(a)
Interpretation:
The most populated rotational level for a sample of
Concept introduction:
An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant. This is known as the Franck-Condon principle.
Answer to Problem 14.32E
The most populated rotational level for a sample of
Explanation of Solution
The most populated rotational level is calculated by the formula as shown below.
Where,
•
•
•
The rotational constant is calculated by the formula as shown below.
Where,
•
•
•
The reduced mass is calculated by the formula as shown below.
Where,
•
•
Substitute the value of mass of lithium and hydrogen in equation (3).
Convert
Substitute the value of reduced mass, bond length, Planck’s constant in equation (2).
Substitute the value of rotational constant, Boltzmann’s constant and
Therefore, the most populated rotational level for a sample of
the most populated rotational level for a sample of
(b)
Interpretation:
The most populated rotational level for a sample of
Concept introduction:
An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant. This is known as the Franck-Condon principle.
Answer to Problem 14.32E
The most populated rotational level for a sample of
Explanation of Solution
The most populated rotational level is calculated by the formula as shown below.
Where,
•
•
•
The rotational constant is calculated by the formula as shown below.
Where,
•
•
•
The reduced mass is calculated by the formula as shown below.
Where,
•
•
Substitute the value of mass of lithium and hydrogen in equation (3).
Convert
Substitute the value of reduced mass, bond length, Planck’s constant in equation (2).
Substitute the value of rotational constant, Boltzmann’s constant and
Therefore, the most populated rotational level for a sample of
The most populated rotational level for a sample of
(c)
Interpretation:
The most populated rotational level for a sample of
Concept introduction:
An electronic state of energy has its own vibrational states. The energy between the electronic states is large followed by vibrational states and then rotational states. During an electronic transition, electron from ground state moves straight to the excited state keeping the internuclear distance constant. This is known as the Franck-Condon principle.
Answer to Problem 14.32E
The most populated rotational level for a sample of
Explanation of Solution
The most populated rotational level is calculated by the formula as shown below.
Where,
•
•
•
The rotational constant is calculated by the formula as shown below.
Where,
•
•
•
The reduced mass is calculated by the formula as shown below.
Where,
•
•
Substitute the value of mass of lithium and hydrogen in equation (3).
Convert
Substitute the value of reduced mass, bond length, Planck’s constant in equation (2).
Substitute the value of rotational constant, Boltzmann’s constant and
Therefore, the most populated rotational level for a sample of
The most populated rotational level for a sample of
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Chapter 14 Solutions
Physical Chemistry
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- 5. For carbon monoxide at 298K, determine the fraction of molecules in the rotational levels for J=0, 5, 10, 15, and 20. The rotational constant (B) is 3.83x10^-23 Joules.arrow_forward4. What is the form of the total vibrational partition function for a polyatomic molecule?arrow_forward1. Consider a linear rotar in the energy levels with J=0 and J= 5 at 298K.calculate the relative population for the rotational constant, B= 271cm_1.arrow_forward
- Calculate the relative numbers of Br2 molecules ( ᷉v = 321 cm−1) in the second and first excited vibrational states at (i) 298 K, (ii) 800 K.arrow_forwardCalculate (i) the thermal wavelength, (ii) the translational partition function of a Ne atom in a cubic box of side 1.00 cm at 300 K and 3000 K.arrow_forwardEstimate the values of γ = Cp,m/CV,m for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the experimental value at 25 °C? Hint: Note that Cp,m − CV,m = R for a perfect gas.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning