The rigid rotor model treats a diatomic molecule as two masses connected by a fixed distance that rotate around the center of mass like a spinning dumbbell. This model can be simplified using the concept of reduced mass to treat it as a single rotating body. The rotational energy of the system depends on the moment of inertia, which for a diatomic rigid rotor is equal to the reduced mass times the square of the bond length.
Reference,
https://en.wikipedia.org/wiki/Term_symbol
James E. Huheey, Ellen A. Keiter, Richard L.Keiter and Okhil K. Medhi, Inorganic Chemistry, Principles of Structure and Reactivity. 4th Edn. Pearsons
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
Reference,
https://en.wikipedia.org/wiki/Term_symbol
James E. Huheey, Ellen A. Keiter, Richard L.Keiter and Okhil K. Medhi, Inorganic Chemistry, Principles of Structure and Reactivity. 4th Edn. Pearsons
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
Analytical Mechanics of Magnetic Particles Suspended in Magnetorheological FluidDr. Amarjeet Singh
In this paper, the behavior of MR particles has been systematically investigated within the scope of analytical mechanics. . A magnetorheological fluid belongs to a class of smart materials. In magnetorheological fluids, the motion of magnetic particles is controlled by the action of internal and external forces. This paper presents analytical mechanics for the interaction of system of particles in MR fluid. In this paper, basic principles of Analytical Mechanics are utilized for the construction of equations.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
Analytical Solutions of the Modified Coulomb Potential using the Factorizatio...ijrap
We have solved exactly Schrödinger equation with modified Coulomb Potential under the framework of factorization method. Energy levels and the corresponding wave functions in terms of associated Laquerre
function are also obtained. For further guide to interested readers we have computed the energy eigenvalue for some selected elements for various values of n and l .
Influence of donor-donor transport on excitation energy transfer in binary sy...iosrjce
IOSR Journal of Applied Physics (IOSR-JAP) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Robots play important roles in day to day
activities of human endeavour and can perform
complex tasks speedily and accurately. Robots are
employed to imitate human behaviours and then
apply these behaviours to the skills that lead to
achieving a certain task in solving the challenges
faced by impaired people in society. This robotic arm
was achieved using light-weight steel iron for the
frames, a moderate torque MG995 Towerpro, and
servo motor. Two Atmega328 Arduino
microcontroller was employed to control the motors
through the use of pulse width modulation
technique. Mathematical models were developed for
the mechanism to represent the kinematics involved
at each joint with mathematical variables. Then, the
stability of the system was carried out using a step
input signal being a type zero system.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2. This is to certified that this presentation on
“RIGID ROTOR” has prepared by ANURAG
GIRI a student of M.Sc. Previous of KALYAN
PG COLLEGE,BHILAI. He has submitted the
presentation during the academic session
2018-2019 towards partial fulfillment as per
requirement of the DURG UNIVERSITY.
Dr. D. N. Sharma
Head of department
chemistry
3. I would like to express my profound sense of respect
and heartfelt gratitude to our lecturer DEEPA MAM
under whose able guidance and support ,I have my
seminar on topic.
I also express my heartfelt thanks to our
respected sir Dr. D. N. SHARMA HOD of chemistry
for this cooperation and providing facilities available
in the college which helped me in presenting the
project in a nice form.
Deepa mam. Anurag Giri
MSc previous
4. INTRODUCTION
RIGID ROTOR MODEL
MOMENT OF INERTIA
ANGULAR MOMENTUM
ENERGY OF THE SYSTEM
CONCLUSION
REFERENCE
5. The rotation of a diatomic molecule can be
described by the rigid rotor model. To
imagine this model think of a spinning
dumbbell. The dumbbell has two masses set
at a fixed distance from one another and spin
around its centre of mass (COM). This model
can be further simplified using the concept of
reduced mass which allows the problem to be
treated as a single body system.
6. A diatomic molecule
consist of two masses
m1 and m2 bound
together. The
distance between
the masses or bond
length(R).C is
centre of mass and
distance of masses
from this centre is r1
and r2 respectively.
7. The system can be simplified using the concept
of reduced mass which allows it to be treated
as one rotating body. Relationship between
the radii of rotation and bond length are
derived from the COM given by;
m1 r1 = m2 r2 (1)
Where R is the sum of two radii of rotation
R = r1 + r2 (2)
8. let, r2 =R – r1
Put value of r2 in equation (1)
m1 r1= m2( R – r1)
m1 r1= m2 R – m2 r1
m1 r1 + m2 r1 = m2 R
(m1 + m2) r1 = m2 R
r1 = m2 Rm1+m2 (3)
Similarly, r2 = m1 Rm1+m2
As we know total moment of inertia of diatomic
molecule is define as;
I = m1 r1
2 + m2 r2
2 (4)
I = m1 r1 r1 + m2 r2 r2
9. I = m2 r2 r1 + m1 r1 r2
From (m2 r2 = m1r1 )
I = (m1+m2) r1 r2
I =[m1m2 /(m1+m2)]R2 (5)
µ = m1m2 /(m1+m2)
Where µ is reduced mass of the system
From above
I = µR2 (6)
This equation is simplest form of moment of
inertia of diatomic molecule
10. Another important concept when dealing with
rotating systems is the angular momentum
defined by:
L= Iω
Looking back at the kinetic energy:
K = Iω2/2
Multiply by I in denominator and numerator
K = I2 ω2/2I
K = L2/2I
11. The kinetic energy of the system will be
K = m1v1
2/2 + m2v2
2/2 (1)
Where v1 and v2 are the linear velocity of the
particle
The relationship between linear velocity and
angular velocity is define by
v = rω
So v1 = ωr1 , v2 = ωr2 put this value in eq. 1
K = K = Iω2/2
Multiply by I in denominator and numerator
K = I2 ω2/2I
K = L2/2I (2)
Where L is angular momentum
12. Using the equation 2 the operator for energy,
Hamiltonian may be written as;
Ĥ = L2/2I (3)
Where L is total angular momentum operator
As we know L2 operator is equal to
L2 =−ℏ2 [(1/sinθ)∂/∂θ(sinθ ∂/∂θ)+(1/sinθ2)(∂2/∂ϕ2)]
Putting the value of L2 operator on equation 3
Ĥ=1/2I[−ℏ2[(1/sinθ)∂/∂θ(sinθ∂/∂θ)+(1/sinθ2)(∂2/∂ϕ2)]
Ĥ=h2/8∏2I[1/sinθ)∂/∂θ(sinθ∂/∂θ)+(1/sinθ2)(∂2/∂ϕ2)]
This is our energy of the rigid rotor in the form of
Schrödinger wave equation.
13. The rigid rotor is a mechanical model that is
used to explain rotating system.
This model can be used in quantum
mechanics to predict the rotational energy of
a diatomic molecule.
The rotational energy depends on the
moment of inertia for the system.