Concept explainers
Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following species. (a) Hydrogen sulfide,
(a)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. 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.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for nonlinear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(b)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. 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.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(c)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. 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.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for nonlinear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(d)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. 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.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for nonlinear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(e)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. 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.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of
(f)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of a linear molecule having
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. 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.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of a linear molecule having
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of a nonlinear molecule having
(g)
Interpretation:
The number of total degrees of freedom and vibrational degrees of freedom of a linear molecule having
Concept introduction:
Spectroscopy method is used to identify the structure of the molecule. It is based on the interactions between matter and electromagnetic radiations. 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.
Answer to Problem 14.46E
The number of total degrees of freedom and vibrational degrees of freedom of a nonlinear molecule having
Explanation of Solution
The number of total degrees of freedom is calculated by the formula shown below.
Where,
•
Substitute
The number of vibrational degrees of freedom for linear molecule is calculated by the formula shown below.
Substitute
The number of total degrees of freedom and vibrational degrees of freedom of a nonlinear molecule having
Want to see more full solutions like this?
Chapter 14 Solutions
Physical Chemistry
- Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following molecules. a Hydrogen fluoride, HF b Hydrogen telluride, H2Te c Buckminsterfullerene, C60 d Phenylalanine, C6H5CH2CHNH2COOH e Naphthalene, C10H8 f The linear isomer of the C4 radical g The bent isomer of C4 radical.arrow_forwardThe rotational constant for CO is 1.9314 cm−1 and 1.6116 cm−1 in the ground and first excited vibrational states, respectively. By how much does the internuclear distance change as a result of this transition?arrow_forwardThe vibrational wavenumber of the oxygen molecule in its electronic ground state is 1580 cm−1, whereas that in the excited state (B 3Σu−), to which there is an allowed electronic transition, is 700 cm−1. Given that the separation in energy between the minima in their respective potential energy curves of these two electronic states is 6.175 eV, what is the wavenumber of the lowest energy transition in the band of transitions originating from the v = 0 vibrational state of the electronic ground state to this excited state? Ignore any rotational structure or anharmonicity.arrow_forward
- The 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_forwardExplain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.arrow_forwardRotational 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
- How many normal modes of vibration are there for the following molecules and, in each case, briefly explain why this is so: (i) C6H6, (ii) C6H5CH3, and (iii) HC≡C−C≡CH?arrow_forwardExplain the occurrence of P and R branches in the rotational fine structure of a vibrational transition of a diatomic molecule such as HCl or CO.arrow_forwardConsider the vibrational mode that corresponds to the uniform expansion of the benzene ring. Is it (i) Raman, (ii) infrared active?arrow_forward
- 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_forwardTreat a vibrating HI molecule as a hydrogen atom oscillating towards and away from a stationary iodine atom. Given the force constant of the HI bond is 314 N m-1, calculate the vibrational frequency of the molecule.arrow_forwardThis question pertains to rotational spectroscopy. Which of the following molecules would have a pure rotational spectrum and why? HCl, N2O, O3, SF4 What information is obtained from the rotational spectrum of a diatomic molecule and how can it be used to determine the bond length of a diatomic molecule? What is the selection rule for rotational spectroscopy? The rotational constant of 127I35Cl is 3.424 GHz. Calculate the ICl bond length.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