels and Quantum Mechanics**: The
energy levels of these transitions depend on the
atomic number, making each element’s X-ray
spectrum unique. The energy differences between
levels are large in heavier elements, yielding high-
energy X-rays.

19. #### Components of Atomic X-ray Spectra
- **K-series**: When an electron fills a vacancy in the
K-shell (n=1), X-rays emitted are designated as K-
series, with transitions labeled Kα, Kβ, etc.,
corresponding to the movement of electrons from the
L, M, etc., shells into the K-shell.
- **L-series**: For transitions filling vacancies in the L-
shell (n=2), we observe L-series X-rays (Lα, Lβ, etc.).
These characteristic lines allow for the identification of
elements (X-ray fluorescence analysis) and provide
insight into atomic structure and electron
configurations.

20. Molecular X-ray Spectra
Molecular X-ray spectra arise from the interaction of X-rays with
molecules rather than individual atoms. While atomic X-ray
spectra focus on transitions between core-level electronic states in
atoms, molecular X-ray spectra are influenced by additional
factors due to the molecular environment.
#### Key Features
- **Core Electron Transitions**: Similar to atomic X-ray spectra,
molecular X-ray spectra involve core electron transitions. However,
the presence of chemical bonds and molecular orbitals influences
the energies of these transitions.
- **Chemical Shifts**: X-ray absorption edges in molecules can
shift due to the molecular environment. Chemical shifts are the
result of changes in the electron density surrounding atoms
within a molecule, affected by the bonding and the types of atoms
in proximity.

21. This shift provides detailed information about chemical bonding and
electronic structure.
- **X-ray Absorption Near Edge Structure (XANES)**: This part of
the spectrum is sensitive to the oxidation state, coordination
geometry, and local chemical environment of atoms in a molecule.
The structure near the absorption edge provides valuable data about
the electronic states and symmetry of the molecule.
- **Extended X-ray Absorption Fine Structure (EXAFS)**: EXAFS
appears beyond the X-ray absorption edge and gives information
about the distances, coordination numbers, and types of
neighboring atoms around a particular atom in a molecule. It’s
useful in understanding molecular geometry and bond lengths.

22. ### Techniques Involving X-ray Spectra
1. **X-ray Fluorescence Spectroscopy (XRF)**: Used to
analyze the elemental composition of a sample by observing
the characteristic X-rays emitted after excitation.
2. **X-ray Photoelectron Spectroscopy (XPS)**: Analyzes
the kinetic energy of electrons emitted by X-rays to study the
surface chemistry and composition of materials.
3. **X-ray Absorption Spectroscopy (XAS)**: Involves
examining both the XANES and EXAFS regions for molecular
structure analysis.

23. ### Applications in Atomic and Molecular
Physics
- **Material Analysis**: Identifying the elemental
composition and chemical states in complex
materials, including biological samples, metals, and
minerals.
- **Structural Determination**: Understanding
molecular structures, bonding, and electronic
configurations.
- **Chemical Bonding Studies**: Analyzing the
effects of molecular bonds on core-level electron
transitions.

24. Summary:-
In summary, atomic X-ray spectra offer insights into
electron transitions within atoms, while molecular X-
ray spectra reveal information about bonding,
molecular structure, and the chemical environment
surrounding atoms. Both are essential tools in
atomic and molecular physics for probing matter at
the atomic and molecular scales.