(a)
Interpretation:
The excited-state and the ground-state population ratios for HCI:
Concept introduction:
The excited-state of an atom, molecule or electron is a state in which the electrons have sufficient energy to jump in to another orbital. The ground-state is the state of zero energy level. In this state the electron does not have sufficient energy to jump from the orbital.
The Boltzmann equation is used to calculate the ratio of the exited-state and ground state. The concept of the energy difference between these states is also used to calculate the required ratio.
(b)
Interpretation:
The excited-state and the ground-state population ratios for HCI:
Concept introduction:
The excited-state of an atom, molecule or electron is a state in which the electrons have sufficient energy to jump in to another orbital. The ground-state is the state of zero energy level. In this state the electron does not have sufficient energy to jump from the orbital.
The Boltzmann equation is used to calculate the ratio of the exited-state and ground state. The concept of the energy difference between these states is also used to calculate the required ratio.
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Chapter 16 Solutions
Principles of Instrumental Analysis
- Consider the rotational spectrum of a linear molecule at 298 K with a moment of inertia of 1.23×10−461.23\times10^{-46}1.23×10−46 kg m2 . (a) What is the frequency for the transition from J = 2 to J = 3? (b) What is the most populated rotational level for this molecule? Would the transition in (a) give the most intense signal in the rotational spectrum?arrow_forwardCalculate the standard deviation of the bond length ox of the diatomic molecule 'H1°F when it is in the ground state and first excited state using the quantum harmonic oscillator wavefunctions. The fundamental harmonic vibrational frequency of HF is 4,460 cm-1 and the equilibrium bond length is 0.091nm. How do you interpret the change in the ratio of average bond length to ox as a function of energy in the vibration?arrow_forwardConsider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance equal to the bond length of the molecule). The rotational constant of the diatomic AB is 25.5263 cm-1. (a) What is the difference in energy, expressed in wavenumbers, between the energy levels of AB with J = 10 and J = 6? (b) Consider now a diatomic A'B', for which the atomic masses are ma 0.85 mA and mB' 0.85 mB and for its bond length ra'B' = 0.913 rAB. What is the difference in energy, expressed in wavenumbers, between the energy levels of the A'B' molecule with J = 9 and J = 7?arrow_forward
- Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?arrow_forward(hydrogen iodide, the superscripts represent the atomic mass number) (a) How fast will HI molecules rotate at the quantized rotational state with the rotational quantun number J of 2, given the bond length of 0.161 nim? (b) Calculate the effective force constant of the vibrational mode of HI at a wavenumber of 2300 cm' measured by infrared absorption spectrum. (c) HI has the bond energy of 3.06 eV. Applying the parabolic approximation to estimate the longest distance in which H and I atoms can be stretched before the dissociation of the molecular bondarrow_forwardA molecule in a liquid undergoes about 1.0 × 1013 collisions in each second. Suppose that (i) every collision is effective in deactivating the molecule vibrationally and (ii) that one collision in 100 is effective. Calculate the width (in cm−1) of vibrational transitions in the molecule.arrow_forward
- (c) When a gas is expanded very rapidly, its temperature can fall to a few degrees Kelvin. At these low temperatures, unusual molecules like ArHCl (Argon weakly bonded to HCl) can form on mixing. For the isotopic species Ar H$CI, the following rotational transitions were observed: J (1 → 2): 6714.44 MHz J (2 → 3): 10068.90 MHz Assume the molecule can be treated as a linear diatomic molecule (ArCl). (i) Calculate the rotational constant (B) and centrifugal distortion (D) constant for this molecule.arrow_forwardEstimate the ratio of the number of molecules in the firstexcited vibrational state of the molecule N2 to the numberin the ground state, at a temperature of 450 K. The vibrational frequency of N2 is 7.07 × 1013 s-1.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_forward
- (b) The lowest three vibrational energy levels of 127|35CI lie at 191.77, 573.06, and 951.34 cm-1. Determine the force constant, zero-point energy, well- depth and bond dissociation energy for 127135CI.arrow_forward4. The infrared absorption spectrum of a diatomic molecule is shown in the figure. (a) Give the initial (J") and final (J') rotational quantum numbers corresponding to the peaks labeled A and B. (b) Estimate the vibrational frequency in wavenumbers (i) and the rotational constant in wavenumbers (B). (c) From the spacings of the peaks near 2700 cm and near 3050 cm, determine whether the average bond length increases or decreases with increasing vibrational quantum number. 20 18 A 14 12 2500 2600 2700 2800 2900 3000 3100 3200 wavenumber absorption intensityarrow_forwardThe vibrational temperature of a molecule prepared in a supersonic jet can be estimated from the observed popula- tions of its vibrational levels, assuming a Boltzmann distri- bution. The vibrational frequency of HgBr is 5.58 × 1012 s-1, and the ratio of the number of molecules in the n = 1 state to the number in the n = 0 state is 0.127. Estimate the vibra- tional temperature under these conditions.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