UPSC Exam > UPSC Questions > The separation of energy levels in the rotati...
Start Learning for Free
The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO?
Most Upvoted Answer
The separation of energy levels in the rotational spectrum of CO is 3....
Understanding Rotational Spectrum of CO
The rotational spectrum of a diatomic molecule like carbon monoxide (CO) can be analyzed using quantum mechanics. The separation of energy levels gives insight into the molecular bond length.
Energy Level Separation
- The given energy level separation is 3.8626 cm^-1.
- This value corresponds to the rotational transitions of CO, which can be described by the formula for rotational energy levels: E_J = B J (J + 1), where B is the rotational constant and J is the rotational quantum number.
Rotational Constant and Bond Length
- The rotational constant (B) is related to the moment of inertia (I) of the molecule:
B = h / (8π^2cI)
- Moment of inertia (I) for a diatomic molecule is given by:
I = μr^2
where μ is the reduced mass and r is the bond length.
Calculating Bond Length
1. Reduced Mass (μ):
- For CO, the atomic masses are approximately 12 amu for Carbon and 16 amu for Oxygen.
- μ = (m_C * m_O) / (m_C + m_O)
2. Finding B:
- Convert the separation from cm^-1 to SI units for calculations.
3. Applying the Formulas:
- Substitute B into the equation to find I, and then use I to solve for bond length (r).
Conclusion
After performing the calculations, the bond length (r) for CO can be determined and rounded off to two decimal places. Given the typical bond lengths for CO, the expected value will be in the range of 1.13 Å or approximately 1.13 x 10^-10 m.
This method provides a detailed understanding of how the rotational spectrum can inform us about the molecular structure of CO.
The rotational spectrum of a diatomic molecule like carbon monoxide (CO) can be analyzed using quantum mechanics. The separation of energy levels gives insight into the molecular bond length.
Energy Level Separation
- The given energy level separation is 3.8626 cm^-1.
- This value corresponds to the rotational transitions of CO, which can be described by the formula for rotational energy levels: E_J = B J (J + 1), where B is the rotational constant and J is the rotational quantum number.
Rotational Constant and Bond Length
- The rotational constant (B) is related to the moment of inertia (I) of the molecule:
B = h / (8π^2cI)
- Moment of inertia (I) for a diatomic molecule is given by:
I = μr^2
where μ is the reduced mass and r is the bond length.
Calculating Bond Length
1. Reduced Mass (μ):
- For CO, the atomic masses are approximately 12 amu for Carbon and 16 amu for Oxygen.
- μ = (m_C * m_O) / (m_C + m_O)
2. Finding B:
- Convert the separation from cm^-1 to SI units for calculations.
3. Applying the Formulas:
- Substitute B into the equation to find I, and then use I to solve for bond length (r).
Conclusion
After performing the calculations, the bond length (r) for CO can be determined and rounded off to two decimal places. Given the typical bond lengths for CO, the expected value will be in the range of 1.13 Å or approximately 1.13 x 10^-10 m.
This method provides a detailed understanding of how the rotational spectrum can inform us about the molecular structure of CO.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO?
Question Description
The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO?.
The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO?.
Solutions for The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? defined & explained in the simplest way possible. Besides giving the explanation of
The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO?, a detailed solution for The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? has been provided alongside types of The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? theory, EduRev gives you an
ample number of questions to practice The separation of energy levels in the rotational spectrum of CO is 3.8626c * m ^ - 1 The bond length (assume it does not change during rotation) of (rounded off to two decimal places) is CO? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup