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Classical Theory of the Raman Effect:- 

The basic concept of this spectroscopy depends on the polarizability of a molecule and the applied Electric field.When a molecule is put into a static electric field it suffers some distortion, the positively charged nuclei being attracted towards the negative pole of the field, the electrons to the positive pole.


Molecular Polarizability:

The size of the induced dipole μ, depends both on the magnitude of the applied field,
E, and on the ease with which the molecule can be distorted

μ = αE

Least Polarisibility:-

Electrons forming the bond are less easily displaced by the field across the bond axis

Greatest Polarisibility:-

Electrons forming the bond are more easily displaced by the field along the bond axis 

Polarizability Ellipsoid:-

The polarizability of a molecule in various directions is conventionally represented by  drawing a polarizability ellipsoid.




The polarizability of a molecule in various directions is conventionally represented by
drawing a polarizability ellipsoid.


In general a polarizability ellipsoid is defined as a three-dimensional surface whose distance from the electrical centre of the molecule in H2 this is also the (centre of gravity) is proportional to alfa. where α i the polarizability along the line joining a point i on the ellipsoid with the electrical centre. 

Points to remember:-

• The student must not make the mistake of confusing a polarizability ellipsoid
with electron orbitals or electron clouds.
• In a sense the polarizability ellipsoid is the inverse of an electron cloud-where
the electron cloud is largest the electrons are further from the nucleus and so are
most easily polarized.
• This, as we have seen, is represented by a small axis for the polarizability
ellipsoid.


Molecular Polarizability


When a molecules is subjected to a beam of radiation of frequency ‘ν’ the electric
field experienced by each molecule varies according to the equation
𝐸 = 𝐸0 𝑠𝑖𝑛 2𝜋νt
and thus the induced dipole also undergoes oscillations of frequency ν :
𝜇 = 𝛼𝐸
or, 𝝁 = 𝜶𝑬𝟎 𝒔𝒊𝒏 𝟐𝝅𝝂𝐭
This is the classical explanation of Rayleigh scattering. Here the oscillating dipole emits
radiation of its own oscillation frequency ν.

If, in addition, the molecule undergoes some internal motion, such as vibration or
rotation, which changes the polarizability periodically, then the oscillating dipole will
have superimposed upon it the vibrational or rotational oscillation.
𝛼 = 𝛼0 + 𝛽 𝑠𝑖𝑛2𝜋𝜈𝑣𝑖𝑏𝑡
𝜇 = 𝛼𝐸
𝜇 = (𝛼0 + 𝛽 𝑠𝑖𝑛2𝜋𝜈𝑣𝑖𝑏𝑡)𝐸0 𝑠𝑖𝑛 2𝜋𝜈𝑡
We know the trigonometric expression,
sin A sin B = 1 /2 {cos 𝐴 − 𝐵 − cos(𝐴 + 𝐵) 
𝜇 = (𝛼0 + 𝛽 𝑠𝑖𝑛2𝜋𝜈𝑣𝑖𝑏𝑡)𝐸0 𝑠𝑖𝑛 2𝜋𝜈𝑡
𝜇 = 𝛼0𝐸0 𝑠𝑖𝑛 2𝜋𝜈𝑡 +𝛽 𝑠𝑖𝑛2𝜋𝜈𝑣𝑖𝑏𝑡 · 𝐸0 𝑠𝑖𝑛 2𝜋𝜈𝑡
𝜇 = 𝛼0𝐸0 𝑠𝑖𝑛 2𝜋𝜈𝑡 + 1 2 𝛽𝐸0{cos 2𝜋(𝜈 − 𝜈𝑣𝑖𝑏) − cos 2𝜋(𝜈 + 𝜈𝑣𝑖𝑏) 𝑡}.

In order to be Raman active a molecular rotation or vibration must cause some
change in a component of the molecular polarizability. A change in polarizability is,
of course, reflected by a change in either the magnitude or the direction of the
polarizability ellipsoid.




ity

Classical Theory of the Raman Effect: Molecular Polarizability

 


Introduction:-

The Raman effect was named after one of its discoverers, the Indian scientist C. V. Raman, who observed the effect in organic liquids in 1928 together with K. S. Krishnan, and independently by Grigory Landsberg and Leonid Mandelstam in inorganic crystals.


Raman won the Nobel Prize in Physics in 1930 for this discovery.


The first observation of Raman spectra in gases was in 1929 by Franco Rasetti.

Quantum Theory of Raman Effect










                                                                    

Raman Scattering could be understood in terms of the quantum theory of radiations.Photons can be imagined to undergo collisions with molecules.









Radiation scattered with a frequency lower than that of the incident beam is referred to as Stokes' radiation, while that at higher frequency is called anti-Stokes' radiation.






Quantum Theory of Raman Effect : Raman Spectroscopy




When the wave particle jump from lower rotational energy level to higher rotational energy level so it can absorb energy and it can be unstable at higher energy level so it come back its ground state (i.e emission spectra).One rotational energy level to second rotation energy level  which transition is required- Microwave Spectroscopy Region.

Condition of roational active molecule:- 

1- Molecules can always in gaseous state because in case of solid and liquid state  the molecules are very close to each other,so inter attraction force are maximum it mean molecule are easily bind thats result rotation can not be possible,incase gases state the molecule are not close to each other it mean rotation is possible.

2- Molecules must have a permanent dipole moment.Dipole moment can occur when there is seperation of charge and it measure the polarity of the molecule.Moment of inertia depend upon the dipole moment.

Q1- Can C02 molecule show a rotational spectrum ?

Answer:- No CO2 molecule can not show the rotational spectrum because it have linear structure it mean the value of (u = 0 )

Due to the rotation it can create moment of inertia in a molecule because moment of inertia depend upon the dipole moment.

Rotational Spectroscopy

 दिल्ली के स्कूल 1 सितंबर से चरणबद्ध तरीके से फिर से खुलने वाले हैं। कक्षा 9 से 12 कक्षा 1 सितंबर से शारीरिक कक्षाओं में भाग ले सकते हैं। दूसरी ओर, सूत्रों के अनुसार, कक्षा 6 से 8 तक एक सप्ताह के बाद ऑफ़लाइन कक्षाएं फिर से शुरू हो सकती हैं।


कक्षा 9वीं से 12वीं कक्षा 1 सितंबर से खुलेगी, जबकि कक्षा 6वीं से 8वीं तक के स्कूल 8 सितंबर से फिर से खुलेंगे।


स्कूलों को चरणबद्ध तरीके से फिर से खोलने पर चर्चा के लिए दिल्ली सरकार के अधिकारियों और दिल्ली आपदा प्रबंधन प्राधिकरण (डीडीएमए) के बीच बैठक के बाद यह घोषणा की गई। डीडीएमए की विशेषज्ञ समिति ने बैठक के दौरान कथित तौर पर कक्षा 9 से 12 के लिए स्कूलों को फिर से खोलने का सुझाव दिया, फिर मिडिल स्कूल और अंतिम प्राथमिक स्कूलों में।


दिल्ली के उपमुख्यमंत्री मनीष सिसोदिया ने घोषणा के बारे में विस्तार से बताया कि दिल्ली में स्कूलों, कॉलेजों और कोचिंग गतिविधियों के अलावा चरणबद्ध तरीके से सभी सावधानियों के साथ 1 सितंबर से शुरू होगा। उन्होंने यह भी कहा कि सामाजिक दूरी के मानदंडों का सख्ती से पालन किया जाएगा। का पालन करें। उन्होंने कहा कि किसी भी छात्र को स्कूल आने के लिए बाध्य नहीं किया जाएगा और छात्रों के आने के लिए अभिभावकों की सहमति जरूरी होगी.

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1 सितंबर से चरणबद्ध तरीके से फिर से खुलेंगे दिल्ली के स्कूल : Delhi Reopen School News:-

  Class-12 Chapter-3 (MATRICES)  

Miscellaneous solutions:- 





Ncert Mathematics Solution Chapter- 2 Exercise- 2.1 Inverse Trignometrey Notes Pdf.


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Notes is based on the board examination i.e CBSE,UP,UTTRAKHAND,HP BOSE & other state board examination. These notes is made by aniket ncert with the help our team members. Official website is gkncertsolution.in,youtube channel is aniket ncert ,facebook page is Made in jee ,Instagram is aniket technical.12th class physics,mathematics and chemistry notes are avilable here. In these blog 12th class exercise- 2.1 notes avilable here. 



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12th Class Mathematics Solution Class-12 Chapter-3 Exercise- 3.1 (Matrices) Solutions:-

 Class-12 Chapter-2 (Inverse Trignometrey)  

Miscellaneous solutions:- 





Ncert Mathematics Solution Chapter- 2 Exercise- 2.1 Inverse Trignometrey Notes Pdf.


Genaeral Introduction:- 

Notes is based on the board examination i.e CBSE,UP,UTTRAKHAND,HP BOSE & other state board examination. These notes is made by aniket ncert with the help our team members. Official website is gkncertsolution.in,youtube channel is aniket ncert ,facebook page is Made in jee ,Instagram is aniket technical.12th class physics,mathematics and chemistry notes are avilable here. In these blog 12th class exercise- 2.1 notes avilable here. 



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12th Class Mathematics Solution Class-12 Chapter-2 (Inverse Trignometrey) Miscellaneous solutions:-

  Class-12 Chapter-2 (Inverse Trignometrey)  Exercise- 2.2





Ncert Mathematics Solution Chapter- 2 Exercise- 2.1 Inverse Trignometrey Notes Pdf.


Genaeral Introduction:- 

Notes is based on the board examination i.e CBSE,UP,UTTRAKHAND,HP BOSE & other state board examination. These notes is made by aniket ncert with the help our team members. Official website is gkncertsolution.in,youtube channel is aniket ncert ,facebook page is Made in jee ,Instagram is aniket technical.12th class physics,mathematics and chemistry notes are avilable here. In these blog 12th class exercise- 2.1 notes avilable here. 



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12th Class Mathematics Solution Chapter- 2 Exercise- 2.2 Handwritten Notes Pdf Here


Optical Methods of Analysis -

  • Origin of Spectra
  • Interaction of radiation with matter
  • Fundamental laws of spectroscopy and selection rules
  • Validity of Beer-Lambert’s law


WHAT IS SPECTROSCOPY?

  • Atoms and molecules interact with electromagnetic radiation (EMR) in a wide variety of ways.
  • Atoms and molecules may absorb and/or emit EMR.
  • Absorption of EMR stimulates different types of motion in atoms or molecules.
  • The patterns of absorption (wavelengths absorbed) and/or emission (wavelengths emitted) are called spectra.
  • The field of spectroscopy is concerned with the interpretation of spectra in terms of atomic and molecular structure (and environment).

Fundamentals of Spectroscopy

Spectroscopy deals with interactions of matter and electromagnetic radiations.

There are various forms of electromagnetic radiations such as UV, IR….. Etc.



  1. Produced by the oscillation of electric charge and magnetic field residing on the atom
  2. Characterized by their λ, ν and wavenumber
  3. The energy of electromagnetic radiation, E α ν,E = hν i.e. photon
  4.  All radiations travel with the same velocity
  5.  When visible light is passed through a prism, it is splitted up into 7 colours (i. e. dispersion of light)
  6. The group of electromagnetic radiations can be splitted up into various components for analysis
  7. Absorbance and emission spectra
  8.  When radiations of certain λ are passed through the substance under analysis, the radiations of certain λ are absorbed by the substance. This is due to the presence of specific functional group
  9.  If the light is passed through a prism, a spectrum is obtained which is calledan Absorption Spectra.
  10. As a result of energy absorption, atoms/molecules pass from the ground state (low energy) to the excited state (high energy) during the excitation process, when its is quantized.
  11. The electromagnetic radiation that is absorbed has energy exactly equal to the difference between the excited and ground states . 




Spectrophotometry: 

A method which uses light source to measure the concentrations i.e. the quantitative measurement of the intensity of electromagnetic radiation at one/more λ with photodetector.  
Absorption of light:
                  The energy of molecule increases.
                                            (Excited State)
Emission of light:
                  The energy of molecule decreases.
                                             (Ground State)


Absorption

When light is absorbed by a sample, the radiant power of the beam is decreased.
                  A = log I0/I = -logT
       I0 :  initial intensity
       I   :  the intensity after passing through thickness
       T  : Transmittance, the fraction of incident light
                which is transmitted.

The obtained spectra are called absorption spectra.


Spectroscopy,Fundamentals of Spectroscopy and Optical Methods of Analysis

 Class-12 Chapter-2 (Inverse Trignometrey)  Exercise- 2.1





Ncert Mathematics Solution Chapter- 2 Exercise- 2.1 Inverse Trignometrey Notes Pdf.


Genaeral Introduction:- 

Notes is based on the board examination i.e CBSE,UP,UTTRAKHAND,HP BOSE & other state board examination. These notes is made by aniket ncert with the help our team members. Official website is gkncertsolution.in,youtube channel is aniket ncert ,facebook page is Made in jee ,Instagram is aniket technical.12th class physics,mathematics and chemistry notes are avilable here. In these blog 12th class exercise- 2.1 notes avilable here. 



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12th class ncert notes,12th class ncert mathematics notes,12th class mathematics chapter- 2 solutions,Ncert Mathematics Notes Here,12th Class Chemistry Notes,PCM notes download now,Ncert solution,ncert books pdf,Mathematics solution class- 12 

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12th Class Mathematics Solution Chapter- 2 Exercise- 2.1 Handwritten Notes Pdf Here

Class-12 Chapter- 1 (Relation & Function)  Exercise- 1.1





Genaeral Introduction:- 

Notes is based on the board examination i.e CBSE,UP,UTTRAKHAND,HP BOSE & other state board examination. These notes is made by aniket ncert with the help our team members. Official website is gkncertsolution.in,youtube channel is aniket ncert ,facebook page is Made in jee ,Instagram is aniket technical 


Any query about these notes you can tell me on email i.e aniketgautam494@gmail.com and other social media i.e whatsapp,facebook and instagram.


Weightage this exercise is 4 in board examination and helpful exercise for competitive and jee main examinations.

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Ncert Mathematics notes Class-12 Chapter- 1 (Relation & Function) Exercise- 1.3