Concept explainers
Which of the following molecules should have pure rotational spectra?
(a) Deuterium,
(b) Carbon monoxide,
(c)
(d)
(e) Chloroform,
(f) Buckminsterfullerene,
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Chapter 14 Solutions
Physical Chemistry
- 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_forwardThe 14 N160 molecule undergoes a transition between its rotational ground state and its rotational first excited state. Approximating the diatomic molecule as a rigid rotor, and given that the bond length of NO is 1.152 Angstroms, calculate the energy of the transition. As your final answer, calculate the temperature T in Kelvin, such that Ethermal = kBT equals the %3D energy of the transition between NO's rotational ground state and fırst excited state.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_forward
- (b) The lowest frequency rotational transition of ²H³³C1 occurs at 10.92 cm1. Determine (i) The rotational constant, B, in Hz (ii) The bond lengtharrow_forward3. ^14N^16O (the superscripts represent the atomic mass number) (a) NO molecules rotate at an angular velocity of 2.01x10^12 rev/s, at the quantized rotational state with the rotational quantum number J of 3. Calculate the bond length of NO molecules. (b) Can NO molecules rotate under light irradiation? Explain your answer. (c) Calculate the effective force constant of the vibrational mode of NO at a frequency of 5.63x10^13 Hz measured by the infrared absorption spectrum. (d) NO has a bond energy of 6.29 eV. Applying the parabolic approximation to estimate the longest distance in which N and O atoms can be stretched before the dissociation of the molecular bondarrow_forwardA rotating methane molecule is described by the quantum numbers J, MJ, and K. (a) For methane, how many rotational states have an energy equal to hBJ(J + 1) with J= 8? (b) Now consider chloromethane. How many rotationalstates have an energy equal to hBJ(J + 1) with J = 8?arrow_forward
- Consider 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_forwardCalculate the rotational constant (B) for the molecule H12C14N, given that the H-C and C-N bond distances are 106.6 pm and 115.3 pm respectively.arrow_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_forwardRecall the selection rules for purely rotational microwave spectra: ΔJ = ±1. This came from angular momentum conservation (a photon has spin angular momentum ħ). In Raman scattering, one photon comes in and one photon goes out. What are the selection rules for rotational Raman transitions?(A) ΔJ = ±1(B) ΔJ = 0, ±1, ±2(C) ΔJ = 0, ±2 *(D) ΔJ = 0This is because a photon comes in and transfers one unit of ħ to the molecule, and one photon comes out again, which again has one unit of ħ. If the incoming and outgoing photons have the same spin, ΔJ = 0. If they have opposite spins, ΔJ = ±2. ____.arrow_forwardBut molecules combine both vibrational and rotational states in such a way that both selection rules must be satisfied if we are only talking about absorption or emission of electromagnetic radiation (i.e. photons). 5 1 images from Krane Ch 9. Relative absorption : 0.330 L=3 to L=2 L=2 to L = 1 Electronic excited state. Electronic ground state L→ L-1 L = 1 to L = 0 Ť 0.340 0.350 SE Energy (eV) 2B 0.360 : hf L=0 L=1 L=2 to to to L = 1 L = 2 L = 3 Photo 4 1 3 1 2 1 1 0 1 1 5 0 4 0 30 20 1 0 0 0 LN L→ L+1 0.370 0.380 no emission here because AL # 0, AL = +1 AN = ±1, HCI spectra. In the middle of the gap is the energy hf that would correspond to a pure vibrational transition, which would violate the rotational selection rule. What is the value of hf for the HCI spectra?arrow_forward
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