10. The first five vibrational energy levels of ¹H³5Cl are at 1481.86, 4367.50, 7149.04, 9826.48, and 12399.8 cm ¹. Calculate the dissociation energy of the molecule in units of reciprocal centimetres (cm¯¹). [Note: Assume the second order anharmonicity constant, ye, to be zero.] [Note: Graph paper is available.]

10. The first five vibrational energy levels of ¹H³5Cl are at 1481.86, 4367.50, 7149.04, 9826.48, and 12399.8 cm ¹. Calculate the dissociation energy of the molecule in units of reciprocal centimetres (cm¯¹). [Note: Assume the second order anharmonicity constant, ye, to be zero.] [Note: Graph paper is available.]

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter20: Molecular Spectroscopy And Photochemistry

Section: Chapter Questions

Problem 12P

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10. The first five vibrational energy levels of ¹H³5Cl are at 1481.86, 4367.50, 7149.04, 9826.48, and 12399.8 cm ¹. Calculate the dissociation energy of the molecule in units of reciprocal centimetres (cm¯¹). [Note: Assume the second order anharmonicity constant, ye, to be zero.] [Note: Graph paper is available.]
559.7 cm¹, and a rotational constant, B = 0.244 cm ¹¹. 18. Chlorine has a vibrational constant, U = From this information, determine (a) the force constant and (b) the equilibrium bond length.
The vibrational energy levels for XO molecule can be described by the following formula: E(n) in Joule = 1.88x10-20(n+1/2) – 2.68x10-22(n+1/2)² where n is the vibrational quantum number. What would be the equilibrium dissociation energy (De) of the XO molecule in a kJ mol-1?
Explain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.
1B. Explain how a vibrationally excited molecule is able to withstand up a billion of collisions without losing its excitation.
Energy of a hydrogen molecule in its ground state equilibrium configuration is -31.7 eV. Calculate its dissociation energy.
Calculate the CO and CS bond lengths in OCS from the rotational constants B(16O12C32S) = 6081.5MHz, B(16O12C34S) = 5932.8MHz.
3. ^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 bond
We can use the classical harmonic oscillator to think about molecular bonds. The HCI molecule has a force constant k = 481 N/m. For the mass, use the reduced mass, which is defined as µ = (m₁m₂)/(m₁+m₂). a) Plot the potential energy of HCl from -1 to 1 Å. What happens to the curvature of the potential as the force constant is varied? What does this mean physically? b) Plot position as a function of time for a total energy of 6 x 10-20 J. What is the period of the motion? How does the period change as the force constant is varied? Explain why this makes sense physically.
A 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.
The rotational constant of 12C16O2 (from Raman spectroscopy) is 11.70 GHz. What is the CO bond length in the molecule?
The Morse potential energy is very useful as a simple representation of the actual molecular potential energy. When 85Rb1H was studied, it was found that ˜ν = 936.8 cm−1 and x_eν˜ = 14.15 cm−1. Plot the potential energy curve from 50 pm to 800 pm aroundRe = 236.7 pm. Then go on to explore how the rotation of a molecule may weaken its bond by allowing for the kinetic energy of rotation of a molecule and plotting V∗ = V + hcBJ˜ (J + 1) with B˜. Plot these curves on the same diagram for J = 40, 80, and 100, and observe how the dissociation energy is affected by the rotations. Hints: Taking B˜ = 3.020 cm−1 as the equilibrium bond length will greatly simplify the calculation. The mass of 85Rb is 84.9118mu