The vibrational frequency of Br2 is 414 cm-1. At 800K what is the percentage of particles in (1) the ground state and in (2) the first excited state?
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The vibrational frequency of Br2 is 414 cm-1. At 800K what is the percentage of particles in (1) the ground state and in (2) the first excited state?
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- What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?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?E rotational is 2.777×10−20 J
- For a 1H nucleus (a proton), what are the magnitude of the spin angular momentum and what are its allowed components along the z-axis? Express your answer in multiples of ħ. What angles does the angular momentum make with the z-axis?Using the rigid rotor model, calculate the energies in Joules of the first three rotational levels of HBr, using for its moment of inertia I = μR2, with μ = mHmX/(mH + mX) and equilibrium internuclear distance = 1.63 Å. To put these energies into units that make sense to us, convert energy to kJ/mol. (Simply estimate atomic masses from the average atomic weights of the elements given in the periodic table).The lines of the rotational spectrum of HBr are 5.10 x 10^11 Hz apart in frequency. Find the internuclear distance in HBr. (Notes: Since the Br atom is about 80 times more massive than the proton, the reduced mass of an HBr molecule can be taken as just the 1H mass.)
- 4) Calculate the energies E of the first three rotational levels (those giving the minimal energy) of 1H35Cl molecule that is free to rotate in three dimensions. For its moment of inertia I = μeffR2 use the effective mass with μeff = mH * mCl / (mH + mCl) and bond length R = 127 pm.7) Explain the basis of the Franck-Condon principle and how it leads to the formation of a vibrational progression.Calculate the separation between the two lowest levels for an O2 molecule in a one-dimensional container of length 5.0 cm. At what value of n does the energy of the molecule reach 1/2kT at 300 K, and what is the separation of this level from the one immediately below?
- (i) Explain how the mass of the particle(s) involved affects the separation between energy levels in quantum mechanics. (ii) Explain why the sensitivity of an NMR experiment is affected by the strength of the applied magnetic field. (iii) Explain why, to a good approximation, rotational and vibrational transitions do not change the energies of electrons.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?The spacing of lines in the microwave spectrum of 27Al1H is 12.604 cm−1; calculate the moment of inertia and bond length of the molecule.
