Interpretation:
The values of rotational constants
Concept introduction:
In a molecule, the rotational energy level corresponds to the different probable ways in which the portion of a molecule rotates around the chemical bond that binds it to the rest of the molecule. Every rotational energy level possesses degeneracy.
The asymmetric top refers to a rotor that has the different value for all moments of inertia. For asymmetric top molecule,
Answer to Problem 14.18E
The values of rotational constant
The values of rotational constant
The values of rotational constant
Explanation of Solution
Water is an asymmetric top molecule. For asymmetric top molecule,
The value of
Where,
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•
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The relation between reduced Planck’s constant and Planck’s constant is shown below.
Substitute the values of
Therefore, the rotational constant
The conversion of J into
Therefore, the conversion of
Therefore, the rotational constant
The rotational constant
Substitute the values of
Therefore, the rotational constant
The conversion of J into
Therefore, the conversion of
Therefore, the rotational constant
The rotational constant
Substitute the values of
Therefore, the rotational constant
The conversion of J into
Therefore, the conversion of
Therefore, the rotational constant
The values of rotational constant
The values of rotational constant
The values of rotational constant
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Chapter 14 Solutions
Student Solutions Manual for Ball's Physical Chemistry, 2nd
- Evaluate Δx = (⟨x2⟩ − ⟨x⟩2)1/2 and Δpx = (⟨px2⟩ − ⟨px⟩2)1/2 for the ground state of (a) a particle in a box of length L and (b) a harmonic oscillator. Discuss these quantities with reference to the uncertainty principle.arrow_forwardVibrations in the diatomic molecule CO can be approximated as a harmonic oscillator, where the angular frequency w = 6.505 x 1013 Hz and the reduced mass is equal to u = 1.14 × 10-27 kg. Assume the molecule is in its fırst excited vibrational state. Its vibrational wavefunction can then be written as V1 (x) = (4) /2a xe where a = . If we were to measure the bond length of the molecule, what is the most likely displacement from the equilibrium bond distance in the first excited vibrational state? Give your answer in Angstroms [Note: The equilibrium displacement in the Quantum harmonic oscillator corresponds to r = 0, ie the coordinate x measures displacement from equilibrium]arrow_forwardCalculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.arrow_forward
- Calculate the energy of the quantum involved in the excitation of (i) an electronic oscillation of period 1.0 fs, (ii) a molecular vibration of period 10 fs, (iii) a pendulum of period 1.0 s. Express the results in joules and kilojoules per mole.arrow_forwardA diatomic molecule containing 35Cl and another atom has a rotational transition from J=0 to J=1 corresponding to a frequency of 7.70×109 Hz. The bond length is 267 pm. Use this information to calculate the reduced mass of the molecule, then find the atomic mass number of the other atom.arrow_forwardA rotating diatomic molecule absorbs radiation and has moment of inertia, I, equal to 1.00 x 10-46 kg m², a. which is the frequency of radiation when the molecule undergoes a transition from J = 4 to J=3?arrow_forward
- Calculate the energy of the quantum involved in the excitation of (i) an electronic oscillation of period 2.50 fs, (ii) a molecular vibration of period 2.21 fs, (iii) a balance wheel of period 1.0 ms. Express the results in joules and kilojoules per mole.arrow_forwardE rotational is 2.777×10−20 Jarrow_forwardQ/ The bond length of the C0O molecule is 112.8 pm. Calculate the following (a) The reduced mass. (b) The rotational constant of CO when moment of inertia (I) is 1.4486 x 1046 kg.m² (c) Calculate the wavelength of the photon absorbed when a CO molecule initially in the J=2 level. makes a transition to the J=3 level.arrow_forward
- Emission of microwave radiation from the J = 10 transition of a molecule has been detected at 88.63 GHz from a region of interstellar space in which there is evidence of thermal equilibrium and a temperature of around 50 K. Estimate the frequency and relative intensity of the J = 2 → 1 transition of the same molecule.arrow_forwardThe J = 0 to J = 1 rotational transition of the CO molecule occurs at a frequency of 1.15 x 1011 Hz.(A) Use this information to calculate the moment of inertia of the molecule. (B) Calculate the bond length of the molecule.arrow_forwardA normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2 sin(πx/L). Suppose that L = 10.0 nm. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm, (c) between x = 9.90 nm and 10.00 nm, (d) between x = 5.00 nm and 10.00 nm.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