The force constant for HF is 966 N m-1. Using the harmonic oscillator model, calculate the relative population of the first excited state and the ground state at 300 K.
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The force constant for HF is 966 N m-1. Using the harmonic oscillator model, calculate the relative population of the first excited state and the ground state at 300 K.
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- Explain the importance of the quantization of vibrational, rotational, and translational energy as it relates to the behavior of atoms and molecules.The force constant for HBr is 412 N m-1. Using the harmonic oscillator model, calculate the relative population of the first excited state and the ground state at 300 K.Calculate 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?
- Q 1. Use the equipartition principle to estimate the value of γ = Cpm/CVm for gaseous CH3COOH. Do this calculation WITH the vibrational contribution to the energy.As noted in lecture, the rigid rotor model can be improved by recognizing that in a realistic anharmonic potential, the bond length increases with the vibrational quantum number v. Thus, the rotational constant depends on v, and it can be shown that By = Be – ae(v +). For 'H®Br, B = 8.473 cm1 and a = 0.226 cm². Use this information to calculate the bond length for HBr a) as a rigid rotor, and b) as a nonrigid rotor in the ground vibrational state. Find a literature value for this bond length (cite your source) and compare your answers. Under what conditions would you expect the nonrigid rotor to be a significantly better model?Treat 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.
- Calculate 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.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.The 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.
- 3. Determine the internal energy of an HCl molecule having one quantum of vibrational excitation (v=1) and three quanta (J=3) of rotational excitation. (v = 2990.9 cm³¹ and B = 10.59 cm ¹)In a molecule of hydrogen iodide HI (HI is used in organic and inorganic synthesis as one of the main sources of iodine and as a reducing agent) the vibrational frequency of the molecule is 6.69x10^13 Hz. Iodine is much more heavier than hydrogen, so I can be considered immobile compared to H. Determine the expected value of the potential energy for the hydrogen atom in this molecule in the ground state. Use this to calculate the expected value of the kinetic energy.Estimate the ratio of the number of molecules in the first excited vibrational state of the molecule N2 to the number in the ground state, at a temperature of 450 K. The vibrational frequency of N2 is 7.07 × 1013 s-1.